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Elwes translation
SPINOZAE ETHICA
ORDINE GEOMETRICO DEMONSTRATA
IN QUINQUE PARTES DISTINCTA
Part I  Concerning God PARS PRIMA DE DEO
DEFINITIONS DEFINITIONES [about definitions]
1d01 causa sui 1d01 causa sui  [notes] [geomap]
I. By that which is self-caused, I mean that of which the essence involves existence, or that of which the nature is only conceivable as existent. I. Per causam sui intelligo id cujus essentia involvit existentiam sive id cujus natura non potest concipi nisi existens.
1d02 in suo genere finita^absoluta infinita 1d02 in suo genere finita^absoluta infinita  [notes] [geomap]
II. A thing is called finite after its kind, when it can be limited by another thing of the same nature; for instance, a body is called finite because we always conceive another greater body. So, also, a thought is limited by another thought, but a body is not limited by thought, nor a thought by body. II. Ea res dicitur in suo genere finita quae alia ejusdem naturae terminari potest. Exempli gratia corpus dicitur finitum quia aliud semper majus concipimus. Sic cogitatio alia cogitatione terminatur. At corpus non terminatur cogitatione nec cogitatio corpore.
1d03 substantia 1d03 substantia [notes] [geomap]
III. By substance, I mean that which is in itself, and is conceived through itself: in other words, that of which a conception can be formed independently of any other conception. III. Per substantiam intelligo id quod in se est et per se concipitur hoc est id cujus conceptus non indiget conceptu alterius rei a quo formari debeat.
1d04 attributus 1d04 attributus [notes] [geomap]
IV. By attribute, I mean that which the intellect perceives as constituting the essence of substance. IV. Per attributum intelligo id quod intellectus de substantia percipit tanquam ejusdem essentiam constituens.
1d05 modus 1d05 modus [notes] [geomap]
V. By mode, I mean the modifications [Lat: affectiones] of substance, or that which exists in, and is conceived through, something other than itself. V. Per modum intelligo  substantiae affectiones sive  [mng eqv] id quod in alio est, per quod etiam concipitur.
1d06 deus 1d06 deus [notes] [geomap]
VI. By God, I mean a being absolutely infinite-that is, a substance consisting in infinite attributes, of which each expresses eternal and infinite essentiality. VI. Per Deum intelligo ens absolute infinitum hoc est [new mng eqv] substantiam constantem infinitis attributis quorum unumquodque aeternam et infinitam essentiam exprimit.
1d06e absolutus-suo genere infinitus 1d06e absolutus-suo genere infinitus
Explanation-I say absolutely infinite, not infinite after its kind: for, of a thing infinite only after its kind, infinite attributes may be denied; but that which is absolutely infinite, contains in its essence whatever expresses reality, and involves no negation. EXPLICATIO: Dico absolute infinitum, non autem in suo genere; quicquid enim in suo genere tantum infinitum est, infinita de eo attributa negare possumus; quod autem absolute infinitum est, ad ejus essentiam pertinet quicquid essentiam exprimit et negationem nullam involvit.
1d07 liber^necessarius 1d07 liber^necessarius [notes] [geomap]
VII. That thing is called free, which exists solely by the necessity of its own nature, and of which the action is determined by itself alone. On the other hand, that thing is necessary, or rather constrained, which is determined by something external to itself to a fixed and definite method of existence or operation. VII. Ea res libera dicitur quae ex sola suae naturae necessitate existit et a se sola ad agendum determinatur. Necessaria autem vel potius coacta quae ab alio determinatur ad existendum et operandum certa ac determinata ratione.
1d08 aeternitas 1d08 aeternitas [notes] [geomap]
VIII. By eternity, I mean existence itself, in so far as it is conceived necessarily to follow solely from the definition of that which is eternal. VIII. Per aeternitatem intelligo ipsam existentiam quatenus ex sola rei  aeternae definitione necessario sequi concipitur.
1d08e aeternitas duratio 1d08e aeternitas duratio
Explanation-Existence of this kind is conceived as an eternal truth, like the essence of a thing, and, therefore, cannot be explained by means of continuance or time, though continuance may be conceived without a beginning or end. EXPLICATIO : Talis enim existentia ut aeterna veritas sicut rei essentia concipitur proptereaque per durationem aut tempus explicari non potest tametsi duratio principio et fine carere concipiatur.
AXIOMS AXIOMATA
1a01 vel se alio 1a01 vel se alio [geomap]
I. Everything which exists, exists either in itself or in something else. I. Omnia quae sunt vel [excl exh] in se vel [excl exh] in alio sunt.
1a02 Id quod non per aliud, per se 1a02 Id quod non per aliud, per se [geomap]
II. That which cannot be conceived through anything else must be conceived through itself. II. Id quod per aliud non potest concipi, per se concipi debet
1a03 de causae effectus 1a03 de causae effectus [geomap]
III. From a given definite cause an effect necessarily follows; and, on the other hand, if no definite cause be granted, it is impossible that an effect can follow. III. Ex data causa determinata necessario sequitur effectus et contra si nulla detur determinata causa, impossibile est ut effectus sequatur.
1a04 causa effectus cognitio 1a04 causa effectus cognitio [geomap]
IV. The knowledge of an effect depends on and involves the knowledge of a cause.  IV. Effectus cognitio a cognitione causae dependet et eandem involvit.
1a05 commune intelligi 1a05 commune intelligi [geomap]
V. Things which have nothing in common cannot be understood, the one by means of the other; the conception of one does not involve the conception of the other. V. Quae nihil commune cum se invicem habent, etiam per se invicem intelligi non possunt sive  [mng eqv] conceptus unius alterius conceptum non involvit.
1a06 idea convenire 1a06 idea convenire [geomap]
VI. A true idea must correspond with its ideate or object. VI. Idea vera debet cum suo ideato convenire.
1a07 essentia existentia 1a07 essentia existentia [geomap]
VII. If a thing can be conceived as non-existing, its essence does not involve existence. VII. Quicquid ut non existens potest concipi, ejus essentia non involvit existentiam.
PROPOSITIONS PROPOSITIONES
1p01 substantia prior 1p01 substantia prior [geomap]
PROP. I. Substance is by nature prior to its modifications [Lat: affectiones]. PROPOSITIO I: Substantia prior est natura suis affectionibus.
Proof.-This is clear from Deff. iii. and v. DEMONSTRATIO: Patet ex definitione 3 {1d03} et 5 {1d05}.
1p02 substantiae nihil commune 1p02 substantiae nihil commune [geomap]
PROP. II. Two substances, whose attributes are different, have nothing in common. PROPOSITIO II: Du  substantiae diversa attributa habentes nihil inter se commune habent.
Proof.-Also evident from Def. iii. For each must exist in itself, and be conceived through itself; in other words, the conception of one does not imply the conception of the other. DEMONSTRATIO: Patet etiam ex definitione 3 {1d03}. Unaquque enim in se debet esse et per se debet concipi sive  [mng eqv] conceptus unius conceptum alterius non involvit.
1p03 nihil commune non causa 1p03 nihil commune non causa [geomap]
PROP. III. Things which have nothing in common cannot be one the cause of the other. PROPOSITIO III: quae res nihil commune inter se habent, earum una alterius causa esse non potest.
Proof.-If they have nothing in common, it follows that one cannot be apprehended by means of the other (Ax. v.), and, therefore, one cannot be the cause of the other (Ax. iv.). Q.E.D. DEMONSTRATIO: Si nihil commune cum se invicem habent, ergo (per axioma 5 {1a05}) nec per se invicem possunt intelligi adeoque (per axioma 4 {1a04}) una alterius causa esse non potest. Q.E.D.
1p04 distinctae attributorum vel affectionum 1p04 distinctae attributorum vel affectionum [geomap]
PROP. IV. Two or more distinct things are distinguished one from the other, either by the difference of the attributes of the substances, or by the difference of their modifications [Lat: affectiones]. PROPOSITIO IV: duae aut [excl exh] plures res distinctae vel [excl exh] inter se distinguuntur ex diversitate attributorum substantiarum vel [excl exh] ex diversitate earundem affectionum.
Proof.-Everything which exists, exists either in itself or in something else (Ax. i.),-that is (by Deff. iii. and v.), nothing is granted in addition to the understanding, except substance and its modifications [Lat: affectiones]. Nothing is, therefore, given besides the understanding, by which several things may be distinguished one from the other, except the substances, or, in other words (see Ax. iv.), their attributes and modifications [Lat: affectiones]. Q.E.D. DEMONSTRATIO: Omnia quae sunt vel [excl exh] in se vel [excl exh] in alio sunt (per axioma 1 {1a01}) hoc est [new mng eqv] (per definitiones 3  {1d03} et 5 {1d05}) extra intellectum nihil datur praeter substantias earumque affectiones. Nihil ergo extra intellectum datur per quod plures res distingui inter se possunt praeter substantias sive  [prf eqv] quod idem est (per definitionem 4 {1d04}) earum attributa earumque affectiones. Q.E.D.
1p05 in rerum natura 1p05 in rerum natura [geomap]
PROP. V. There cannot exist in the universe two or more substances having the same nature or attribute. PROPOSITIO V: In rerum natura non possunt dari duae aut [hence] plures  substantiae ejusdem naturae sive  [mng eqv]  attributi.
Proof.If several distinct substances be granted, they must be distinguished one from the other, either by the difference of their attributes, or by the difference of their modifications [Lat: affectiones] (Prop. iv.). If only by the difference of their attributes, it will be granted that there cannot be more than one with an identical attribute. If by the difference of their modifications [Lat: affectiones]as substance is naturally prior to its modifications [Lat: affectiones] (Prop. i.),it follows that setting the modifications [Lat: affectiones] aside, and considering substance in itself, that is truly, (Deff. iii. and vi.), there cannot be conceived one substance different from another,that is (by Prop. iv.), there cannot be granted several substances, but one substance only. Q.E.D. DEMONSTRATIO: Si darentur plures distinct, deberent inter se distingui vel [excl exh] ex diversitate attributorum vel [excl exh] ex diversitate affectionum (per propositionem praecedentem {1p04}). Si tantum ex diversitate attributorum, concedetur ergo non dari nisi unam ejusdem attributi. At si ex diversitate affectionum, cum substantia sit prior natura suis affectionibus (per propositionem 1 {1p01}) depositis ergo affectionibus et in se considerata hoc est (per definitionem 3  {1d03} et axioma 6 {1a06}) vere considerata, non poterit concipi ab alia distingui hoc est (per propositionem praecedentem {1p04}) non poterunt dari plures sed tantum una. Q.E.D.
1p06 substantia produci substantia 1p06 substantia produci substantia [geomap]
PROP. VI. One substance cannot be produced by another substance. PROPOSITIO VI: Una substantia non potest produci ab alia substantia.
Proof.-It is impossible that there should be in the universe two substances with an identical attribute, i.e. which have anything common to them both (Prop. ii.), and, therefore (Prop. iii.), one cannot be the cause of the other, neither can one be produced by the other. Q.E.D. DEMONSTRATIO: In rerum natura non possunt dari duae  substantiae ejusdem attributi (per propositionem praecedentem {1p05}) hoc est (per propositionem 2 {1p02}) quae aliquid inter se commune habent. Adeoque (per propositionem 3 {1p03}) una alterius causa esse nequit sive  [mng eqv]  ab alia non potest produci. Q.E.D.
Another proof: This is easier proven by reductio to absurdity. Because if a substance could be produced by another one, the knowledge of it would depend (by {1a04} on the knowledge of its cause), therefore (by {1d03}) would not be substance. ALITER: Demonstratur hoc etiam facilius ex absurdo contradictorio. Nam si substantia ab alio posset produci, ejus cognitio a cognitione suae causae deberet pendere (per axioma 4) adeoque (per definitionem 3) non esset substantia.
1p06c substantia ab alio produci 1p06c substantia ab alio produci [geomap]
Corollary.-Hence it follows that a substance cannot be produced by anything external to itself. For in the universe nothing is granted, save substances and their modifications [Lat: affectiones] (as appears from Ax. i. and Deff. iii. and v.). Now (by the last Prop.) substance cannot be produced by another substance, therefore it cannot be produced by anything external to itself. Q.E.D. This is shown still more readily by the absurdity of the contradictory. For, if substance be produced by an external cause, the knowledge of it would depend on the knowledge of its cause (Ax. iv.), and (by Def. iii.) it would itself not be substance. COROLLARIUM: Hinc sequitur substantiam ab alio produci non posse. Nam in rerum natura nihil datur praeter substantias earumque affectiones ut patet ex axiomate 1 {1a01} et definitionibus 3 {1d03} et 5 {1d05}. Atqui a substantia produci non potest (per praecedentem propositionem {1p05}). Ergo substantia absolute ab alio produci non potest. Q.E.D.
1p07 substanti existere 1p07  substantiae existere [geomap]
PROP. VII. Existence belongs to the nature of substances. PROPOSITIO VII: Ad naturam  substantiae pertinet existere.
Proof.-Substance cannot be produced by anything external (Corollary, Prop vi.), it must, therefore, be its own cause-that is, its essence necessarily involves existence, or existence belongs to its nature. DEMONSTRATIO: Substantia non potest produci ab alio (per corollarium propositionis praecedentis {1p06c}); erit itaque causa sui id est (per definitionem 1 {1d01}) ipsius essentia involvit necessario existentiam sive  [mng eqv]  ad ejus naturam pertinet existere. Q.E.D.
1p08 substantia infinita 1p08 substantia infinita [geomap]
PROP. VIII. Every substance is necessarily infinite. PROPOSITIO VIII: Omnis substantia est necessario infinita.
Proof.-There can only be one substance with an identical attribute, and existence follows from its nature (Prop. vii.); its nature, therefore, involves existence, either as finite or infinite. It does not exist as finite, for (by Def. ii.) it would then be limited by something else of the same kind, which would also necessarily exist (Prop. vii.); and there would be two substances with an identical attribute, which is absurd (Prop. v.). It therefore exists as infinite. Q.E.D. DEMONSTRATIO: Substantia unius attributi non nisi unica existit (per propositionem 5 {1p05}) et ad ipsius naturam pertinet existere (per propositionem 7 {1p07}). Erit ergo de ipsius natura vel [excl exh] finita vel [excl exh] infinita existere. At non finita. Nam (per definitionem 2 {1d02}) deberet terminari ab alia ejusdem naturae quae etiam necessario deberet existere (per propositionem 7 {1p07}) adeoque darentur du  substantiae ejusdem attributi, quod est absurdum (per propositionem 5 {1p05}). Existit ergo infinita. Q.E.D.
1p08s1 absoluta affirmatio 1p08s1 absoluta affirmatio
Note I.-As finite existence involves a partial negation, and infinite existence is the absolute affirmation of the given nature, it follows (solely from Prop. vii.) that every substance is necessarily infinite. SCHOLIUM I: Cum finitum esse revera sit ex parte negatio et infinitum absoluta affirmatio existentiae alicujus natur, sequitur ergo ex sola 7 propositione omnem substantiam debere esse infinitam.
1p08s2 modificationum non existentium 1p08s2 modificationum non existentium
Note II.-No doubt it will be difficult for those who think about things loosely, and have not been accustomed to know them by their primary causes, to comprehend the demonstration of Prop. vii.: for such persons make no distinction between the modifications [Lat: affectiones] of substances and the substances themselves, and are ignorant of the manner in which things are produced; hence they may attribute to substances the beginning which they observe in natural objects. SCHOLIUM II: Non dubito quin omnibus qui de rebus confuse judicant nec res per primas suas causas cognoscere consueverunt, difficile sit demonstrationem 7 propositionis concipere; nimirum quia non distinguunt inter modificationes substantiarum et ipsas substantias neque sciunt quomodo res producuntur. Unde fit ut principium quod res naturales habere vident, substantiis affingant;
Those who are ignorant of true causes, make complete confusion-think that trees might talk just as well as men-that men might be formed from stones as well as from seed; and imagine that any form might be changed into any other.
So, also, those who confuse the two natures, divine and human, readily attribute human passions to the deity, especially so long as they do not know how passions originate in the mind
qui enim veras rerum causas ignorant, omnia confundunt et sine ulla mentis repugnantia tam arbores quam homines loquentes fingunt et homines tam ex lapidibus quam ex semine formari et quascunque formas in alias quascunque mutari imaginantur.
Sic etiam qui naturam divinam cum humana confundunt, facile Deo affectus humanos tribuunt praesertim quamdiu etiam ignorant quomodo affectus in mente producuntur.
But, if people would consider the nature of substance, they would have no doubt about the truth of Prop. vii. In fact, this proposition would be a universal axiom, and accounted a truism.
For, by substance, would be understood that which is in itself, and is conceived through itself-that is, something of which the conception requires not the conception of anything else; whereas modifications [Lat: affectiones] exist in something external to themselves, and a conception of them is formed by means of a conception of the thing in which they exist.
Si autem homines ad naturam  substantiae attenderent, minime de veritate 7 propositionis dubitarent; imo haec propositio omnibus axioma esset et inter notiones communes numeraretur.
Nam per substantiam intelligerent id quod in se est et per se concipitur hoc est id cujus cognitio non indiget cognitione alterius rei. Per modificationes autem id quod in alio est et quarum conceptus a conceptu rei in qua sunt, formatur :
Therefore, we may have true ideas of non-existent modifications [Lat: affectiones]; for, although they may have no actual existence apart from the conceiving intellect, yet their essence is so involved in something external to themselves that they may through it be conceived. Whereas the only truth substances can have, external to the intellect, must consist in their existence, because they are conceived through themselves. quocirca modificationum non existentium veras ideas possumus habere quandoquidem quamvis non existant actu extra intellectum, earum tamen essentia ita in alio comprehenditur ut per idem concipi possint. Verum substantiarum veritas extra intellectum non est nisi in se ipsis quia per se concipiuntur.
 Therefore, for a person to say that he has a clear and distinct-that is, a true-idea of a substance, but that he is not sure whether such substance exists, would be the same as if he said that he had a true idea, but was not sure whether or no it was false (a little consideration will make this plain); or if anyone affirmed that substance is created, it would be the same as saying that a false idea was true-in short, the height of absurdity. Si quis ergo diceret se claram et distinctam hoc est veram ideam  substantiae habere et nihilominus dubitare num talis substantia existat, idem hercle esset ac si diceret se veram habere ideam et nihilominus dubitare num falsa sit (ut satis attendentiae sit manifestum); vel si quis statuat substantiam creari, simul statuit ideam falsam factam esse veram, quo sane nihil absurdius concipi potest
It must, then, necessarily be admitted that the existence of substance as its essence is an eternal truth. And we can hence conclude by another process of reasoning-that there is but one such substance.  adeoque fatendum necessario est  substantiae existentiam sicut ejus essentiam aeternam esse veritatem. Atque hinc alio modo concludere possumus non dari nisi unicam ejusdem naturae,
I think that this may profitably be done at once; and, in order to proceed regularly with the demonstration, we must premise:--
1. The true definition of a thing neither involves nor expresses anything beyond the nature of the thing defined. From this it follows that--2. No definition implies or expresses a certain number of individuals, inasmuch as it expresses nothing beyond the nature of the thing defined. For instance, the definition of a triangle expresses nothing beyond the actual nature of a triangle: it does not imply any fixed number of triangles.3. There is necessarily for each individual existent thing a cause why it should exist.4. This cause of existence must either be contained in the nature and definition of the thing defined, or must be postulated apart from such definition.
quod hic ostendere oper pretium esse duxi.
Ut autem hoc ordine faciam notandum est I. veram uniuscujusque rei definitionem nihil involvere neque exprimere praeter rei definitae naturam. Ex quo sequitur hoc II. nempe nullam definitionem certum aliquem numerum individuorum involvere neque exprimere quandoquidem nihil aliud exprimit quam naturam rei definit. Exempli gratia definitio trianguli nihil aliud exprimit quam simplicem naturam trianguli; at non certum aliquem triangulorum numerum. III. notandum dari necessario uniuscujusque rei existentis certam aliquam causam propter quam existit. IV. denique notandum hanc causam propter quam aliqua res existit, vel debere contineri in ipsa natura et definitione rei existentis (nimirum quod ad ipsius naturam pertinet existere) vel debere extra ipsam dari.
It therefore follows that, if a given number of individual things exist in nature, there must be some cause for the existence of exactly that number, neither more nor less. His positis sequitur quod si in natura certus aliquis numerus individuorum existat, debeat necessario dari causa cur illa individua et cur non plura nec pauciora existunt.
For example, if twenty men exist in the universe (for simplicity's sake, I will suppose them existing simultaneously, and to have had no predecessors), and we want to account for the existence of these twenty men, it will not be enough to show the cause of human existence in general; we must also show why there are exactly twenty men, neither more nor less: for a cause must be assigned for the existence of each individual. Si exempli gratia in rerum natura 20 homines existant (quos majoris perspicuitatis causa suppono simul existere nec alios antea in natura exstitisse) non satis erit (ut scilicet rationem reddamus cur 20 homines existant) causam naturae humanae in genere ostendere sed insuper necesse erit causam ostendere cur non plures nec pauciores quam 20 existant quandoquidem (per III notam) uniuscujusque debet necessario dari causa cur existat.
Now this cause cannot be contained in the actual nature of man, for the true definition of man does not involve any consideration of the number twenty. Consequently, the cause for the existence of these twenty men, and, consequently, of each of them, must necessarily be sought externally to each individual. At haec causa (per notam II et III) non potest in ipsa natura humana contineri quandoquidem vera hominis definitio numerum vicenarium non involvit adeoque (per notam IV) causa cur hi vigintiae homines existunt et consequenter cur unusquisque existit, debet necessario extra unumquemque dari
Hence we may lay down the absolute rule, that everything which may consist of several individuals must have an external cause. And, as it has been shown already that existence appertains to the nature of substance, existence must necessarily be included in its definition; and from its definition alone existence must be deducible. et propterea absolute concludendum omne id cujus naturae plura individua existere possunt, debere necessario ut existant causam externam habere. Jam quoniam ad naturam  substantiae (per jam ostensa in hoc scholio) pertinet existere, debet ejus definitio necessariam existentiam involvere et consequenter ex sola ejus definitione debet ipsius existentia concludi.
But from its definition (as we have shown, notes ii., iii.), we cannot infer the existence of several substances; therefore it follows that there is only one substance of the same nature. Q.E.D. At ex ipsius definitione (ut jam ex nota II et III ostendimus) non potest sequi plurium substantiarum existentia; sequitur ergo ex ea necessario unicam tantum ejusdem naturae existere, ut proponebatur.
1p09 plus realitatis plura attributa 1p09 plus realitatis plura attributa [geomap]
PROP. IX. The more reality or being a thing has, the greater the number of its attributes PROPOSITIO IX: Quo plus realitatis aut [mng eqv] esse unaquque res habet eo plura attributa ipsi competunt.
Proof.(Def. iv.). DEMONSTRATIO: Patet ex definitione 4 {1d04}.
1p10 attributum concipi per se 1p10 attributum concipi per se  [geomap]
PROP. X. Each particular attribute of the one substance must be conceived through itself. PROPOSITIO X: Unumquodque unius  substantiae attributum per se concipi debet.
Proof.-An attribute is that which the intellect perceives of substance, as constituting its essence (Def. iv.), and, therefore, must be conceived through itself (Def. iii.). Q.E.D. DEMONSTRATIO: Attributum enim est id quod intellectus de substantia percipit tanquam ejus essentiam constituens (per definitionem 4 {1d04}) adeoque (per definitionem 3 {1d03}) per se concipi debet. Q.E.D.
1p10s attributa non entia sive substantias distincta 1p10s attributa non entia sive substantias distincta
Note-It is thus evident that, though two attributes are, in fact, conceived as distinct-that is, one without the help of the other-yet we cannot, therefore, conclude that they constitute two entities, or two different substances. For it is the nature of substance that each of its attributes is conceived through itself, inasmuch as all the attributes it has have always existed simultaneously in it, and none could be produced by any other; but each expresses the reality or being of substance. It is, then, far from an absurdity to ascribe several attributes to one substance: for nothing in nature is more clear than that each and every entity must be conceived under some attribute, and that its reality or being is in proportion to the number of its attributes expressing necessity or eternity and infinity. Consequently it is abundantly clear, that an absolutely infinite being must necessarily be defined as consisting in infinite attributes, each of which expresses a certain eternal and infinite essence. If anyone now ask, by what sign shall he be able to distinguish different substances, let him read the following propositions, which show that there is but one substance in the universe, and that it is absolutely infinite, wherefore such a sign would be sought in vain. SCHOLIUM: Ex his apparet quod quamvis duo attributa realiter distincta concipiantur hoc est unum sine ope alterius, non possumus tamen inde concludere ipsa dua entia sive duas diversas substantias constituere; id enim est de natura  substantiae ut unumquodque ejus attributorum per se concipiatur quandoquidem omnia quae habet attributa, simul in ipsa semper fuerunt nec unum ab alio produci potuit sed unumquodque realitatem sive esse  substantiae exprimit. Longe ergo abest ut absurdum sit uni  substantiae plura attributa tribuere; quin nihil in natura clarius quam quod unumquodque ens sub aliquo attributo debeat concipi et quo plus realitatis aut esse habeat eo plura attributa quae et necessitatem sive aeternitatem et infinitatem exprimunt, habeat et consequenter nihil etiam clarius quam quod ens absolute infinitum necessario sit definiendum (ut definitione 6 tradidimus) ens quod constat infinitis attributis quorum unumquodque aeternam et infinitam certam essentiam exprimit. Si quis autem jam qurit ex quo ergo signo diversitatem substantiarum poterimus dignoscere, legat sequentes propositiones, quae ostendunt in rerum natura non nisi unicam substantiam existere eamque absolute infinitam esse, quapropter id signum frustra qureretur.
1p11 Deus sive substantia necessario existit 1p11 Deus sive substantia necessario existit [geomap]
PROP. XI. God, or substance, consisting of infinite attributes, of which each expresses eternal and infinite essentiality, necessarily exists. PROPOSITIO XI: Deus sive [prf eqv] substantia constans infinitis attributis quorum unumquodque aeternam et infinitam essentiam exprimit, necessario existit.
Proof.-If this be denied, conceive, if possible, that God does not exist: then his essence does not involve existence. But this (Prop. vii.) is absurd. Therefore God necessarily exists. DEMONSTRATIO: Si negas, concipe si fieri potest, Deum non existere. Ergo (per axioma 7 {1a7}) ejus essentia non involvit existentiam. Atqui hoc (per propositionem 7 {1p7}) est absurdum : ergo Deus necessario existit. Q.E.D.
Another proof.-Of everything whatsoever a cause or reason must be assigned, either for its existence, or for its non-existence-e.g. if a triangle exist, a reason or cause must be granted for its existence; if, on the contrary, it does not exist, a cause must also be granted, which prevents it from existing, or annuls its existence. This reason or cause must either be contained in the nature of the thing in question, or be external to it. For instance, the reason for the  non-existence of a square circle is indicated in its nature, namely, because it would involve a contradiction. On the other hand, the existence of substance follows also solely from its nature, inasmuch as its nature involves existence. (See Prop. vii.) But the reason for the existence of a triangle or a circle does not follow from the nature of those figures, but from the order of universal nature in extension. From the latter it must follow, either that a triangle necessarily exists, or that it is impossible that it should exist. So much is self-evident. It follows therefrom that a thing necessarily exists, if no cause or reason be granted which prevents its existence. If, then, no cause or reason can be given, which prevents the existence of God, or which destroys his existence, we must certainly conclude that he necessarily does exist. If such a reason or cause should be given, it must either be drawn from the very nature of God, or be external to him-that is, drawn from another substance of another nature. For if it were of the same nature, God, by that very fact, would be admitted to exist. But substance of another nature could have nothing in common with God (by Prop. ii.), and therefore would be unable either to cause or to destroy his existence.
As, then, a reason or cause which would annul the divine existence cannot be drawn from anything external to the divine nature, such cause must perforce, if God does not exist, be drawn from God's own nature, which would involve a contradiction. To make such an affirmation about a being absolutely infinite and supremely perfect is absurd; therefore, neither in the nature of God, nor externally to his nature, can a cause or reason be assigned which would annul his existence. Therefore, God necessarily exists. Q.E.D.
ALITER: Cujuscunque rei assignari debet causa seu ratio tam cur existit quam cur non existit. Exempli gratia si triangulus existit, ratio seu causa dari debet cur existit; si autem non existit, ratio etiam seu causa dari debet quae impedit quominus existat sive quae ejus existentiam tollat. Haec vero ratio seu causa vel in natura rei contineri debet vel extra ipsam. Exempli gratia rationem cur circulus quadratus non existat, ipsa ejus natura indicat; nimirum quia contradictionem involvit. Cur autem contra substantia existat, ex sola etiam ejus natura sequitur quia scilicet existentiam involvit (vide propositionem 7). At ratio cur circulus vel triangulus existit vel cur non existit, ex eorum natura non sequitur sed ex ordine universae naturae corpore; ex eo enim sequi debet vel jam triangulum necessario existere vel impossibile esse ut jam existat. Atque haec per se manifesta sunt. Ex quibus sequitur id necessario existere cujus nulla ratio nec causa datur quae impedit quominus existat. Si itaque nulla ratio nec causa dari possit quae impedit quominus Deus existat vel quae ejus existentiam tollat, omnino concludendum est eundem necessario existere. At si talis ratio seu causa daretur, ea vel in ipsa Dei natura vel extra ipsam dari deberet hoc est in alia substantia alterius natur. Nam si ejusdem naturae esset, eo ipso concederetur dari Deum. At substantia quae alterius esset natur, nihil cum Deo commune habere (per 2 propositionem) adeoque neque ejus existentiam ponere neque tollere posset. Cum igitur ratio seu causa quae divinam existentiam tollat, extra divinam naturam dari non possit, debebit necessario dari, siquidem non existit, in ipsa ejus natura, quae propterea contradictionem involveret. Atqui hoc de Ente absolute infinito et summe perfecto affirmare absurdum est; ergo nec in Deo nec extra Deum ulla causa seu ratio datur quae ejus existentiam tollat ac proinde Deus necessario existit. Q.E.D.
Another proof.-The potentiality of non-existence is a negation of power, and contrariwise the potentiality of existence is a power, as is obvious. If, then, that which necessarily exists is nothing but finite beings, such finite beings are more powerful than a being absolutely infinite, which is obviously absurd; therefore, either nothing exists, or else a being absolutely infinite necessarily exists also. Now we exist either in ourselves, or in something else which necessarily exists (see Axiom. i. and Prop. vii.). Therefore a being absolutely infinite-in other words, God (Def. vi.)-necessarily exists. Q.E.D. ALITER: Posse non existere impotentia est et contra posse existere potentia est (ut per se notum). Si itaque id quod jam necessario existit, non nisi entia finita sunt, sunt ergo entia finita potentiora Ente absolute infinito atque hoc (ut per se notum) absurdum est; ergo vel nihil existit vel Ens absolute infinitum necessario etiam existit. Atqui nos vel in nobis vel in alio quod necessario existit, existimus (vide axioma 1 et propositionem 7). Ergo Ens absolute infinitum hoc est (per definitionem 6) Deus necessario existit. Q.E.D.
1p11s posteriori priori 1p11s posteriori priori
Note.-In this last proof, I have purposely shown God's existence posteriori, so that the proof might be more easily followed, not because, from the same premises, God's existence does not follow priori. For, as the potentiality of existence is a power, it follows that, in proportion as reality increases in the nature of a thing, so also will it increase its strength for existence. Therefore a being absolutely infinite, such as God, has from himself an absolutely infinite power of existence, and hence he does absolutely exist. Perhaps there will be many who will be unable to see the force of this proof, inasmuch as they are accustomed only to consider those things which flow from external causes. Of such things, they see that those which quickly come to pass-that is, quickly come into existence-quickly also disappear; whereas they regard as more difficult of accomplishment-that is, not so easily brought into existence-those things which they conceive as more complicated.
However, to do away with this misconception, I need not here show the measure of truth in the proverb, "What comes quickly, goes quickly," nor discuss whether, from the point of view of universal nature, all things are equally easy, or otherwise: I need only remark that I am not here speaking of things, which come to pass through causes external to themselves, but only of substances which (by Prop. vi.) cannot be produced by any external cause. Things which are produced by external causes, whether they consist of many parts or few, owe whatsoever perfection or reality they possess solely to the efficacy of their external cause; and therefore their existence arises solely from the perfection of their external cause, not from their own. Contrariwise, whatsoever perfection is possessed by substance is due to no external cause; wherefore the existence of substance must arise solely from its own nature, which is nothing else but its essence. Thus, the perfection of a thing does not annul its existence, but, on the contrary, asserts it. Imperfection, on the other hand, does annul it; therefore we cannot be more certain of the existence of anything, than of the existence of a being absolutely infinite or perfect-that is, of God. For inasmuch as his essence excludes all imperfection, and involves absolute perfection, all cause for doubt concerning his existence is done away, and the utmost certainty on the question is given. This, I think, will be evident to every moderately attentive reader.
SCHOLIUM: In hac ultima demonstratione Dei existentiam a posteriori ostendere volui ut demonstratio facilius perciperetur; non autem propterea quod ex hoc eodem fundamento Dei existentia a priori non sequatur. Nam cum posse existere potentia sit, sequitur quo plus realitatis alicujus rei naturae competit eo plus virium a se habere ut existat adeoque Ens absolute infinitum sive Deum infinitam absolute potentiam existendi a se habere, qui propterea absolute existit. Multi tamen forsan non facile hujus demonstrationis evidentiam videre poterunt quia assueti sunt eas solummodo res contemplari quae a causis externis fiunt et ex his quae cito fiunt hoc est quae facile existunt, eas etiam facile perire vident et contra eas res factu difficiliores judicant hoc est ad existendum non adeo faciles ad quas plura pertinere concipiunt. Verum ut ab his praejudiciis liberentur, non opus habeo hic ostendere qua ratione hoc enunciatum "quod cito fit cito perit" verum sit nec etiam an respectu totius naturae omnia que facilia sint an secus. Sed hoc tantum notare sufficit me hic non loqui de rebus quae a causis externis fiunt sed de solis substantiis, quae (per propositionem 6) a nulla causa externa produci possunt. Res enim quae a causis externis fiunt, sive e multis partibus constent sive paucis, quicquid perfectionis sive realitatis habent, id omne virtutiae causae externae debetur adeoque earum existentia ex sola perfectione causae externae, non autem suae oritur. Contra quicquid substantia perfectionis habet, nulli  causae externae debetur; quare ejus etiam existentia ex sola ejus natura sequi debet, quae proinde nihil aliud est quam ejus essentia. Perfectio igitur rei existentiam non tollit sed contra ponit; imperfectio autem contra eandem tollit adeoque de nullius rei existentia certiores esse possumus quam de existentia Entis absolute infiniti seu perfecti hoc est Dei. Nam quandoquidem ejus essentia omnem imperfectionem secludit absolutamque perfectionem involvit, eo ipso omnem causam dubitandi de ipsius existentia tollit summamque de eadem certitudinem dat, quod mediocriter attendenti perspicuum fore credo.
1p12 substanti dividi 1p12  substantiae dividi [geomap]
PROP. XII. No attribute of substance can be conceived from which it would follow that substance can be divided. PROPOSITIO XII: Nullum  substantiae attributum potest vere concipi ex quo sequatur substantiam posse dividi.
Proof.-The parts into which substance as thus conceived would be divided either will retain the nature of substance, or they will not. If the former, then (by Prop. viii.) each part will necessarily be infinite, and (by Prop. vi.) self-caused, and (by Prop. v.) will perforce consist of a different attribute, so that, in that case, several substances could be formed out of one substance, which (by Prop. vi.) is absurd. Moreover, the parts (by Prop. ii.) would have nothing in common with their whole, and the whole (by Def. iv. and Prop. x.) could both exist and be conceived without its parts, which everyone will admit to be absurd. If we adopt the second alternative-namely, that the parts will not retain the nature of substance-then, if the whole substance were divided into equal parts, it would lose the nature of substance, and would cease to exist, which (by Prop. vii.) is absurd. DEMONSTRATIO: Partes enim in quas substantia sic concepta divideretur, vel [excl exh] naturam  substantiae retinebunt vel [excl exh] non. Si primum, tum (per 8 propositionem {1p08}) unaquque pars debebit esse infinita et (per propositionem 6 {1p06}) causa sui et (per propositionem 5 {1p05}) constare debebit ex diverso attributo adeoque ex una substantia plures constitui poterunt, quod (per propositionem 6 {1p06}) est absurdum. Adde quod partes (per propositionem 2 {1p02}) nihil commune cum suo toto haberent et totum (per definitionem 4  {1d04} et propositionem 10 {1p10}) absque suis partibus et esse et concipi posset, quod absurdum esse nemo dubitare poterit. Si autem secundum ponatur quod scilicet partes naturam substantiae non retinebunt, ergo cum tota substantia in quales partes esset divisa, naturam substantiae amitteret et esse desineret, quod (per propositionem 7 {1p07}) est absurdum.
1p13 Substantia indivisibilis 1p13 Substantia indivisibilis [geomap]
PROP. XIII. Substance absolutely infinite is indivisible. PROPOSITIO XIII: Substantia absolute infinita est indivisibilis.
Proof.-If it could be divided, the parts into which it was divided would either retain the nature of absolutely infinite substance, or they would not. If the former, we should have several substances of the same nature, which (by Prop. v.) is absurd. If the latter, then (by Prop. vii.) substance absolutely infinite could cease to exist, which (by Prop. xi.) is also absurd. DEMONSTRATIO: Si enim divisibilis esset, partes in quas divideretur vel [excl exh] naturam  substantiae absolute infinitae retinebunt vel non. Si primum, dabuntur ergo plures  substantiae ejusdem naturae, quod (per propositionem 5 {1p05}) est absurdum. Si secundum ponatur, ergo (ut supra {1p07}) poterit substantia absolute infinita desinere esse, quod (per propositionem 11 {1p11}) est etiam absurdum.
1p13c consequenter nullam substantiam corpoream 1p13c consequenter nullam substantiam corpoream [geomap]
Corollary.-It follows, that no substance, and consequently no extended substance, in so far as it is substance, is divisible. COROLLARIUM {1p13}: Ex his sequitur nullam substantiam et consequenter nullam substantiam corpoream, quatenus substantia est, esse divisibilem.
1p13s infinita finita 1p13s infinita finita
Note.-The indivisibility of substance may be more easily understood as follows. The nature of substance can only be conceived as infinite, and by a part of substance, nothing else can be understood than finite substance, which (by Prop. viii) involves a manifest contradiction. SCHOLIUM: Quod substantia sit indivisibilis, simplicius ex hoc solo intelligitur quod natura  substantiae non potest concipi nisi infinita et quod per partem  substantiae nihil aliud intelligi potest quam substantia finita, quod (per propositionem 8) manifestam contradictionem implicat.
1p14 Praeter Deum nulla 1p14 praeter Deum nulla [geomap]
PROP. XIV. Besides God no substance can be granted or conceived. PROPOSITIO XIV: praeter Deum nulla dari neque concipi potest substantia.
Proof.-As God is a being absolutely infinite, of whom no attribute that expresses the essence of substance can be denied (by Def. vi.), and he necessarily exists (by Prop. xi.); if any substance besides God were granted, it would have to be explained by some attribute of God, and thus two substances with the same attribute would exist, which (by Prop. v.) is absurd; therefore, besides God no substance can be granted, or, consequently, be conceived. If it could be conceived, it would necessarily have to be conceived as existent; but this (by the first part of this proof) is absurd. Therefore, besides God no substance can be granted or conceived. Q.E.D. DEMONSTRATIO: Cum Deus sit ens absolute infinitum de quo nullum attributum quod essentiam  substantiae exprimit, negari potest (per definitionem 6 {1d06}) isque necessario existat (per propositionem 11 {1p11}) si aliqua substantia praeter Deum daretur, ea explicari deberet per aliquod attributum Dei sicque du  substantiae ejusdem attributi existerent, quod (per propositionem 5 {1p05}) est absurdum adeoque nulla substantia extra Deum dari potest et consequenter non etiam concipi. Nam si posset concipi, deberet necessario concipi ut existens; atqui hoc (per primam partem hujus demonstrationis) est absurdum. Ergo extra Deum nulla dari neque concipi potest substantia. Q.E.D.
1p14c1 Deum unicum infinitam 1p14c1 Deum unicum infinitam [geomap]
Corollary I.-Clearly, therefore: 1. God is one, that is (by Def. vi.) only one substance can be granted in the universe, and that substance is absolutely infinite, as we have already indicated (in the note to Prop. x.). COROLLARIUM {1p14} I: Hinc clarissime sequitur I. Deum esse unicum hoc est (per definitionem 6 {1d06}) in rerum natura non nisi unam substantiam dari eamque absolute infinitam esse, ut in scholio propositionis 10 {non-deductive reference} jam innuimus.
1p14c2 rem vel attributa vel affectiones 1p14c2 rem vel attributa vel affectiones [geomap]
Corollary II.-It follows: 2. That extension and thought are either attributes of God or (by Ax. i.) accidents (affectiones) of the attributes of God. COROLLARIUM {1p14} II: Sequitur II. rem extensam et rem cogitantem vel [excl exh] Dei attributa esse vel (per axioma 1 {1a01}) affectiones attributorum Dei.
1p15 est in Deo est 1p15 est in Deo est [geomap]
PROP. XV. Whatsoever is, is in God, and without God nothing can be, or be conceived. PROPOSITIO XV: Quicquid est, in Deo est et nihil sine Deo esse neque concipi potest.
Proof.-Besides God, no substance is granted or can be conceived (by Prop. xiv.), that is (by Def. iii.) nothing which is in itself and is conceived through itself. But modes (by Def. v.) can neither be, nor be conceived without substance; wherefore they can only be in the divine nature, and can only through it be conceived. But substances and modes form the sum total of existence (by Ax. i.), therefore, without God nothing can be, or be conceived. Q.E.D. DEMONSTRATIO: praeter Deum nulla datur neque concipi potest substantia (per 14 propositionem {1p14}) hoc est (per definitionem 3) res quae in se est et per se concipitur. Modi autem (per definitionem 5 {1d05}) sine substantia nec esse nec concipi possunt; quare hi in sola divina natura esse et per ipsam solam concipi possunt. Atqui praeter substantias et modos nil datur (per axioma 1 {1a01}). Ergo nihil sine Deo  esse neque concipi potest. Q.E.D.
1p15s Deum hominis corpore et mente 1p15s Deum hominis corpore et mente
Note.-Some assert that God, like a man, consists of body and mind, and is susceptible of passions. How far such persons have strayed from the truth is sufficiently evident from what has been said. But these I pass over. For all who have in anywise reflected on the divine nature deny that God has a body. Of this they find excellent proof in the fact that we understand by body a definite quantity, so long, so broad, so deep, bounded by a certain shape, and it is the height of absurdity to predicate such a thing of God, a being absolutely infinite. But meanwhile by other reasons with which they try to prove their point, they show that they think corporeal or extended substance wholly apart from the divine nature, and say it was created by God. Wherefrom the divine nature can have been created, they are wholly ignorant; thus they clearly show, that they do not know the meaning of their own words. I myself have proved sufficiently clearly, at any rate in my own judgment (Coroll. Prop. vi, and note 2, Prop. viii.), that no substance can be produced or created by anything other than itself. Further, I showed (in Prop. xiv.), that besides God no substance can be granted or conceived. Hence we drew the conclusion that extended substance is one of the infinite attributes of God. However, in order to explain more fully, I will refute the arguments of my adversaries, which all start from the following points:--
Extended substance, in so far as it is substance, consists, as they think, in parts, wherefore they deny that it can be infinite, or consequently, that it can appertain to God. This they illustrate with many examples, of which I will take one or two. If extended substance, they say, is infinite, let it be conceived to be divided into two parts; each part will then be either finite or infinite. If the former, then infinite substance is composed of two finite parts, which is absurd. If the latter, then one infinite will be twice as large as another infinite, which is also absurd.
Further, if an infinite line be measured out in foot lengths, it will consist of an infinite number of such parts; it would equally consist of an infinite number of parts, if each part measured only an inch: therefore, one infinity would be twelve times as great as the other.
Lastly, if from a single point there be conceived to be drawn two diverging lines which at first are at a definite distance apart, but are produced to infinity, it is certain that the distance between the two lines will be continually increased, until at length it changes from definite to indefinable. As these absurdities follow, it is said, from considering quantity as infinite, the conclusion is drawn, that extended substance must necessarily be finite, and, consequently, cannot appertain to the nature of God.
The second argument is also drawn from God's supreme perfection. God, it is said, inasmuch as he is a supremely perfect being, cannot be passive; but extended substance, insofar as it is divisible, is passive. It follows, therefore, that extended substance does not appertain to the essence of God.
Such are the arguments I find on the subject in writers, who by them try to prove that extended substance is unworthy of the divine nature, and cannot possibly appertain thereto. However, I think an attentive reader will see that I have already answered their propositions; for all their arguments are founded on the hypothesis that extended substance is composed of parts, and such a hypothesis I have shown (Prop. xii., and Coroll. Prop. xiii.) to be absurd. Moreover, anyone who reflects will see that all these absurdities (if absurdities they be, which I am not now discussing), from which it is sought to extract the conclusion that extended substance is finite, do not at all follow from the notion of an infinite quantity, but merely from the notion that an infinite quantity is measurable, and composed of finite parts therefore, the only fair conclusion to be drawn is that: infinite quantity is not measurable, and cannot be composed of finite parts. This is exactly what we have already proved (in Prop. xii.). Wherefore the weapon which they aimed at us has in reality recoiled upon themselves. If, from this absurdity of theirs, they persist in drawing the conclusion that extended substance must be finite, they will in good sooth be acting like a man who asserts that circles have the properties of squares, and, finding himself thereby landed in absurdities, proceeds to deny that circles have any center, from which all lines drawn to the circumference are equal. For, taking extended substance, which can only be conceived as infinite, one, and indivisible (Props. viii., v., xii.) they assert, in order to prove that it is finite, that it is composed of finite parts, and that it can be multiplied and divided.
So, also, others, after asserting that a line is composed of points, can produce many arguments to prove that a line cannot be infinitely divided. Assuredly it is not less absurd to assert that extended substance is made up of bodies or parts, than it would be to assert that a solid is made up of surfaces, a surface of lines, and a line of points. This must be admitted by all who know clear reason to be infallible, and most of all by those who deny the possibility of a vacuum. For if extended substance could be so divided that its parts were really separate, why should not one part admit of being destroyed, the others remaining joined together as before? And why should all be so fitted into one another as to leave no vacuum? Surely in the case of things, which are really distinct one from the other, one can exist without the other, and can remain in its original condition. As, then, there does not exist a vacuum in nature (of which anon), but all parts are bound to come together to prevent it, it follows from this that the parts cannot really be distinguished, and that extended substance in so far as it is substance cannot be divided.
If anyone asks me the further question, Why are we naturally so prone to divide quantity? I answer, that quantity is conceived by us in two ways; in the abstract and superficially, as we imagine it; or as substance, as we conceive it solely by the intellect. If, then, we regard quantity as it is represented in our imagination, which we often and more easily do, we shall find that it is finite, divisible, and compounded of parts; but if we regard it as it is represented in our intellect, and conceive it as substance, which it is very difficult to do, we shall then, as I have sufficiently proved, find that it is infinite, one, and indivisible. This will be plain enough to all who make a distinction between the intellect and the imagination, especially if it be remembered, that matter is everywhere the same, that its parts are not distinguishable, except in so far as we conceive matter as diversely modified, whence its parts are distinguished, not really, but modally. For instance, water, in so far as it is water, we conceive to be divided, and its parts to be separated one from the other; but not in so far as it is extended substance; from this point of view it is neither separated nor divisible. Further, water, in so far as it is water, is produced and corrupted; but, in so far as it is substance, it is neither produced nor corrupted.
I think I have now answered the second argument; it is, in fact, founded on the same assumption as the first-namely, that matter, in so far as it is substance, is divisible, and composed of parts. Even if it were so, I do not know why it should be considered unworthy of the divine nature, inasmuch as besides God (by Prop. xiv.) no substance can be granted, wherefrom it could receive its modifications [Lat: affectiones]. All things, I repeat, are in God, and all things which come to pass, come to pass solely through the laws of the infinite nature of God, and follow (as I will shortly show) from the necessity of his essence. Wherefore it can in nowise be said, that God is passive in respect to anything other than himself, or that extended substance is unworthy of the Divine nature, even if it be supposed divisible, so long as it is granted to be infinite and eternal. But enough of this for the present.
SCHOLIUM: Sunt qui Deum instar hominis corpore et mente constantem atque passionibus obnoxium fingunt sed quam longe hi a vera Dei cognitione aberrent, satis ex jam demonstratis constat. Sed hos mitto : nam omnes qui naturam divinam aliquo modo contemplati sunt, Deum esse corporeum negant. Quod etiam optime probant ex eo quod per corpus intelligimus quamcunque quantitatem longam, latam et profundam, certa aliqua figura terminatam, quo nihil absurdius de Deo, ente scilicet absolute infinito, dici potest. Attamen interim aliis rationibus quibus hoc idem demonstrare conantur, clare ostendunt se substantiam ipsam corpoream sive extensam a natura divina omnino removere atque ipsam a Deo creatam statuunt. Ex qua autem divina potentia creari potuerit, prorsus ignorant; quod clare ostendit illos id quod ipsimet dicunt, non intelligere. Ego saltem satis clare meo quidem judicio demonstravi (vide corollarium propositionis 6 et scholium II propositionis 8) nullam substantiam ab alio produci vel creari. Porro propositione 14 ostendimus praeter Deum nullam dari neque concipi posse substantiam atque hinc conclusimus substantiam extensam unum ex infinitis Dei attributis esse. Verum ad pleniorem explicationem adversariorum argumenta refutabo quae omnia huc redeunt primo quod substantia corporea quatenus substantia constat ut putant partibus et ideo eandem infinitam posse esse et consequenter ad Deum pertinere posse negant. Atque hoc multis exemplis explicant ex quibus unum aut alterum afferam. Si substantia corporea aiunt est infinita, concipiatur in duas partes dividi; erit unaquque pars vel finita vel infinita. Si illud, componitur ergo infinitum ex duabus partibus finitis, quod est absurdum. Si hoc, datur ergo infinitum duplo majus alio infinito, quod etiam est absurdum. Porro si quantitas infinita mensuratur partibus pedes quantibus, infinitis talibus partibus constare debebit ut et si partibus mensuretur digitos quantibus ac propterea unus numerus infinitus erit duodecies major alio infinito. Denique si ex uno puncto infinitae cujusdam quantitatis concipiatur duas lineas ut AB, AC, certa ac determinata in initio distantia in infinitum protendi, certum est distantiam inter B et C continuo augeri et tandem ex determinata indeterminabilem fore. Cum igitur haec absurda sequantur ut putant ex eo quod quantitas infinita supponitur, inde concludunt substantiam corpoream debere esse finitam et consequenter ad Dei essentiam non pertinere. Secundum argumentum petitur etiam a summa Dei perfectione. Deus enim inquiunt cum sit ens summe perfectum, pati non potest : atqui substantia corporea quandoquidem divisibilis est, pati potest; sequitur ergo ipsam ad Dei essentiam non pertinere. Haec sunt quae apud scriptores invenio argumenta quibus ostendere conantur substantiam corpoream divina natura indignam esse nec ad eandem posse pertinere. Verumenimvero si quis recte attendat, me ad haec jam respondisse comperiet quandoquidem haec argumenta in eo tantum fundantur quod substantiam corpoream ex partibus componi supponunt, quod jam (per propositionem 12 cum corollario propositionis 13) absurdum esse ostendi. Deinde si quis rem recte perpendere velit, videbit omnia illa absurda (siquidem omnia absurda sunt, de quo non jam disputo) ex quibus concludere volunt substantiam extensam finitam esse, minime ex eo sequi quod quantitas infinita supponatur sed quod quantitatem infinitam mensurabilem et ex partibus finitis conflari supponunt; quare ex absurdis quae inde sequuntur, nihil aliud concludere possunt quam quod quantitas infinita non sit mensurabilis et quod ex partibus finitis conflari non possit. Atque hoc idem est quod nos supra (propositione 12 etc.) jam demonstravimus. Quare telum quod in nos intendunt, in se ipsos revera conjiciunt. Si igitur ipsi ex suo hoc absurdo concludere tamen volunt substantiam extensam debere esse finitam, nihil aliud hercle faciunt quam si quis ex eo quod finxit circulum quadrati proprietates habere, concludit circulum non habere centrum ex quo omnes ad circumferentiam duct line sunt quales. Nam substantiam corpoream quae non nisi infinita, non nisi unica et non nisi indivisibilis potest concipi (vide propositiones 8, 5 et 12) eam ipsi ad concludendum eandem esse finitam, ex partibus finitis conflari et multiplicem esse et divisibilem concipiunt. Sic etiam alii postquam fingunt lineam ex punctis componi, multa sciunt invenire argumenta quibus ostendant lineam non posse in infinitum dividi. Et profecto non minus absurdum est ponere quod substantia corporea ex corporibus sive partibus componatur quam quod corpus ex superficiebus, superficies ex lineis, line denique ex punctis componantur. Atque hoc omnes qui claram rationem infallibilem esse sciunt, fateri debent et imprimis ii qui negant dari vacuum. Nam si substantia corporea ita posset dividi ut ejus partes realiter distinctae essent, cur ergo una pars non posset annihilari manentibus reliquis ut ante inter se connexis? et cur omnes ita aptari debent ne detur vacuum? Sane rerum quae realiter ab invicem distinctae sunt, una sine alia esse et in suo statu manere potest. Cum igitur vacuum in natura non detur (de quo alias) sed omnes partes ita concurrere debent ne detur vacuum, sequitur hinc etiam easdem non posse realiter distingui hoc est substantiam corpoream quatenus substantia est, non posse dividi. Si quis tamen jam qurat cur nos ex natura ita propensi simus ad dividendam quantitatem? ei respondeo quod quantitas duobus modis a nobis concipitur, abstracte scilicet sive superficialiter prout nempe ipsam imaginamur vel ut substantia, quod a solo intellectu fit. Si itaque ad quantitatem attendimus prout in imaginatione est, quod spe et facilius a nobis fit, reperietur finita, divisibilis et partibus conflata; si autem ad ipsam prout in intellectu est, attendimus et eam quatenus substantia est, concipimus, quod difficillime fit, tum ut jam satis demonstravimus, infinita, unica et indivisibilis reperietur. Quod omnibus qui inter imaginationem et intellectum distinguere sciverint, satis manifestum erit, praecipue si ad hoc etiam attendatur quod materia ubique eadem est nec partes in eadem distinguuntur nisi quatenus materiam diversimode affectam esse concipimus, unde ejus partes modaliter tantum distinguuntur, non autem realiter. Exempli gratia aquam quatenus aqua est, dividi concipimus ejusque partes ab invicem separari; at non quatenus substantia est corporea; eatenus enim neque separatur neque dividitur. Porro aqua quatenus aqua generatur et corrumpitur; at quatenus substantia nec generatur nec corrumpitur. Atque his me ad secundum argumentum etiam respondisse puto quandoquidem id in eo etiam fundatur quod materia quatenus substantia divisibilis sit et partibus confletur. Et quamvis hoc non esset, nescio cur divina natura indigna esset quandoquidem (per propositionem 14) extra Deum nulla substantia dari potest a qua ipsa pateretur. Omnia inquam in Deo sunt et omnia quae fiunt per solas leges infinitae Dei naturae fiunt et ex necessitate ejus essentiae (ut mox ostendam) sequuntur; quare nulla ratione dici potest Deum ab alio pati aut substantiam extensam divina natura indignam esse tametsi divisibilis supponatur dummodo aeterna et infinita concedatur. Sed de his impraesentiarum satis.
1p16 infinita infinitis modis sequi 1p16 infinita infinitis modis sequi [geomap]
PROP. XVI. From the necessity of the divine nature must follow an infinite number of things in infinite ways-that is, all things which can fall within the sphere of infinite intellect. PROPOSITIO XVI: Ex necessitate divinae naturae infinita infinitis modis (hoc est omnia quae sub intellectum infinitum cadere possunt) sequi debent.
Proof.-This proposition will be clear to everyone, who remembers that from the given definition of any thing the intellect infers several properties, which really necessarily follow therefrom (that is, from the actual essence of the thing defined); and it infers more properties in proportion as the definition of the thing expresses more reality, that is, in proportion as the essence of the thing defined involves more reality. Now, as the divine nature has absolutely infinite attributes (by Def. vi.), of which each expresses infinite essence after its kind, it follows that from the necessity of its nature an infinite number of things (that is, everything which can fall within the sphere of an infinite intellect) must necessarily follow. Q.E.D. DEMONSTRATIO: Haec propositio unicuique manifesta esse debet si modo ad hoc attendat quod ex data cujuscunque rei definitione plures proprietates intellectus concludit, quae revera ex eadem (hoc est ipsa rei essentia) necessario sequuntur et eo plures quo plus realitatis rei definitio exprimit hoc est quo plus realitatis rei definitae essentia involvit. Cum autem natura divina infinita absolute attributa habeat (per definitionem 6 {1d06}) quorum etiam unumquodque infinitam essentiam in suo genere exprimit, ex ejusdem ergo necessitate infinita infinitis modis (hoc est omnia quae sub intellectum infinitum cadere possunt) necessario sequi debent. Q.E.D.
1p16c1 intellectum infinitum 1p16c1 intellectum infinitum  [geomap]
Corollary I.-Hence it follows, that God is the efficient cause of all that can fall within the sphere of an infinite intellect. COROLLARIUM {1p16} I: Hinc sequitur Deum omnium rerum quae sub intellectum infinitum cadere possunt, esse causam efficientem.
1p16c2 non accidens 1p16c2 non accidens [geomap]
Corollary II.-It also follows that God is a cause in himself, and not through an accident of his nature. COROLLARIUM {1p16} II: Sequitur II. Deum causam esse per se, non vero per accidens.
1p16c3 causam primam 1p16c3 causam primam [geomap]
Corollary III.-It follows, thirdly, that God is the absolutely first cause. COROLLARIUM {1p16}  III: Sequitur III. Deum esse absolute causam primam.
1p17 Deus nemine coactus 1p17 Deus nemine coactus [geomap]
PROP. XVII. God acts solely by the laws of his own nature, and is not constrained by anyone. PROPOSITIO XVII: Deus ex solis suae naturae legibus et a nemine coactus agit.
Proof.-We have just shown (in Prop. xvi.), that solely from the necessity of the divine nature, or, what is the same thing, solely from the laws of his nature, an infinite number of things absolutely follow in an infinite number of ways; and we proved (in Prop. xv.), that without God nothing can be nor be conceived but that all things are in God. Wherefore nothing can exist; outside himself, whereby he can be conditioned or constrained to act. Wherefore God acts solely by the laws of his own nature, and is not constrained by anyone. Q.E.D. DEMONSTRATIO: Ex sola divinae naturae necessitate vel [mng eqv] (quod idem est) ex solis ejusdem naturae legibus infinita absolute sequi modo propositione 16 {1p16} ostendimus et propositione 15 {1p15} demonstravimus nihil sine Deo esse nec concipi posse sed omnia in Deo esse; quare nihil extra ipsum esse potest a quo ad agendum determinetur vel [a fortiori] cogatur atque adeo Deus ex solis suae naturae legibus et a nemine coactus agit. Q.E.D.
1p17c1 extrinsece vel intrinsece 1p17c1 extrinsece vel intrinsece [geomap]
Corollary I.-It follows: 1. That there can be no cause which, either extrinsically or intrinsically, besides the perfection of his own nature, moves God to act. COROLLARIUM {1p17} I: Hinc sequitur I. nullam dari causam quae Deum extrinsece vel [excl exh] intrinsece praeter ipsius naturae perfectionem incitet ad agendum.
1p17c2 solum Deum causam liberam 1p17c2 solum Deum causam liberam [geomap]
Corollary II.-It follows: 2. That God is the sole free cause. For God alone exists by the sole necessity of his nature (by Prop. xi. and Prop. xiv., Coroll. i.), and acts by the sole necessity of his own nature, wherefore God is (by Def. vii.) the sole free cause. Q.E.D. COROLLARIUM {1p17} II: Sequitur II. solum Deum esse causam liberam. Deus enim solus ex sola suae naturae  necessitate existit (per propositionem 11 {1p11} et corollarium I propositionis 14 {1p14c1}) et ex sola suae naturae necessitate agit (per propositionem praecedentem {1p16}). Adeoque (per definitionem 7 {1d07}) solus est causa libera. Q.E.D.
1p17s Deum causam liberam 1p17s Deum causam liberam
Note.-Others think that God is a free cause, because he can, as they think, bring it about, that those things which we have said follow from his nature-that is, which are in his power, should not come to pass, or should not be produced by him. But this is the same as if they said, that God could bring it about, that it should follow from the nature of a triangle that its three interior angles should not be equal to two right angles; or that from a given cause no effect should follow, which is absurd. SCHOLIUM: Alii putant Deum esse causam liberam propterea quod potest ut putant efficere ut ea quae ex ejus natura sequi diximus hoc est quae in ejus potestate sunt, non fiant sive ut ab ipso non producantur. Sed hoc idem est ac si dicerent quod Deus potest efficere ut ex natura trianguli non sequatur ejus tres angulos quales esse duobus rectis sive ut ex data causa non sequatur effectus, quod est absurdum.
Moreover, I will show below, without the aid of this proposition, that neither intellect nor will appertain to God's nature. I know that there are many who think that they can show, that supreme intellect and free will do appertain to God's nature; for they say they know of nothing more perfect, which they can attribute to God, than that which is the highest perfection in ourselves. Porro infra absque ope hujus propositionis ostendam ad Dei naturam neque intellectum neque voluntatem pertinere. Scio equidem plures esse qui putant se posse demonstrare ad Dei naturam summum intellectum et liberam voluntatem pertinere; nihil enim perfectius cognoscere sese aiunt quod Deo tribuere possunt quam id quod in nobis summa est perfectio.
Further, although they conceive God as actually supremely intelligent, they yet do not believe that he can bring into existence everything which he actually understands, for they think that they would thus destroy God's power. Porro tametsi Deum actu summe intelligentem concipiant, non tamen credunt eum posse omnia quae actu intelligit, efficere ut existant nam se eo modo Dei potentiam destruere putant.
If, they contend, God had created everything which is in his intellect, he would not be able to create anything more, and this, they think, would clash with God's omnipotence; Si omnia inquiunt quae in ejus intellectu sunt, creavisset, nihil tum amplius creare potuisset, quod credunt Dei omnipotenti repugnare
therefore, they prefer to assert that God is indifferent to all things, and that he creates nothing except that which he has decided, by some absolute exercise of will, to create. ideoque maluerunt Deum ad omnia indifferentem statuere nec aliud creantem praeter id quod absoluta quadam voluntate decrevit creare.
However, I think I have shown sufficiently clearly (by Prop. xvi.), that from God's supreme power, or infinite nature, an infinite number of things-that is, all things have necessarily flowed forth in an infinite number of ways, or always flow from the same necessity; in the same way as from the nature of a triangle it follows from eternity and for eternity, that its three interior angles are equal to two right angles. Verum ego me satis clare ostendisse puto (vide propositionem 16) a summa Dei potentia sive infinita natura infinita infinitis modis hoc est omnia necessario effluxisse vel semper eadem necessitate sequi eodem modo ac ex natura trianguli ab aeterno et in aeternum sequitur ejus tres angulos quari duobus rectis.
Wherefore the omnipotence of God has been displayed from all eternity, and will for all eternity remain in the same state of activity. Quare Dei omnipotentia actu ab aeterno fuit et in aeternum in eadem actualitate manebit.
This manner of treating the question attributes to God an omnipotence, in my opinion, far more perfect. Et hoc modo Dei omnipotentia longe meo quidem judicio perfectior statuitur. Imo adversarii Dei omnipotentiam (liceat aperte loqui) negare videntur.
For, otherwise, we are compelled to confess that God understands an infinite number of creatable things, which he will never be able to create, for, if he created all that he understands, he would, according to this showing, exhaust his omnipotence, and render himself imperfect. Coguntur enim fateri Deum infinita creabilia intelligere quae tamen nunquam creare poterit. Nam alias si scilicet omnia quae intelligit crearet, suam juxta ipsos exhauriret omnipotentiam et se imperfectum redderet.
Wherefore, in order to establish that God is perfect, we should be reduced to establishing at the same time, that he cannot bring to pass everything over which his power extends; this seems to be a hypothesis most absurd, and most repugnant to God's omnipotence. Ut igitur Deum perfectum statuant, eo rediguntur ut simul statuere debeant ipsum non posse omnia efficere ad quae ejus potentia se extendit, quo absurdius aut Dei omnipotenti magis repugnans non video quid fingi possit.
Further (to say a word here concerning the intellect and the will which we attribute to God), if intellect and will appertain to the eternal essence of God, we must take these words in some significance quite different from those they usually bear. Porro ut de intellectu et voluntate quos Deo communiter tribuimus, hic etiam aliquid dicam, si ad aeternam Dei essentiam intellectus scilicet et voluntas pertinent, aliud sane per utrumque hoc attributum intelligendum est quam quod vulgo solent homines.
For intellect and will, which should constitute the essence of God, would perforce be as far apart as the poles from the human intellect and will, in fact, would have nothing in com mon with them but the name; there would be about as much correspondence between the two as there is between the Dog, the heavenly constellation, and a dog, an animal that barks. Nam intellectus et voluntas qui Dei essentiam constituerent, a nostro intellectu et voluntate toto clo differre deberent nec in ulla re praeterquam in nomine convenire possent; non aliter scilicet quam inter se conveniunt canis, signum cleste et canis, animal latrans.
This I will prove as follows. If intellect belongs to the divine nature, it cannot be in nature, as ours is generally thought to be, posterior to, or simultaneous with the things understood, inasmuch as God is prior to all things by reason of his causality (Prop. xvi., Coroll. i.). Quod sic demonstrabo. Si intellectus ad divinam naturam pertinet, non poterit uti noster intellectus posterior (ut plerisque placet) vel simul natura esse cum rebus intellectis quandoquidem Deus omnibus rebus prior est causalitate (per corollarium I propositionis 16)
On the contrary, the truth and formal essence of things is as it is, because it exists by representation as such in the intellect of God. Wherefore the intellect of God, in so far as it is conceived to constitute God's essence, is, in reality, the cause of things, both of their essence and of their existence. sed contra veritas et formalis rerum essentia ideo talis est quia talis in Dei intellectu existit objective. Quare Dei intellectus quatenus Dei essentiam constituere concipitur, est revera causa rerum tam earum essentiae quam earum existenti,
This seems to have been recognized by those who have asserted, that God's intellect, God's will, and God's power, are one and the same. As, therefore, God's intellect is the sole cause of things, namely, both of their essence and existence, it must necessarily differ from them in respect to its essence, and in respect to its existence. For a cause differs from a thing it causes, precisely in the quality which the latter gains from the former. quod ab iis videtur etiam fuisse animadversum qui Dei intellectum, voluntatem et potentiam unum et idem esse asseruerunt. Cum itaque Dei intellectus sit unica rerum causa videlicet (ut ostendimus) tam earum essentiae quam earum existenti, debet ipse necessario ab iisdem differre tam ratione essentiae quam ratione existenti. Nam causatum differt a sua causa praecise in eo quod a causa habet.
For example, a man is the cause of another man's existence, but not of his essence (for the latter is an eternal truth), and, therefore, the two men may be entirely similar in essence, but must be different in existence; and hence if the existence of one of them cease, the existence of the other will not necessarily cease also; but if the essence of one could be destroyed, and be made false, the essence of the other would be destroyed also. Exempli gratia homo est causa existenti, non vero essentiae alterius hominis; est enim haec aeterna veritas et ideo secundum essentiam prorsus convenire possunt; in existendo autem differre debent et propterea si unius existentia pereat, non ideo alterius peribit sed si unius essentia destrui posset et fieri falsa, destrueretur etiam alterius essentia.
Wherefore, a thing which is the cause both of the essence and of the existence of a given effect, must differ from such effect both in respect to its essence, and also in respect to its existence. Quapropter res quae et essentiae et existenti alicujus effectus est causa, a tali effectu differre debet tam ratione essentiae quam ratione existenti.
Now the intellect of God is the cause both of the essence and the existence of our intellect; therefore, the intellect of God in so far as it is conceived to constitute the divine essence, differs from our intellect both in respect to essence and in respect to existence, nor can it in anywise agree therewith save in name, as we said before. The reasoning would be identical in the case of the will, as anyone can easily see. Atqui Dei intellectus est et essentiae et existenti nostri intellectus causa; ergo Dei intellectus quatenus divinam essentiam constituere concipitur, a nostro intellectu tam ratione essentiae quam ratione existenti differt nec in ulla re praeterquam in nomine cum eo convenire potest, ut volebamus. Circa voluntatem eodem modo proceditur, ut facile unusquisque videre potest.
1p18 Deus immanens transiens 1p18 Deus immanens transiens [geomap]
PROP. XVIII. God is the indwelling and not the transient cause of all things. PROPOSITIO XVIII: Deus est omnium rerum causa immanens, non vero transiens.
Proof.-All things which are, are in God, and must be conceived through God (by Prop. xv.), therefore (by Prop. xvi., Coroll. i.) God is the cause of those things which are in him. This is our first point. Further, besides God there can be no substance (by Prop. xiv.), that is nothing in itself external to God. This is our second point. God, therefore, is the indwelling and not the transient cause of all things. Q.E.D. DEMONSTRATIO: Omnia quae sunt, in Deo sunt et per Deum concipi debent (per propositionem 15 {1p15}) adeoque (per corollarium I propositionis 16 hujus {1p16c1}) Deus rerum quae in ipso sunt, est causa, quod est primum. Deinde extra Deum nulla potest dari substantia (per propositionem 14 {1p14}) hoc est (per definitionem 3 {1d03}) res quae extra Deum in se sit, quod erat secundum. Deus ergo est omnium rerum causa immanens, non vero transiens. Q.E.D.
1p19 Deus aeterna 1p19 Deus aeterna [geomap]
PROP. XIX. God, and all the attributes of God, are eternal. PROPOSITIO XIX: Deus sive [non-excl non-exh] omnia Dei attributa sunt aeterna.
Proof.-God (by Def. vi.) is substance, which (by Prop. xi.) necessarily exists, that is (by Prop. vii.) existence appertains to its nature, or (what is the same thing) follows from its definition; therefore, God is eternal (by Def. viii.). Further, by the attributes of God we must understand that which (by Def. iv.) expresses the essence of the divine substance-in other words, that which appertains to substance: that, I say, should be involved in the attributes of substance. Now eternity appertains to the nature of substance (as I have already shown in Prop. vii.); therefore, eternity must appertain to each of the attributes, and thus all are eternal. Q.E.D. DEMONSTRATIO: Deus enim (per definitionem 6 {1d06}) est [mng eqv] substantia quae (per propositionem 11 {1p11}) necessario existit hoc est [mng eqv] (per propositionem 7 {1p07}) ad cujus naturam pertinet existere sive [mng eqv] (quod idem est) ex cujus definitione sequitur ipsum existere adeoque [mng eqv] (per definitionem 8) est aeternus. Deinde per Dei attributa intelligendum est id quod (per definitionem 4 {1d04}) divinae  substantiae essentiam exprimit hoc est [mng eqv] id quod ad substantiam pertinet : id ipsum inquam ipsa attributa involvere debent. Atqui ad naturam  substantiae (ut jam ex propositione 7 demonstravi) pertinet aeternitas. Ergo unumquodque attributorum aeternitatem involvere debet adeoque omnia sunt aeterna. Q.E.D.
1p19s aliter (content of scholium is aliter) 1p19s aliter (content of scholium is aliter)
Note.-This proposition is also evident from the manner in which (in Prop. xi.) I demonstrated the existence of God; it is evident, I repeat, from that proof, that the existence of God, like his essence, is an eternal truth. Further (in Prop. xix. of my "Principles of the Cartesian Philosophy"), I have proved the eternity of God, in another manner, which I need not here repeat. SCHOLIUM: Haec propositio quam clarissime etiam patet ex modo quo (propositione 11) Dei existentiam demonstravi; ex ea inquam demonstratione constat Dei existentiam sicut ejus essentiam aeternam esse veritatem. Deinde (propositione 19 Principiorum Cartesii) alio etiam modo Dei aeternitatem demonstravi nec opus est eum hic repetere.
1p20 Deus existentia essentia idem 1p20 Deus existentia essentia idem [geomap]
PROP. XX. The existence of God and his essence are one and the same. PROPOSITIO XX: Dei existentia ejusque essentia unum et idem sunt.
Proof.-God (by the last Prop.) and all his attributes are eternal, that is (by Def. viii.) each of his attributes expresses existence. Therefore the same attributes of God which explain his eternal essence, explain at the same time his eternal existence-in other words, that which constitutes God's essence constitutes at the same time his existence. Wherefore God's existence and God's essence are one and the same. Q.E.D. DEMONSTRATIO: Deus (per antecedentem propositionem {1p19}) ejusque omnia attributa sunt aeterna hoc est (per definitionem 8 {1d08}) unumquodque ejus attributorum existentiam exprimit. Eadem ergo Dei attributa quae (per definitionem 4 {1d04}) Dei aeternam essentiam explicant, ejus simul aeternam existentiam explicant hoc est illud ipsum quod essentiam Dei constituit, constituit simul ipsius existentiam adeoque haec et ipsius essentia unum et idem sunt. Q.E.D.
1p20c1 aeternam veritatem 1p20c1 aeternam veritatem [geomap]
Coroll. I.-Hence it follows that God's existence, like his essence, is an eternal truth. COROLLARIUM {1p20} I: Hinc sequitur I. Dei existentiam sicut ejus essentiam aeternam esse veritatem.
1p20c2 immutabilia 1p20c2 immutabilia [geomap]
Coroll. II-Secondly, it follows that God, and all the attributes of God, are unchangeable. For if they could be changed in respect to existence, they must also be able to be changed in respect to essence-that is, obviously, be changed from true to false, which is absurd. COROLLARIUM {1p20} II: Sequitur II. Deum sive [non-excl exh] omnia Dei attributa esse immutabilia. Nam si ratione existenti mutarentur, deberent etiam (per propositionem praecedentem {1p18}) ratione essentiae mutari hoc est (ut per se notum) ex veris falsa fieri, quod est absurdum.
1p21 Omnia sequuntur infinita aeterna 1p21 Omnia sequuntur infinita aeterna [geomap]
PROP. XXI. All things which follow from the absolute nature of any attribute of God must always exist and be infinite, or, in other words, are eternal and infinite through the said attribute. PROPOSITIO XXI: Omnia quae ex absoluta natura alicujus attributi Dei sequuntur, semper et infinita existere debuerunt sive [mng eqv]  per idem attributum aeterna et infinita sunt.
Proof.-Conceive, if it be possible (supposing the proposition to be denied), that something in some attribute of God can follow from the absolute nature of the said attribute, and that at the same time it is finite, and has a conditioned existence or duration; for instance, the idea of God expressed in the attribute thought. Now thought, in so far as it is supposed to be an attribute of God, is necessarily (by Prop. xi.) in its nature infinite. DEMONSTRATIO: Concipe si fieri potest (siquidem neges) aliquid in aliquo Dei attributo ex ipsius absoluta natura sequi quod finitum sit et determinatam habeat existentiam sive [prf eqv]  durationem; exempli gratia ideam Dei in cogitatione. At cogitatio quandoquidem Dei attributum supponitur, est necessario (per propositionem 11 {1p11}) sua natura infinita.
But, in so far as it possesses the idea of God, it is supposed finite. It cannot, however, be conceived as finite, unless it be limited by thought (by Def. ii.); but it is not limited by thought itself, in so far as it has constituted the idea of God (for so far it is supposed to be finite); therefore, it is limited by thought, in so far as it has not constituted the idea of God, which nevertheless (by Prop. xi.) must necessarily exist. Verum quatenus ipsa ideam Dei habet, finita supponitur. At (per definitionem 2 {1d02}) finita concipi non potest nisi per ipsam cogitationem determinetur. Sed non per ipsam cogitationem quatenus ideam Dei constituit; eatenus enim finita supponitur esse : ergo per cogitationem quatenus ideam Dei non constituit, quae tamen (per propositionem 11) necessario existere debet.
We have now granted, therefore, thought not constituting the idea of God, and, accordingly, the idea of God does not naturally follow from its nature in so far as it is absolute thought (for it is conceived as constituting, and also as not constituting, the idea of God), which is against our hypothesis. Datur igitur cogitatio non constituens ideam Dei ac propterea ex ejus natura quatenus est absoluta cogitatio, non sequitur necessario idea Dei (concipitur enim ideam Dei constituens et non constituens). Quod est contra hypothesin.
Wherefore, if the idea of God expressed in the attribute thought, or, indeed, anything else in any attribute of God (for we may take any example, as the proof is of universal application) follows from the necessity of the absolute nature of the said attribute, the said thing must necessarily be infinite, which was our first point. Quare si idea Dei in cogitatione aut [excl exh] aliquid (perinde est quicquid sumatur quandoquidem demonstratio universalis est) in aliquo Dei attributo ex necessitate absolutae naturae ipsius attributi sequatur, id debet necessario esse infinitum; quod erat primum.
Furthermore, a thing which thus follows from the necessity of the nature of any attribute cannot have a limited duration. For if it can, suppose a thing, which follows from the necessity of the nature of some attribute, to exist in some attribute of God, for instance, the idea of God expressed in the attribute thought, and let it be supposed at some time not to have existed, or to be about not to exist. Deinde id quod ex necessitate naturae alicujus attributi ita sequitur, non potest determinatam habere existentiam sive [mng eqv]  durationem. Nam si neges, supponatur res quae ex necessitate naturae alicujus attributi sequitur, dari in aliquo Dei attributo exempli gratia idea Dei in cogitatione eaque supponatur aliquando non exstitisse vel [excl non-exh] non exstitura.
Now thought being an attribute of God, must necessarily exist unchanged (by Prop. xi., and Prop. xx., Coroll. ii.); and beyond the limits of the duration of the idea of God (supposing the latter at some time not to have existed, or not to be going to exist) thought would perforce have existed without the idea of God, which is contrary to our hypothesis, for we supposed that, thought being given, the idea of God necessarily flowed therefrom. Cum autem cogitatio Dei attributum supponatur, debet et necessario et immutabilis existere (per propositionem 11 et corollarium II propositionis 20 {1p20c2}). Quare ultra limites durationis ideae Dei (supponitur enim aliquando non exstitisse aut [excl non-exh] non exstitura) cogitatio sine idea Dei existere debebit; atqui hoc est contra hypothesin; supponitur enim ex data cogitatione necessario sequi ideam Dei.
Therefore the idea of God expressed in thought, or anything which necessarily follows from the absolute nature of some attribute of God, cannot have a limited duration, but through the said attribute is eternal, which is our second point. Bear in mind that the same proposition may be affirmed of anything, which in any attribute necessarily follows from God's absolute nature. Ergo idea Dei in cogitatione aut [excl non-exh] aliquid quod necessario ex absoluta natura alicujus attributi Dei sequitur, non potest determinatam habere durationem sed per idem attributum aeternum est, quod erat secundum. Nota hoc idem esse affirmandum de quacunque re quae in aliquo Dei attributo ex Dei absoluta natura necessario sequitur.
1p22 modificatione infinitum 1p22 modificatione infinitum [geomap]
PROP. XXII. Whatsoever follows from any attribute of God, in so far as it is modified into a modification which exists necessarily and as infinite through the said attribute, must also exist necessarily and as infinite. PROPOSITIO XXII: Quicquid ex aliquo Dei attributo quatenus modificatum est tali modificatione quae et necessario et infinita per idem existit, sequitur, debet quoque et necessario et infinitum existere.
Proof.-The proof of this proposition is similar to that of the preceding one.
DEMONSTRATIO: Hujus propositionis demonstratio procedit eodem modo ac demonstratio praecedentis. [, which used:  Concipe, ideam, cogitatione, {1p11}, {1d02}, Datur, {1p20c2}). B.H.]
1p23 modus infinitus absoluta 1p23 modus infinitus absoluta  [geomap]
PROP. XXIII. Every mode, which exists both necessarily and as infinite, must necessarily follow either from the absolute nature of some attribute of God, or from an attribute modified by a modification [Lat: modificatione] which exists necessarily, and as infinite. PROPOSITIO XXIII: Omnis modus qui et necessario et infinitus existit, necessario sequi debuit vel [excl non-exh] ex absoluta natura alicujus attributi Dei vel ex aliquo attributo modificato modificatione quae et necessario et infinita existit.
Proof.-A mode exists in something else, through which it must be conceived (Def. v.), that is (Prop. xv.), it exists solely in God, and solely through God can be conceived. If therefore a mode is conceived as necessarily existing and infinite, it must necessarily be inferred or perceived through some attribute of God, in so far as such attribute is conceived as expressing the infinity and necessity of existence, in other words (Def. viii.) eternity; that is, in so far as it is considered absolutely. A mode, therefore, which necessarily exists as infinite, must follow from the absolute nature of some attribute of God, either immediately (Prop. xxi.) or through the means of some modification [Lat: affectiones], which follows from the absolute nature of the said attribute; that is (by Prop. xxii.), which exists necessarily and as infinite. DEMONSTRATIO: Modus enim in alio est per quod concipi debet (per definitionem 5) {1d05} hoc est (per propositionem 15) {1p15} in solo Deo est et per solum Deum concipi potest. Si ergo modus concipitur necessario existere et infinitus esse, utrumque hoc debet necessario concludi sive [excl non-exh]  percipi per aliquod Dei attributum quatenus idem concipitur infinitatem et necessitatem existentiae sive [prf eqv] (quod per definitionem 8 idem est) aeternitatem exprimere hoc est (per definitionem 6 {1d06} et propositionem 19 {1p19}) quatenus absolute consideratur. Modus ergo qui et necessario et infinitus existit, ex absoluta natura alicujus Dei attributi sequi debuit hocque vel [excl exh] immediate (de quo vide propositionem 21 {1p21}) vel mediante aliqua modificatione quae ex ejus absoluta natura sequitur hoc est (per propositionem praecedentem) quae et necessario et infinita existit. Q.E.D.
1p24 Rerum essentia existentiam 1p24 Rerum essentia existentiam [geomap]
PROP. XXIV. The essence of things produced by God does not involve existence. PROPOSITIO XXIV: Rerum a Deo productarum essentia non involvit existentiam.
Proof.-This proposition is evident from Def. i. For that of which the nature (considered in itself) involves existence is self-caused, and exists by the sole necessity of its own nature. DEMONSTRATIO: Patet ex definitione 1 {1d01}. Id enim cujus natura (in se scilicet considerata) involvit existentiam, causa est sui et ex sola suae naturae necessitate existit.
1p24c deum causam perseverent 1p24c deum causam perseverent [geomap]
Corollary.-Hence it follows that God is not only the cause of things coming into existence, but also of their continuing in existence, that is, in scholastic phraseology, God is cause of the being of things (essendi rerum). For whether things exist, or do not exist, whenever we contemplate their essence, we see that it involves neither existence nor duration; consequently, it cannot be the cause of either the one or the other. God must be the sole cause, inasmuch as to him alone does existence appertain. (Prop. xiv. Coroll. i.) Q.E.D. COROLLARIUM: Hinc sequitur Deum non tantum esse causam ut res incipiant existere sed etiam ut in existendo perseverent sive [mng eqv] (ut termino scholastico utar) Deum esse causam essendi rerum. Nam sive [excl exh] res existant sive [excl exh] non existant, quotiescunque ad earum essentiam attendimus, eandem nec existentiam nec durationem involvere comperimus adeoque earum essentia neque suae existenti neque suae durationis potest esse causa sed tantum Deus ad cujus solam naturam pertinet existere (per corollarium I propositionis 14 {1p14c1}).
1p25 Deus causa essenti 1p25 Deus causa essenti [geomap]
PROP. XXV. God is the efficient cause not only of the existence of things, but also of their essence. PROPOSITIO XXV: Deus non tantum est causa efficiens rerum existentiae sed etiam essentiae.
Proof.-If this be denied, then God is not the cause of the essence of things; and therefore the essence of things can (by Ax. iv.) be conceived without God. This (by Prop. xv.) is absurd. Therefore, God is the cause of the essence of things. Q.E.D. DEMONSTRATIO: Si negas, ergo rerum essentiae Deus non est causa adeoque (per axioma 4 {1a04}) potest rerum essentia sine Deo concipi : atqui hoc (per propositionem 15 {1p15}) est absurdum. Ergo rerum etiam essentiae Deus est causa. Q.E.D.
1p25s aliter in scholio 1p25s aliter in scholio
Note.-This proposition follows more clearly from Prop. xvi. For it is evident thereby that, given the divine nature, the essence of things must be inferred from it, no less than their existence-in a word, God must be called the cause of all things, in the same sense as he is called the cause of himself. This will be made still clearer by the following corollary. SCHOLIUM: Haec propositio clarius sequitur ex propositione 16. Ex ea enim sequitur quod ex data natura divina tam rerum essentia quam existentia debeat necessario concludi et ut verbo dicam eo sen su quo Deus dicitur causa sui, etiam omnium rerum causa dicendus est, quod adhuc clarius ex sequenti corollario constabit.
1p25c res particulares attributorum affectiones 1p25c res particulares attributorum affectiones [geomap]
Corollary.-Individual things are nothing but modifications [Lat: affectiones] of the attributes of God, or modes by which the attributes of God are expressed in a fixed and definite manner. The proof appears from Prop. xv. and Def. v. COROLLARIUM: Res particulares nihil sunt nisi [mng eqv] Dei attributorum affectiones sive [mng eqv]  modi quibus Dei attributa certo et determinato modo exprimuntur. Demonstratio patet ex propositione 15 {1p15} et definitione 5 {1d05}.
1p26 non ipsam determinare 1p26 non ipsam determinare [geomap]
PROP. XXVI. A thing which is conditioned to operate in a particular manner, has necessarily been thus conditioned by God; and that which has not been conditioned by God cannot condition itself to operate. PROPOSITIO XXVI: Res quae ad aliquid operandum determinata est, a Deo necessario sic fuit determinata et quae a Deo non est determinata, non potest se ipsam ad operandum determinare.
Proof.-That by which things are said to be conditioned to operate in a particular manner is necessarily something positive (this is obvious); therefore both of its essence and of its existence God by the necessity of his nature is the efficient cause (Props. xxv. and xvi.); this is our first point. Our second point is plainly to be inferred therefrom. For if a thing, which has not been conditioned by God, could condition itself, the first part of our proof would be false, and this, as we have shown is absurd. DEMONSTRATIO: Id per quod res determinatae ad aliquid operandum dicuntur, necessario quid positivum est (ut per se notum). Adeoque tam ejus essentiae quam existenti Deus ex necessitate suae naturae est causa efficiens (per propositiones 25 {1p25}et 16 {1p16}) quod erat primum. Ex quo etiam quod secundo proponitur clarissime sequitur. Nam si res quae a Deo determinata non est, se ipsam determinare posset, prima pars hujus falsa esset, quod est absurdum, ut ostendimus.
1p27 non ipsam indeterminatam reddere 1p27 non ipsam indeterminatam reddere [geomap]
PROP. XXVII. A thing, which has been conditioned by God to operate in a particular way, cannot render itself unconditioned. PROPOSITIO XXVII: Res quae a Deo ad aliquid operandum determinata est, se ipsam indeterminatam reddere non potest.
Proof.-This proposition is evident from the third axiom. DEMONSTRATIO: Haec propositio patet ex axiomate tertio. {1a03}
1p28 nisi alia causa finita 1p28 nisi alia causa finita [geomap]
PROP. XXVIII. Every individual thing, or everything which is finite and has a conditioned existence, cannot exist or be conditioned to operate, unless it be conditioned for existence and operation by a cause other than itself, which also is finite, and has a conditioned existence; and likewise this cause cannot in its turn exist, or be conditioned to operate, unless it be conditioned for existence and operation by another cause, which also is finite, and has a conditioned existence, and so on to infinity. PROPOSITIO XXVIII: Quodcunque singulare sive [mng eqv] quaevis res quae finita est et determinatam habet existentiam, non potest existere nec ad operandum determinarinisi ad existendum et operandum determineturab alia causa quae etiam finita est et determinatam habet existentiam et rursus haec causa non potest etiam existere neque ad operandum determinarinisi ab alia quae etiam finita est et determinatam habet existentiam, determinetur ad existendum et operandumet sic in infinitum.
Proof.-Whatsoever is conditioned to exist and operate, has been thus conditioned by God (by Prop. xxvi. and Prop. xxiv., Coroll.).
But that which is finite, and has a conditioned existence, cannot be produced by the absolute nature of any attribute of God; for whatsoever follows from the absolute nature of any attribute of God is infinite and eternal (by Prop. xxi.). It must, therefore, follow from some attribute of God, in so far as the said attribute is considered as in some way modified; for substance and modes make up the sum total of existence (by Ax. i. and Def. iii., v.), while modes are merely modifications [Lat: affectiones] of the attributes of God. But from God, or from any of his attributes, in so far as the latter is modified by a modification [Lat: affectiones] infinite and eternal, a conditioned thing cannot follow.

Wherefore it must follow from, or be conditioned for, existence and operation by God or one of his attributes, in so far as the latter are modified by some modification which is finite, and has a conditioned existence. This is our first point. Again, this cause or this modification [Lat: affectiones] (for the reason by which we established the first part of this proof) must in its turn be conditioned by another cause, which also is finite, and has a conditioned existence, and, again, this last by another (for the same reason); and so on (for the same reason) to infinity. Q.E.D.
DEMONSTRATIO: Quicquid determinatum est ad existendum et operandum, a Deo sic determinatum est (per propositionem 26 {1p26} et corollarium propositionis 24 {1p24}). At id quod finitum est et determinatam habet existentiam, ab absoluta natura alicujus Dei attributi produci non potuit; quicquid enim ex absoluta natura alicujus Dei attributi sequitur, id infinitum et aeternum est (per propositionem 21 {1p21}). Debuit ergo ex Deo vel [excl exh] aliquo ejus attributo sequi quatenus aliquo modo affectum consideratur; praeter enim substantiam et modos nil datur (per axioma 1 {1a01} et definitionibus 3  {1d03} et 5 {1d05}) et modi (per corollarium propositionis 25 {1p25}) nihil sunt nisi Dei attributorum affectiones. At ex Deo vel [excl exh]aliquo ejus attributo quatenus affectum est modificatione quae aeterna et infinita est, sequi etiam non potuit (per propositionem 22  {1p22}). Debuit ergo sequi vel [mng eqv] ad existendum et operandum determinaria Deo vel  [excl exh] aliquo ejus attributo quatenus modificatum est modificatione quae finita est et determinatam habet existentiam. Quod erat primum. Deinde haec rursus causa sive [mng eqv] hic modus (per eandem rationem qua primam partem hujus jam jam demonstravimus) debuit etiam determinari ab alia quae etiam finita est et determinatam habet existentiam et rursus haec ultima (per eandem rationem) ab alia et sic semper (per eandem rationem) in infinitum. Q.E.D.
1p28s causa absolute proxima remota 1p28s causa absolute proxima remota
Note.-As certain things must be produced immediately by God, namely those things which necessarily follow from his absolute nature, through the means of these primary attributes, which, nevertheless, can neither exist nor be conceived without God, it follows:-1. That God is absolutely the proximate cause of those things immediately produced by him. I say absolutely, not after his kind, as is usually stated. For the effects of God cannot either exist or be conceived without a cause (Prop. xv. and Prop. xxiv. Coroll.). 2. That God cannot properly be styled the remote cause of individual things, except for the sake of distinguishing these from what he immediately produces, or rather from what follows from his absolute nature. For, by a remote cause, we understand a cause which is in no way conjoined to the effect. But all things which are, are in God, and so depend on God, that without him they can neither be nor be conceived. SCHOLIUM: Cum quaedam a Deo immediate produci debuerunt videlicet ea quae ex absoluta ejus natura necessario sequuntur et alia mediantibus his primis quae tamen sine Deo nec esse nec concipi possunt, hinc sequitur I. quod Deus sit rerum immediate ab ipso productarum causa absolute proxima, non vero in suo genere ut aiunt. Nam Dei effectus sine sua causa nec esse nec concipi possunt (per propositionem 15 et corollarium propositionis 24). Sequitur II. quod Deus non potest proprie dici causa esse remota rerum singularium nisi forte ea de causa ut scilicet has ab iis quas immediate produxit vel potius quae ex absoluta ejus natura sequuntur, distinguamus. Nam per causam remotam talem intelligimus quae cum effectu nullo modo conjuncta est. At omnia quae sunt in Deo sunt et a Deo ita dependent ut sine ipso nec esse nec concipi possint.
1p29 contingens necessitate 1p29 contingens necessitate [geomap]
PROP. XXIX. Nothing in the universe is contingent, but all things are conditioned to exist and operate in a particular manner by the necessity of the divine nature. PROPOSITIO XXIX: In rerum natura nullum datur contingens sed omnia ex necessitate divinae naturae determinata sunt ad certo modo existendum et operandum.
Proof.-Whatsoever is, is in God (Prop. xv.). But God cannot be called a thing contingent. For (by Prop. xi.) he exists necessarily, and not contingently. Further, the modes of the divine nature follow therefrom necessarily, and not contingently (Prop. xvi.); and they thus follow, whether we consider the divine nature absolutely, or whether we consider it as in any way conditioned to act (Prop. xxvii.). Further, God is not only the cause of these modes, in so far as they simply exist (by Prop. xxiv, Coroll.), but also in so far as they are considered as conditioned for operating in a particular manner (Prop. xxvi.). If they be not conditioned by God (Prop. xxvi.), it is impossible, and not contingent, that they should condition themselves; contrariwise, if they be conditioned by God, it is impossible, and not contingent, that they should render themselves unconditioned. Wherefore all things are conditioned by the necessity of the divine nature, not only to exist, but also to exist and operate in a particular manner, and there is nothing that is contingent. Q.E.D. DEMONSTRATIO: Quicquid est in Deo est (per propositionem 15 {1p15}) : Deus autem non potest dici res contingens. Nam (per propositionem 11 {1p11}) necessario, non vero contingenter existit. Modi deinde divinae naturae ex eadem etiam necessario, non vero contingenter secuti sunt (per propositionem 16  {1p16}) idque vel [excl exh] quatenus divina natura absolute (per propositionem 21 {1p21}) vel quatenus certo modo ad agendum determinata consideratur (per propositionem 27 {1p27}). Porro horum modorum Deus non tantum est causa quatenus simpliciter existunt (per corollarium propositionis 24 {1p24}) sed etiam (per propositionem 26 {1p26}) quatenus ad aliquid operandum  determinati considerantur. Quod si a Deo (per eandem propositionem) determinati non sint, impossibile, non vero contingens est ut se ipsos determinent et contra (per propositionem 27 {1p27}) si a Deo determinati sint, impossibile, non vero contingens est ut se ipsos indeterminatos reddant. Quare omnia ex necessitate divinae naturae determinata sunt, non tantum ad existendum sed etiam ad certo modo existendum et operandumnullumque datur contingens. Q.E.D.
1p29s natura naturans 1p29s natura naturans
Note.-Before going any further, I wish here to explain, what we should understand by nature viewed as active (natura naturans), and nature viewed as passive (natura naturata). I say to explain, or rather call attention to it, for I think that, from what has been said, it is sufficiently clear, that by nature viewed as active we should understand that which is in itself, and is conceived through itself, or those attributes of substance, which express eternal and infinite essence, in other words (Prop. xiv., Coroll. i., and Prop. xvii., Coroll. ii) God, in so far as he is considered as a free cause.
By nature viewed as passive I understand all that which follows from the necessity of the nature of God, or of any of the attributes of God, that is, all the modes of the attributes of God, in so far as they are considered as things which are in God, and which without God cannot exist or be conceived.
SCHOLIUM: Antequam ulterius pergam, hic quid nobis per Naturam naturantem et quid per Naturam naturatam intelligendum sit, explicare volo vel potius monere. Nam ex antecedentibus jam constare existimo nempe quod per Naturam naturantem nobis intelligendum est id quod in se est et per se concipitur sive talia  substantiae attributa quae aeternam et infinitam essentiam exprimunt hoc est (per corollarium I propositionis 14 et corollarium II propositionis 17) Deus quatenus ut causa libera consideratur. Per naturatam autem intelligo id omne quod ex necessitate Dei naturae sive uniuscujusque Dei attributorum sequitur hoc est omnes Dei attributorum modos quatenus considerantur ut res quae in Deo sunt et quae sine Deo nec esse nec concipi possunt.
1p30 Intellectus comprehendere 1p30 Intellectus comprehendere [geomap]
PROP. XXX. Intellect, in function (actu) finite, or in function infinite, must comprehend the attributes of God and the modifications [Lat: affectiones] of God, and nothing else. PROPOSITIO XXX: Intellectus actu finitus aut [excl exh] actu infinitus Dei attributa Deique affectiones comprehendere debet et nihil aliud.
Proof.-A true idea must agree with its object (Ax. vi.); in other words (obviously), that which is contained in the intellect in representation must necessarily be granted in nature. But in nature (by Prop. xiv., Coroll. i.) there is no substance save God, nor any modifications [Lat: affectiones] save those (Prop. xv.) which are in God, and cannot without God either be or be conceived. Therefore the intellect, in function finite, or in function infinite, must comprehend the attributes of God and the modifications [Lat: affectiones] of God, and nothing else. Q.E.D. DEMONSTRATIO: Idea vera debet convenire cum suo ideato (per axioma 6 {1p06}) hoc est (ut per se notum) id quod in intellectu objective continetur, debet necessario in natura dari. Atqui in natura (per corollarium I propositionis 14 {1p14}) non nisi una substantia datur nempe Deus nec ullae aliae affectiones (per propositionem 15 {1p15}) quam quae in Deo sunt et quae (per eandem propositionem) sine Deo nec esse nec concipi possunt; ergo intellectus actu finitus aut [excl exh] actu infinitus Dei attributa Deique affectiones comprehendere debet et nihil aliud. Q.E.D.
1p31 Intellectus naturatam naturantem 1p31 Intellectus naturatam naturantem [geomap]
PROP. XXXI. The intellect in function, whether finite or infinite, just like will, desire, love, &c., should be referred to passive nature and not to active nature. PROPOSITIO XXXI: Intellectus actu sive [excl exh] is finitus sit sive [excl exh] infinitus, ut et voluntas, cupiditas, amor etc. ad Naturam naturatam, non vero ad naturantem referri debent.
Proof.-By the intellect we (obviously) do not mean absolute thought, but only a certain mode of thinking, differing from other modes, such as love, desire, &c., and therefore (Def. v.) requiring to be conceived through absolute thought. It must (by Prop. xv. and Def. vi.), through some attribute of God which expresses the eternal and infinite essence of thought, be so conceived, that without such attribute it could neither be nor be conceived. It must therefore be referred to nature passive rather than to nature active, as must also the other modes of thinking. Q.E.D. DEMONSTRATIO: Per intellectum enim (ut per se notum) non intelligimus absolutam cogitationem sed certum tantum modum cogitandi, qui modus ab aliis scilicet cupiditate, amore, etc. differt adeoque (per definitionem 5 {1d05}) per absolutam cogitationem concipi debet nempe (per propositionem 15  {1p15} et definitionem 6 {1d06}) per aliquod Dei attributum quod aeternam et infinitam cogitationis essentiam exprimit, ita concipi debet ut sine ipso nec esse nec concipi possit ac propterea (per scholium propositionis 29 {no deductive reference}) ad Naturam naturatam, non vero naturantem referri debet ut etiam reliqui modi cogitandi. Q.E.D.
1p31s intellectu actu potentia 1p31s intellectu actu potentia
Note.-I do not here, by speaking of intellect in function, admit that there is such a thing as intellect in potentiality: but, wishing to avoid all confusion, I desire to speak only of what is most clearly perceived by us, namely, of the very act of understanding [Lat no actio but: "de ipsa scilicet intellectione " BH], than which nothing is more clearly perceived. For we cannot perceive anything without adding to our knowledge of the act of understanding. SCHOLIUM: Ratio cur hic loquar de intellectu actu non est quia concedo ullum dari intellectum potentia sed quia omnem confusionem vitare cupio, nolui loqui nisi de re nobis quam clarissime percepta, de ipsa scilicet intellectione qua nihil nobis clarius percipitur. Nihil enim intelligere possumus quod ad perfectiorem intellectionis cognitionem non conducat.
1p32 Voluntas causa necessaria 1p32 Voluntas causa necessaria [geomap]
PROP. XXXII. Will cannot be called a free cause, but only a necessary cause. PROPOSITIO XXXII: Voluntas non potest vocari causa libera sed tantum necessaria.
Proof.-Will is only a particular mode of thinking, like intellect; therefore (by Prop. xxviii.) no volition can exist, nor be conditioned to operate, unless it be conditioned by some cause other than itself, which cause is conditioned by a third cause, and so on to infinity. But if will be supposed infinite, it must also be conditioned to exist and act by God, not by virtue of his being substance absolutely infinite, but by virtue of his possessing an attribute which expresses the infinite and eternal essence of thought (by Prop. xxiii.). Thus, however it be conceived, whether as finite or infinite, it requires a cause by which it should be conditioned to exist and act. Thus (Def. vii.) it cannot be called a free cause, but only a necessary or constrained cause. Q.E.D. DEMONSTRATIO: Voluntas certus tantum cogitandi modus est sicuti intellectus adeoque (per propositionem 28 {1p28}) unaquque volitio non potest existere neque ad operandum determinarinisi ab alia causa determinetur et haec rursus ab alia et sic porro in infinitum. Quod si voluntas infinita supponatur, debet etiam ad existendum et operandum determinari a Deo, non quatenus substantia absolute infinita est sed quatenus attributum habet quod infinitam et aeternam cogitationis essentiam exprimit (per propositionem 23  {1p23}). Quocunque igitur modo sive [excl exh] finita sive [excl exh] infinita concipiatur, causam requirit a qua ad existendum et operandum determineturadeoque (per definitionem 7 {1d07}) non potest dici causa libera sed tantum necessaria vel [mng eqv] coacta. Q.E.D.
1p32c1 Deum non libertate voluntatis 1p32c1 Deum non libertate voluntatis [geomap]
Coroll. I.-Hence it follows, first, that God does not act according to freedom of the will. COROLLARIUM {1p32} I: Hinc sequitur I. Deum non operari ex libertate voluntatis.
1p32c2 voluntatem et intellectum omnia naturalia 1p32c2 voluntatem et intellectum omnia naturalia [geomap]
Coroll. II.-It follows, secondly, that will and intellect stand in the same relation to the nature of God as do motion, and rest, and absolutely all natural phenomena, which must be conditioned by God (Prop. xxix.) to exist and operate in a particular manner. For will, like the rest, stands in need of a cause, by which it is conditioned to exist and operate in a particular manner. And although, when will or intellect be granted, an infinite number of results may follow, yet God cannot on that account be said to act from freedom of the will, any more than the infinite number of results from motion and rest would justify us in saying that motion and rest act by free will. Wherefore will no more appertains to God than does anything else in nature, but stands in the same relation to him as motion, rest, and the like, which we have shown to follow from the necessity of the divine nature, and to be conditioned by it to exist and act in a particular manner. COROLLARIUM {1p32} II: Sequitur II. voluntatem et intellectum ad Dei naturam ita sese habere ut motus et quies et absolute ut omnia naturalia quae (per propositionem 29 {1p29}) a Deo ad existendum et operandum certo modo determinaridebent. Nam voluntas, ut reliqua omnia, causa indiget a qua ad existendum et operandum certo modo determinetur. Et quamvis ex data voluntate sive [prf eqv] vid. {2p49c}] intellectu infinita sequantur, non tamen propterea Deus magis dici potest ex libertate voluntatis agere quam propter ea quae ex motu et quiete sequuntur (infinita enim ex his etiam sequuntur) dici potest ex libertate motus et quietis agere. Quare voluntas ad Dei naturam non magis pertinet quam reliqua naturalia sed ad ipsam eodem modo sese habet ut motus et quies et omnia reliqua quae ostendimus ex necessitate divinae naturae sequi et ab eadem ad existendum et operandum certo modo determinari.
1p33 res Deo nullo alio modo produci potuerunt 1p33 res Deo nullo alio modo produci potuerunt [geomap]
PROP. XXXIII. Things could not have been brought into being by God in any manner or in any order different from that which has in fact obtained. PROPOSITIO XXXIII: Res nullo alio modo neque alio ordine a Deo produci potuerunt quam productae sunt.
Proof-All things necessarily follow from the nature of God (Prop. xvi.), and by the nature of God are conditioned to exist and operate in a particular way (Prop. xxix.). If things, therefore, could have been of a different nature, or have been conditioned to operate in a different way, so that the order of nature would have been different, God's nature would also have been able to be different from what it now is; and therefore (by Prop. xi.) that different nature also would have perforce existed, and consequently there would have been able to be two or more Gods. This (by Prop. xiv., Coroll. i.) is absurd. Therefore things could not have been brought into being by God in any other manner, &c. Q.E.D. DEMONSTRATIO: Res enim omnes ex data Dei natura necessario sequutae sunt (per propositionem 16 {1p16}) et ex necessitate naturae Dei determinatae sunt ad certo modo existendum et operandum (per propositionem 29 {1p29}). Si itaque res alterius naturae potuissent esse vel [mng eqv]  alio modo ad operandum determinari ut naturae ordo alius esset, ergo Dei etiam natura alia posset esse quam jam est ac proinde (per propositionem 11 {1p11}) illa etiam deberet existere et consequenter duo vel [excl non-exh] plures possent dari Dii, quod (per corollarium I propositionis 14  {1p14}) est absurdum. Quapropter res nullo alio modo neque alio ordine etc. Q.E.D.
1p33s1 contingentes 1p33s1 contingentes
Note I.-As I have thus shown, more clearly than the sun at noonday, that there is nothing to justify us in calling things contingent, I wish to explain briefly what meaning we shall attach to the word contingent; but I will first explain the words necessary and impossible.
A thing is called necessary either in respect to its essence or in respect to its cause; for the existence of a thing necessarily follows, either from its essence and definition, or from a given efficient cause. For similar reasons a thing is said to be impossible; namely, inasmuch as its essence or definition involves a contradiction, or because no external cause is granted, which is conditioned to produce such an effect; but a thing can in no respect be called contingent, save in relation to the imperfection of our knowledge.
A thing of which we do not know whether the essence does or does not involve a contradiction, or of which, knowing that it does not involve a contradiction, we are still in doubt concerning the existence, because the order of causes escapes us,-such a thing, I say, cannot appear to us either necessary or impossible. Wherefore we call it contingent or possible.
SCHOLIUM I: Quoniam his luce meridiana clarius ostendi nihil absolute in rebus dari propter quod contingentes dicantur, explicare jam paucis volo quid nobis per contingens erit intelligendum sed prius quid per necessarium et impossibile. Res aliqua necessaria dicitur vel ratione suae essentiae vel ratione causae. Rei enim alicujus existentia vel ex ipsius essentia et definitione vel ex data causa efficiente necessario sequitur. Deinde his etiam de causis res aliqua impossibilis dicitur; nimirum quia vel ipsius essentia seu definitio contradictionem involvit vel quia nulla causa externa datur ad talem rem producendam determinata. At res aliqua nulla alia de causa contingens dicitur nisi respectu defectus nostrae cognitionis. Res enim cujus essentiam contradictionem involvere ignoramus vel de qua probe scimus eandem nullam contradictionem involvere et tamen de ipsius existentia nihil certo affirmare possumus propterea quod ordo causarum nos latet, ea nunquam nec ut necessaria nec ut impossibilis videri nobis potest ideoque eandem vel contingentem vel possibilem vocamus.
1p33s2 perfectissima 1p33s2 perfectissima
Note II.-It clearly follows from what we have said, that things have been brought into being by God in the highest perfection, inasmuch as they have necessarily followed from a most perfect nature. Nor does this prove any imperfection in God, for it has compelled us to affirm his perfection. From its contrary proposition, we should clearly gather (as I have just shown), that God is not supremely perfect, for if things had been brought into being in any other way, we should have to assign to God a nature different from that, which we are bound to attribute to him from the consideration of an absolutely perfect being.
I do not doubt, that many will scout this idea as absurd, and will refuse to give their minds up to contemplating it, simply because they are accustomed to assign to God a freedom very different from that which we (Def. vii.) have deduced. They assign to him, in short, absolute free will. However, I am also convinced that if such persons reflect on the matter, and duly weigh in their minds our series of propositions, they will reject such freedom as they now attribute to God, not only as nugatory, but also as a great impediment to organized knowledge. There is no need for me to repeat what I have said in the note to Prop. xvii. But, for the sake of my opponents, I will show further, that although it be granted that will pertains to the essence of God, it nevertheless follows from his perfection, that things could not have been by him created other than they are, or in a different order; this is easily proved, if we reflect on what our opponents themselves concede, namely, that it depends solely on the decree and will of God, that each thing is what it is. If it were otherwise, God would not be the cause of all things. Further, that all the decrees of God have been ratified from all eternity by God himself. If it were otherwise, God would be convicted of imperfection or change. But in eternity there is no such thing as when, before, or after; hence it follows solely from the perfection of God, that God never can decree, or never could have decreed anything but what is; that God did not exist before his decrees, and would not exist without them. But, it is said, supposing that God had made a different universe, or had ordained other decrees from all eternity concerning nature and her order, we could not therefore conclude any imperfection in God. But persons who say this must admit that God can change his decrees. For if God had ordained any decrees concerning nature and her order, different from those which he has ordained-in other words, if he had willed and conceived something different concerning nature-he would perforce have had a different intellect from that which he has, and also a different will. But if it were allowable to assign to God a different intellect and a different will, without any change in his essence or his perfection, what would there be to prevent him changing the decrees which he has made concerning created things, and nevertheless remaining perfect? For his intellect and will concerning things created and their order are the same, in respect to his essence and perfection, however they be conceived.
Further, all the philosophers whom I have read admit that God's intellect is entirely actual, and not at all potential; as they also admit that God's intellect, and God's will, and God's essence are identical, it follows that, if God had had a different actual intellect and a different will, his essence would also have been different; and thus, as I concluded at first, if things had been brought into being by God in a different way from that which has obtained, God's intellect and will, that is (as is admitted) his essence would perforce have been different, which is absurd.
As these things could not have been brought into being by God in any but the actual way and order which has obtained; and as the truth of this proposition follows from the supreme perfection of God; we can have no sound reason for persuading ourselves to believe that God did not wish to create all the things which were in his intellect, and to create them in the same perfection as he had understood them.
But, it will be said, there is in things no perfection nor imperfection; that which is in them, and which causes them to be called perfect or imperfect, good or bad, depends solely on the will of God. If God had so willed, he might have brought it about that what is now perfection should be extreme imperfection, and vice versae. What is such an assertion, but an open declaration that God, who necessarily understands that which he wishes, might bring it about by his will, that he should understand things differently from the way in which he does understand them? This (as we have just shown) is the height of absurdity. Wherefore, I may turn the argument against its employers, as follows:-All things depend on the power of God. In order that things should be different from what they are, God's will would necessarily have to be different. But God's will cannot be different (as we have just most clearly demonstrated) from God's perfection. Therefore neither can things be different. I confess, that the theory which subjects all things to the will of an indifferent deity, and asserts that they are all dependent on his fiat, is less far from the truth than the theory of those, who maintain that God acts in all things with a view of promoting what is good. For these latter persons seem to set up something beyond God, which does not depend on God, but which God in acting looks to as an exemplar, or which he aims at as a definite goal. This is only another name for subjecting God to the dominion of destiny, an utter absurdity in respect to God, whom we have shown to be the first and only free cause of the essence of all things and also of their existence. I need, therefore, spend no time in refuting such wild theories.
SCHOLIUM II: Ex praecedentibus clare sequitur res summa perfectione a Deo fuisse productas quandoquidem ex data perfectissima natura necessario secut sunt. Neque hoc Deum ullius arguit imperfectionis; ipsius enim perfectio hoc nos affirmare coegit. Imo ex hujus contrario clare sequeretur (ut modo ostendi) Deum non esse summe perfectum; nimirum quia si res alio modo fuissent product, Deo alia natura esset tribuenda, diversa ab ea quam ex consideratione Entis perfectissimi coacti sumus ei tribuere. Verum non dubito quin multi hanc sententiam ut absurdam explodant nec animum ad eandem perpendendam instituere velint idque nulla alia de causa quam quia Deo aliam libertatem assueti sunt tribuere, longe diversam ab illa quae a nobis (definitione 7) tradita est videlicet absolutam voluntatem. Verum neque etiam dubito si rem meditari vellent nostrarumque demonstrationum seriem recte secum perpendere, quin tandem talem libertatem qualem jam Deo tribuunt, non tantum ut nugatoriam sed ut magnum scienti obstaculum plane rejiciant. Nec opus est ut ea quae in scholio propositionis 17 dicta sunt, hic repetam. Attamen in eorum gratiam adhuc ostendam quod quamvis concedatur voluntatem ad Dei essentiam pertinere, ex ejus perfectione nihilominus sequatur res nullo alio potuisse modo neque ordine a Deo creari; quod facile erit ostendere si prius consideremus id quod ipsimet concedunt videlicet ex solo Dei decreto et voluntate pendere ut unaquque res id quod est sit. Nam alias Deus omnium rerum causa non esset. Deinde quod omnia decreta ab aeterno ab ipso Deo sancita fuerunt. Nam alias imperfectionis et inconstanti argueretur. At cum in aeterno non detur quando, ante nec post, hinc ex sola scilicet Dei perfectione sequitur Deum aliud decernere nunquam posse nec unquam potuisse sive Deum ante sua decreta non fuisse nec sine ipsis esse posse. At dicent quod quamvis supponeretur quod Deus aliam rerum naturam fecisset vel quod ab aeterno aliud de natura ejusque ordine decrevisset, nulla inde in Deo sequeretur imperfectio. Verum si hoc dicant, concedent simul Deum posse sua mutare decreta. Nam si Deus de natura ejusque ordine aliud quam decrevit decrevisset hoc est ut aliud de natura voluisset et concepisset, alium necessario quam jam habet intellectum et aliam quam jam habet voluntatem habuisset. Et si Deo alium intellectum aliamque voluntatem tribuere licet absque ulla ejus essentiae ejusque perfectionis mutatione, quid causae est cur jam non possit sua de rebus creatis decreta mutare et nihilominus que perfectus manere? Ejus enim intellectus et voluntas circa res creatas et earum ordinem in respectu suae essentiae et perfectionis perinde est, quomodocunque concipiatur. Deinde omnes quos vidi philosophi concedunt nullum in Deo dari intellectum potentia sed tantum actu; cum autem et ejus intellectus et ejus voluntas ab ejusdem essentia non distinguantur ut etiam omnes concedunt, sequitur ergo hinc etiam quod si Deus alium intellectum actu habuisset et aliam voluntatem, ejus etiam essentia alia necessario esset ac proinde (ut a principio conclusi) si aliter res quam jam sunt, a Deo product essent, Dei intellectus ejusque voluntas hoc est (ut conceditur) ejus essentia alia esse deberet, quod est absurdum.
Cum itaque res nullo alio modo nec ordine a Deo produci potuerint et hoc verum esse ex summa Dei perfectione sequatur, nulla profecto sana ratio persuadere nobis potest ut credamus quod Deus noluerit omnia quae in suo intellectu sunt, eadem illa perfectione qua ipsa intelligit, creare. At dicent in rebus nullam esse perfectionem neque imperfectionem sed id quod in ipsis est propter quod perfect sunt aut imperfectae et bonae aut malae dicuntur, a Dei tantum voluntate pendere atque adeo si Deus voluisset, potuisset efficere ut id quod jam perfectio est, summa esset imperfectio et contra. Verum quid hoc aliud esset quam aperte affirmare quod Deus qui id quod vult necessario intelligit, sua voluntate efficere potest ut res alio modo quam intelligit, intelligat, quod (ut modo ostendi) magnum est absurdum. Quare argumentum in ipsos retorquere possum hoc modo. Omnia a Dei potestate pendent. Ut res itaque aliter se habere possint, Dei necessario voluntas aliter se habere etiam deberet; atqui Dei voluntas aliter se habere nequit (ut modo ex Dei perfectione evidentissime ostendimus). Ergo neque res aliter se habere possunt. Fateor hanc opinionem quae omnia indifferenti cuidam Dei voluntati subjicit et ab ipsius beneplacito omnia pendere statuit, minus a vero aberrare quam illorum qui statuunt Deum omnia sub ratione boni agere. Nam hi aliquid extra Deum videntur ponere quod a Deo non dependet, ad quod Deus tanquam ad exemplar in operando attendit vel ad quod tanquam ad certum scopum collineat. Quod profecto nihil aliud est quam Deum fato subjicere, quo nihil de Deo absurdius statui potest, quem ostendimus tam omnium rerum essentiae quam earum existenti primam et unicam liberam causam esse. Quare non est ut in hoc absurdo refutando tempus consumam.
1p34 Dei potentia essentia 1p34 Dei potentia essentia [geomap]
PROP. XXXIV. God's power is identical with his essence. PROPOSITIO XXXIV: Dei potentia est ipsa ipsius essentia.
Proof.-From the sole necessity of the essence of God it follows that God is the cause of himself (Prop. xi.) and of all things (Prop. xvi. and Coroll.). Wherefore the power of God, by which he and all things are and act, is identical with his essence. Q.E.D. DEMONSTRATIO: Ex sola enim necessitate Dei essentiae sequitur Deum esse causa sui (per propositionem 11 {1p11}) et (per propositionem 16  {1p16} ejusque corollarium  {1p16c1}) omnium rerum. Ergo potentia Dei qua ipse et omnia sunt et agunt, est ipsa ipsius essentia. Q.E.D.
1p35 Dei potestate esse existere 1p35 Dei potestate esse [geomap]
PROP. XXXV. Whatsoever we conceive to be in the power of God, necessarily exists. PROPOSITIO XXXV: Quicquid concipimus in Dei potestate esse, id necessario est.
Proof.-Whatsoever is in God's power, must (by the last Prop.) be comprehended in his essence in such a manner, that it necessarily follows therefrom, and therefore necessarily exists. Q.E.D. DEMONSTRATIO: Quicquid enim in Dei potestate est, id (per propositionem praecedentem {1p34}) in ejus essentia ita debet comprehendi ut ex ea necessario sequatur adeoque necessario est. Q.E.D.
1p36 de effectus 1p36 de effectus [geomap]
PROP. XXXVI. There is no cause from whose nature some effect does not follow. PROPOSITIO XXXVI: Nihil existit ex cujus natura aliquis effectus non sequatur.
Proof.-Whatsoever exists expresses God's nature or essence in a given conditioned manner (by Prop. xxv., Coroll.); that is, (by Prop. xxxiv.), whatsoever exists, expresses in a given conditioned manner God's power, which is the cause of all things, therefore an effect must (by Prop. xvi.) necessarily follow. Q.E.D. DEMONSTRATIO: Quicquid existit, Dei naturam sive [mng eqv] essentiam certo et determinato modo exprimit (per corollarium propositionis 25 {1p25}) hoc est (per propositionem 34 {1p34}) quicquid existit, Dei potentiam quae omnium rerum causa est, certo et determinato modo exprimit adeoque (per propositionem 16 {1p16}) ex eo aliquis effectus sequi debet. Q.E.D.
1apx 1apx
In the foregoing I have explained the nature and properties of God. I have shown that he necessarily exists, that he is one: that he is, and acts solely by the necessity of his own nature; that he is the free cause of all things, and how he is so; that all things are in God, and so depend on him, that without him they could neither exist nor be conceived; lastly, that all things are predetermined by God, not through his free will or absolute fiat, but from the very nature of God or infinite power. I have further, where occasion afforded, taken care to remove the prejudices, which might impede the comprehension of my demonstrations. Yet there still remain misconceptions not a few, which might and may prove very grave hindrances to the understanding of the concatenation of things, as I have explained it above. I have therefore thought it worth while to bring these misconceptions before the bar of reason.
All such opinions spring from the notion commonly entertained, that all things in nature act as men themselves act, namely, with an end in view. It is accepted as certain, that God himself directs all things to a definite goal (for it is said that God made all things for man, and man that he might worship him). I will, therefore, consider this opinion, asking first, why it obtains general credence, and why all men are naturally so prone to adopt it? secondly, I will point out its falsity; and, lastly, I will show how it has given rise to prejudices about good and bad, right and wrong, praise and blame, order and confusion, beauty and ugliness, and the like. However, this is not the place to deduce these misconceptions from the nature of the human mind: it will be sufficient here, if I assume as a starting point, what ought to be universally admitted, namely, that all men are born ignorant of the causes of things, that all have the desire to seek for what is useful to them, and that they are conscious of such desire. Herefrom it follows, first, that men think themselves free inasmuch as they are conscious of their volitions and desires, and never even dream, in their ignorance, of the causes which have disposed them so to wish and desire. Secondly, that men do all things for an end, namely, for that which is useful to them, and which they seek. Thus it comes to pass that they only look for a knowledge of the final causes of events, and when these are learned, they are content, as having no cause for further doubt. If they cannot learn such causes from external sources, they are compelled to turn to considering themselves, and reflecting what end would have induced them personally to bring about the given event, and thus they necessarily judge other natures by their own. Further, as they find in themselves and outside themselves many means which assist them not a little in the search for what is useful, for instance, eyes for seeing, teeth for chewing, herbs and animals for yielding food, the sun for giving light, the sea for breeding fish, &c., they come to look on the whole of nature as a means for obtaining such conveniences. Now as they are aware, that they found these conveniences and did not make them, they think they have cause for believing, that some other being has made them for their use. As they look upon things as means, they cannot believe them to be self-created; but, judging from the means which they are accustomed to prepare for themselves, they are bound to believe in some ruler or rulers of the universe endowed with human freedom, who have arranged and adapted everything for human use. They are bound to estimate the nature of such rulers (having no information on the subject) in accordance with their own nature, and therefore they assert that the gods ordained everything for the use of man, in order to bind man to themselves and obtain from him the highest honor. Hence also it follows, that everyone thought out for himself, according to his abilities, a different way of worshipping God, so that God might love him more than his fellows, and direct the whole course of nature for the satisfaction of his blind cupidity and insatiable avarice. Thus the prejudice developed into superstition, and took deep root in the human mind; and for this reason everyone strove most zealously to understand and explain the final causes of things; but in their endeavor to show that nature does nothing in vain, i.e. nothing which is useless to man, they only seem to have demonstrated that nature, the gods, and men are all mad together. Consider, I pray you, the result: among the many helps of nature they were bound to find some hindrances, such as storms, earthquakes, diseases, &c.: so they declared that such things happen, because the gods are angry at some wrong done to them by men, or at some fault committed in their worship. Experience day by day protested and showed by infinite examples, that good and evil fortunes fall to the lot of pious and impious alike; still they would not abandon their inveterate prejudice, for it was more easy for them to class such contradictions among other unknown things of whose use they were ignorant, and thus to retain their actual and innate condition of ignorance, than to destroy the whole fabric of their reasoning and start afresh. They therefore laid down as an axiom, that God's judgments far transcend human understanding. Such a doctrine might well have sufficed to conceal the truth from the human race for all eternity, if mathematics had not furnished another standard of verity in considering solely the essence and properties of figures without regard to their final causes. There are other reasons (which I need not mention here) besides mathematics, which might have caused men's minds to be directed to these general prejudices, and have led them to the knowledge of the truth.
I have now sufficiently explained my first point. There is no need to show at length, that nature has no particular goal in view, and that final causes are mere human figments. This, I think, is already evident enough, both from the causes and foundations on which I have shown such prejudice to be based, and also from Prop. xvi., and the Corollary of Prop. xxxii., and, in fact, all those propositions in which I have shown, that everything in nature proceeds from a sort of necessity, and with the utmost perfection. However, I will add a few remarks, in order to overthrow this doctrine of a final cause utterly. That which is really a cause it considers as an effect, and vice versae: it makes that which is by nature first to be last, and that which is highest and most perfect to be most imperfect. Passing over the questions of cause and priority as self-evident, it is plain from Props. xxi., xxii., xxiii. that the effect is most perfect which is produced immediately by God; the effect which requires for its production several intermediate causes is, in that respect, more imperfect. But if those things which were made immediately by God were made to enable him to attain his end, then the things which come after, for the sake of which the first were made, are necessarily the most excellent of all.
Further, this doctrine does away with the perfection of God: for, if God acts for an object, he necessarily desires something which he lacks. Certainly, theologians and metaphysicians draw a distinction between the object of want and the object of assimilation; still they confess that God made all things for the sake of himself, not for the sake of creation. They are unable to point to anything prior to creation, except God himself, as an object for which God should act, and are therefore driven to admit (as they clearly must), that God lacked those things for whose attainment he created means, and further that he desired them.
We must not omit to notice that the followers of this doctrine, anxious to display their talent in assigning final causes, have imported a new method of argument in proof of their theory-namely, a reduction, not to the impossible, but to ignorance; thus showing that they have no other method of exhibiting their doctrine. For example, if a stone falls from a roof on to someone's head, and kills him, they will demonstrate by their new method, that the stone fell in order to kill the man; for, if it had not by God's will fallen with that object, how could so many circumstances (and there are often many concurrent circumstances) have all happened together by chance? Perhaps you will answer that the event is due to the facts that the wind was blowing, and the man was walking that way. "But why," they will insist, "was the wind blowing, and why was the man at that very time walking that way?" If you again answer, that the wind had then sprung up because the sea had begun to be agitated the day before, the weather being previously calm, and that the man had been invited by a friend, they will again insist: "But why was the sea agitated, and why was the man invited at that time?" So they will pursue their questions from cause to cause, till at last you take refuge in the will of God-in other words, the sanctuary of ignorance. So, again, when they survey the frame of the human body, they are amazed; and being ignorant of the causes of so great a work of art, conclude that it has been fashioned, not mechanically, but by divine and supernatural skill, and has been so put together that one part shall not hurt another.
Hence anyone who seeks for the true causes of miracles, and strives to understand natural phenomena as an intelligent being, and not to gaze at them like a fool, is set down and denounced as an impious heretic by those, whom the masses adore as the interpreters of nature and the gods. Such persons know that, with the removal of ignorance, the wonder which forms their only available means for proving and preserving their authority would vanish also. But I now quit this subject, and pass on to my third point.
After men persuaded themselves, that everything which is created is created for their sake, they were bound to consider as the chief quality in everything that which is most useful to themselves, and to account those things the best of all which have the most beneficial effect on mankind. Further, they were bound to form abstract notions for the explanation of the nature of things, such as goodness, badness, order, confusion, warmth, cold, beauty, deformity, and so on; and from the belief that they are free agents arose the further notions of praise and blame, sin and merit.
I will speak of these latter hereafter, when I treat of human nature; the former I will briefly explain here.
Everything which conduces to health and the worship of God they have called good, everything which hinders these objects they have styled bad; and inasmuch as those who do not understand the nature of things do not verify phenomena in any way, but merely imagine them after a fashion, and mistake their imagination for understanding, such persons firmly believe that there is an order in things, being really ignorant both of things and their own nature. When phenomena are of such a kind, that the impression they make on our senses requires little effort of imagination, and can consequently be easily remembered, we say that they are well-ordered; if the contrary, that they are ill-ordered or confused. Further, as things which are easily imagined are more pleasing to us, men prefer order to confusion-as though there were any order in nature, except in relation to our imagination-and say that God has created all things in order; thus, without knowing it, attributing imagination to God, unless, indeed, they would have it that God foresaw human imagination, and arranged everything, so that it should be most easily imagined. If this be their theory, they would not, perhaps, be daunted by the fact that we find an infinite number of phenomena, far surpassing our imagination, and very many others which confound its weakness. But enough has been said on this subject. The other abstract notions are nothing but modes of imagining, in which the imagination is differently affected: though they are considered by the ignorant as the chief attributes of things, inasmuch as they believe that everything was created for the sake of themselves; and, according as they are affected by it, style it good or bad, healthy or rotten and corrupt. For instance, if the motion which objects we see communicate to our nerves be conducive to health, the objects causing it are styled beautiful; if a contrary motion be excited, they are styled ugly.
Things which are perceived through our sense of smell are styled fragrant or fetid; if through our taste, sweet or bitter, full-flavored or insipid; if through our touch, hard or soft, rough or smooth, &c.
Whatsoever affects our ears is said to give rise to noise, sound, or harmony. In this last case, there are men lunatic enough to believe, that even God himself takes pleasure in harmony; and philosophers are not lacking who have persuaded themselves, that the motion of the heavenly bodies gives rise to harmony-all of which instances sufficiently show that everyone judges of things according to the state of his brain, or rather mistakes for things the forms of his imagination. We need no longer wonder that there have arisen all the controversies we have witnessed, and finally skepticism: for, although human bodies in many respects agree, yet in very many others they differ; so that what seems good to one seems bad to another; what seems well ordered to one seems confused to another; what is pleasing to one displeases another, and so on. I need not further enumerate, because this is not the place to treat the subject at length, and also because the fact is sufficiently well known. It is commonly said: "So many men, so many minds; everyone is wise in his own way; brains differ as completely as palates." All of which proverbs show, that men judge of things according to their mental disposition, and rather imagine than understand: for, if they understood phenomena, they would, as mathematicians attest, be convinced, if not attracted, by what I have urged.
We have now perceived, that all the explanations commonly given of nature are mere modes of imagining, and do not indicate the true nature of anything, but only the constitution of the imagination; and, although they have names, as though they were entities, existing externally to the imagination, I call them entities imaginary rather than real; and, therefore, all arguments against us drawn from such abstractions are easily rebutted.
Many argue in this way. If all things follow from a necessity of the absolutely perfect nature of God, why are there so many imperfections in nature? such, for instance, as things corrupt to the point of putridity, loathsome deformity, confusion, evil, sin, &c. But these reasoners are, as I have said, easily confuted, for the perfection of things is to be reckoned only from their own nature and power; things are not more or less perfect, according as they delight or offend human senses, or according as they are serviceable or repugnant to mankind. To those who ask why God did not so create all men, that they should be governed only by reason, I give no answer but this: because matter was not lacking to him for the creation of every degree of perfection from highest to lowest; or, more strictly, because the laws of his nature are so vast, as to suffice for the production of everything conceivable by an infinite intelligence, as I have shown in Prop. xvi.
Such are the misconceptions I have undertaken to note; if there are any more of the same sort, everyone may easily dissipate them for himself with the aid of a little reflection.
APPENDIX: His Dei naturam ejusque proprietates explicui ut quod necessario existit; quod sit unicus; quod ex sola suae naturae necessitate sit et agat; quod sit omnium rerum causa libera et quomodo; quod omnia in Deo sint et ab ipso ita pendeant ut sine ipso nec esse nec concipi possint; et denique quod omnia a Deo fuerint prdeterminata, non quidem ex libertate voluntatis sive absoluto beneplacito sed ex absoluta Dei natura sive infinita potentia. Porro ubicunque data fuit occasio, praejudicia quae impedire poterant quominus me demonstrationes perciperentur, amovere curavi sed quia non pauca adhuc restant praejudicia quae etiam imo maxime impedire poterant et possunt quominus homines rerum concatenationem eo quo ipsam explicui modo, amplecti possint, eadem hic ad examen rationis vocare operae pretium duxi. Et quoniam omnia quae hic indicare suscipio praejudicia pendent ab hoc uno quod scilicet communiter supponant homines omnes res naturales ut ipsos propter finem agere, imo ipsum Deum omnia ad certum aliquem finem dirigere pro certo statuant : dicunt enim Deum omnia propter hominem fecisse, hominem autem ut ipsum coleret. Hoc igitur unum prius considerabo qurendo scilicet primo causam cur plerique hoc in praejudicio acquiescant et omnes natura adeo propensi sint ad idem amplectendum. Deinde ejusdem falsitatem ostendam et tandem quomodo ex hoc orta sint praejudicia de bono et malo, merito et peccato, laude et vituperio, ordine et confusione, pulchritudine et deformitate et de aliis hujus generis. Verum haec ab humanae mentis natura deducere non est hujus loci : satis hic erit si pro fundamento id capiam quod apud omnes debet esse in confesso nempe hoc quod omnes homines rerum causarum ignari nascuntur et quod omnes appetitum habent suum utile quaerendi, cujus rei sunt conscii. Ex his enim sequitur primo quod homines se liberos esse opinentur quandoquidem suarum volitionum suique appetitus sunt conscii et de causis a quibus disponuntur ad appetendum et volendum, quia earum sunt ignari nec per somnium cogitant. Sequitur secundo homines omnia propter finem agere videlicet propter utile quod appetunt; unde fit ut semper rerum peractarum causas finales tantum scire expetant et ubi ipsas audiverint, quiescant; nimirum quia nullam habent causam ulterius dubitandi. Sin autem easdem ex alio audire nequeant, nihil iis restat nisi ut ad semet se convertant et ad fines a quibus ipsi ad similia determinari solent, reflectant et sic ex suo ingenio ingenium alterius necessario judicant. Porro cum in se et extra se non pauca reperiant media quae ad suum utile assequendum non parum conducant ut exempli gratia oculos ad videndum, dentes ad masticandum, herbas et animantia ad alimentum, solem ad illuminandum, mare ad alendum pisces, hinc factum ut omnia naturalia tanquam ad suum utile media considerent et quia illa media ab ipsis inventa, non autem parata esse sciunt, hinc causam credendi habuerunt aliquem alium esse qui illa media in eorum usum paraverit. Nam postquam res ut media consideraverunt, credere non potuerunt easdem se ipsas fecisse sed ex mediis quae sibi ipsi parare solent, concludere debuerunt dari aliquem vel aliquos naturae rectores humana praeditos libertate qui ipsis omnia curaverint et in eorum usum omnia fecerint. Atque horum etiam ingenium quandoquidem de eo nunquam quid audiverant, ex suo judicare debuerunt atque hinc statuerunt Deos omnia in hominum usum dirigere ut homines sibi devinciant et in summo ab iisdem honore habeantur; unde factum ut unusquisque diversos Deum colendi modos ex suo ingenio excogitaverit ut Deus eos supra reliquos diligeret et totam naturam in usum cc illorum cupiditatis et insatiabilis avariti dirigeret. Atque ita hoc praejudicium in superstitionem versum et altas in mentibus egit radices; quod in causa fuit ut unusquisque maximo conatu omnium rerum causas finales intelligere easque explicare studeret. Sed dum qusiverunt ostendere naturam nihil frustra (hoc est quod in usum hominum non sit) agere, nihil aliud videntur ostendisse quam naturam Deosque que ac homines delirare. Vide quso quo res tandem evasit! Inter tot naturae commoda non pauca reperire debuerunt incommoda, tempestates scilicet, terr motus, morbos etc. atque haec statuerunt propterea evenire quod Dii irati essent ob injurias sibi ab hominibus factas sive ob peccata in suo cultu commissa et quamvis experientia indies reclamaret ac infinitis exemplis ostenderet commoda atque incommoda piis que ac impiis promiscue evenire, non ideo ab inveterato praejudicio destiterunt : facilius enim iis fuit hoc inter alia incognita quorum usum ignorabant, ponere et sic praesentem suum et innatum statum ignoranti retinere quam totam illam fabricam destruere et novam excogitare. Unde pro certo statuerunt Deorum judicia humanum captum longissime superare : quae sane unica fuisset causa ut veritas humanum genus in aeternum lateret nisi mathesis, quae non circa fines sed tantum circa figurarum essentias et proprietates versatur, aliam veritatis normam hominibus ostendisset et praeter mathesin ali etiam adsignari possunt causae (quas hic enumerare supervacaneum est) a quibus fieri potuit ut homines communia haec praejudicia animadverterent et in veram rerum cognitionem ducerentur.
His satis explicui id quod primo loco promisi. Ut jam autem ostendam naturam finem nullum sibi praefixum habere et omnes causas finales nihil nisi humana esse figmenta, non opus est multis. Credo enim id jam satis constare tam ex fundamentis et causis unde hoc praejudicium originem suam traxisse ostendi quam ex propositione 16 et corollariis propositionis 32 et praeterea ex iis omnibus quibus ostendi omnia naturae aeterna quadam necessitate summaque perfectione procedere. Hoc tamen adhuc addam nempe hanc de fine doctrinam naturam omnino evertere. Nam id quod revera causa est, ut effectum considerat et contra. Deinde id quod natura prius est, facit posterius. Et denique id quod supremum et perfectissimum est, reddit imperfectissimum. Nam (duobus prioribus omissis quia per se manifesta sunt) ut ex propositionibus 21, 22 et 23 constat, ille effectus perfectissimus est qui a Deo immediate producitur et quo aliquid pluribus causis intermediis indiget ut producatur, eo imperfectius est. At si res quae immediate a Deo product sunt, ea de causa fact essent ut Deus finem assequeretur suum, tum necessario ultim quarum de causa priores fact sunt, omnium praestantissimae essent. Deinde haec doctrina Dei perfectionem tollit nam si Deus propter finem agit, aliquid necessario appetit quo caret. Et quamvis theologi et metaphysici distinguant inter finem indigenti et finem assimilationis, fatentur tamen Deum omnia propter se, non vero propter res creandas egisse quia nihil ante creationem praeter Deum assignare possunt propter quod Deus ageret adeoque necessario fateri coguntur Deum iis propter quae media parare voluit, caruisse eaque cupivisse, ut per se clarum. Nec hic praetereundum est quod hujus doctrin sectatores qui in assignandis rerum finibus suum ingenium ostentare voluerunt, ad hanc suam doctrinam probandam novum attulerunt modum argumentandi reducendo scilicet non ad impossibile sed ad ignorantiam, quod ostendit nullum aliud fuisse huic doctrin argumentandi medium. Nam si exempli gratia ex culmine aliquo lapis in alicujus caput ceciderit eumque interfecerit, hoc modo demonstrabunt lapidem ad hominem interficiendum cecidisse. Ni enim eum in finem Deo id volente ceciderit, quomodo tot circumstanti (spe enim mult simul concurrunt) ca su concurrere potuerunt? Respondebis fortasse id ex eo quod ventus flavit et quod homo illac iter habebat, evenisse. At instabunt, cur ventus illo tempore flavit? Cur homo illo eodemque tempore illac iter habebat? Si iterum respondeas ventum tum ortum quia mare praecedenti die tempore adhuc tranquillo agitari inceperat et quod homo ab amico invitatus fuerat, instabunt iterum quia nullus rogandi finis, cur autem mare agitabatur? cur homo in illud tempus invitatus fuit? et sic porro causarum causas rogare non cessabunt donec ad Dei voluntatem hoc est ignoranti asylum confugeris. Sic etiam ubi corporis humani fabricam vident, stupescunt et ex eo quod tant artis causas ignorant, concludunt eandem non mechanica sed divina vel supernaturali arte fabricari talique modo constitui ut una pars alteram non ldat. Atque hinc fit ut qui miraculorum causas veras qurit quique res naturales ut doctus intelligere, non autem ut stultus admirari studet, passim pro hretico et impio habeatur et proclametur ab iis quos vulgus tanquam naturae Deorumque interpretes adorat. Nam sciunt quod sublata ignorantia stupor hoc est unicum argumentandi tuendque suae auctoritatis medium quod habent, tollitur. Sed haec relinquo et ad id quod tertio loco hic agere constitui, pergo.
Postquam homines sibi persuaserunt omnia quae fiunt propter ipsos fieri, id in unaquaque re praecipuum judicare debuerunt quod ipsis utilissimum et illa omnia praestantissima stimare a quibus optime afficiebantur. Unde has formare debuerunt notiones quibus rerum naturas explicarent scilicet bonum, malum, ordinem, confusionem, calidum, frigidum, pulchritudinem et deformitatem et quia se liberos existimant, inde hae notiones ortae sunt scilicet laus et vituperium, peccatum et meritum sed has infra postquam de natura humana egero, illas autem hic breviter explicabo. Nempe id omne quod ad valetudinem et Dei cultum conducit, bonum, quod autem iis contrarium est, malum vocaverunt. Et quia ii qui rerum naturam non intelligunt sed res tantummodo imaginantur, nihil de rebus affirmant et imaginationem pro intellectu capiunt, ideo ordinem in rebus esse firmiter credunt rerum suque naturae ignari. Nam cum ita sint disposit ut cum nobis per sensus repraesentantur, eas facile imaginari et consequenter earum facile recordari possimus, easdem bene ordinatas, si vero contra, ipsas male ordinatas sive confusas esse dicimus. Et quoniam ea nobis prae caeteris grata sunt quae facile imaginari possumus, ideo homines ordinem confusioni praeferunt quasi ordo aliquid in natura praeter respectum ad nostram imaginationem esset; dicuntque Deum omnia ordine creasse et hoc modo ipsi nescientes Deo imaginationem tribuunt nisi velint forte Deum humanae imaginationi providentem res omnes eo disposuisse modo quo ipsas facillime imaginari possent; nec moram forsan iis injiciet quod infinita reperiantur quae nostram imaginationem longe superant et plurima quae ipsam propter ejus imbecillitatem confundunt. Sed de hac re satis. Caeter deinde notiones etiam praeter imaginandi modos quibus imaginatio diversimode afficitur, nihil sunt et tamen ab ignaris tanquam praecipua rerum attributa considerantur quia ut jam diximus, res omnes propter ipsos factas esse credunt et rei alicujus naturam bonam vel malam, sanam vel putridam et corruptam dicunt prout ab eadem afficiuntur. Exempli gratia si motus quem nervi ab objectis per oculos repraesentatis accipiunt, valetudini conducat, objecta a quibus causatur pulchra dicuntur, quae autem contrarium motum cient, deformia. quae deinde per nares sensum movent, odorifera vel ftida vocant, quae per linguam, dulcia aut amara, sapida aut insipida etc. quae autem per tactum, dura aut mollia, aspera aut lvia etc. Et quae denique aures movent, strepitum, sonum vel harmoniam edere dicuntur quorum postremum homines adeo dementavit ut Deum etiam harmonia delectari crederent. Nec desunt philosophi qui sibi persuaserint motus clestes harmoniam componere. quae omnia satis ostendunt unumquemque pro dispositione cerebri de rebus judicasse vel potius imaginationis affectiones pro rebus accepisse. Quare non mirum est (ut hoc etiam obiter notemus) quod inter homines tot quot experimur, controversi ort sint ex quibus tandem scepticismus. Nam quamvis humana corpora in multis conveniant, in plurimis tamen discrepant et ideo id quod uni bonum, alteri malum videtur; quod uni ordinatum, alteri confusum; quod uni gratum, alteri ingratum est et sic de caeteris quibus hic supersedeo cum quia hujus loci non est de his ex professo agere, tum quia hoc omnes satis experti sunt. Omnibus enim in ore est "quot capita tot sensus", "suo quemque sen su abundare", "non minora cerebrorum quam palatorum esse discrimina" : quae sententi satis ostendunt homines pro dispositione cerebri de rebus judicare resque potius imaginari quam intelligere. Res enim si intellexissent, illae omnes teste mathesi, si non allicerent, ad minimum convincerent.
Videmus itaque omnes notiones quibus vulgus solet naturam explicare, modos esse tantummodo imaginandi nec ullius rei naturam sed tantum imaginationis constitutionem indicare et quia nomina habent, quasi essent entium extra imaginationem existentium, eadem entia non rationis sed imaginationis voco atque adeo omnia argumenta quae contra nos ex similibus notionibus petuntur, facile propulsari possunt. Solent enim multi sic argumentari. Si omnia ex necessitate perfectissim Dei naturae sunt consecuta, unde ergo tot imperfectiones in natura ort? Videlicet rerum corruptio ad ftorem usque, rerum deformitas quae nauseam moveat, confusio, malum, peccatum etc. Sed ut modo dixi, facile confutantur. Nam rerum perfectio ex sola earum natura et potentia est stimanda nec ideo res magis aut minus perfect sunt propterea quod hominum sensum delectant vel offendunt, quod humanae naturae conducunt vel quod eidem repugnant. Iis autem qui qurunt cur Deus omnes homines non ita creavit ut solo rationis ductu gubernarentur? nihil aliud respondeo quam quia ei non defuit materia ad omnia ex summo nimirum ad infimum perfectionis gradum creanda vel magis proprie loquendo quia ipsius naturae leges adeo ampl fuerunt ut sufficerent ad omnia quae ab aliquo infinito intellectu concipi possunt producenda, ut propositione 16 demonstravi.
Haec sunt quae hic notare suscepi praejudicia. Si quaedam hujus farin adhuc restant, poterunt eadem ab unoquoque mediocri meditatione emendari.
Finis partis prim.
2praef NATURA ORIGINE MENTIS 2praef NATURA ORIGINE MENTIS
PART II. ON THE NATURE AND ORIGIN OF THE MIND SPINOZAE ETHICA ORDINE GEOMETRICO DEMONSTRATA ET IN QUINQUE PARTES DISTINCTA PARS  SECUNDA  DE NATURA ET ORIGINE MENTIS 
PREFACE
I now pass on to explaining the results, which must necessarily follow from the essence of God, or of the eternal and infinite being; not, indeed, all of them (for we proved in Part i., Prop. xvi., that an infinite number must follow in an infinite number of ways), but only those which are able to lead us, as it were by the hand, to the knowledge of the human mind and its highest blessedness. Transeo jam ad ea explicanda quae ex Dei sive Entis aeterni et infiniti essentia necessario debuerunt sequi. Non quidem omnia; infinita enim infinitis modis ex ipsa debere sequi propositione 16 partis I demonstravimus sed ea solummodo quae nos ad mentis humanae ejusque summ beatitudinis cognitionem quasi manu ducere possunt.
DEFINITIONS DEFINITIONES [about definitions]
2d01 corpus 2d01 corpus [notes] [geomap]
DEFINITION I. By body I mean a mode which expresses in a certain determinate manner the essence of God, in so far as he is considered as an extended thing. (See Pt. i., Prop. xxv., Coroll.) I. Per corpus intelligo  modum qui Dei essentiam quatenus ut res extensa consideratur, certo et determinato modo exprimit; vide corollarium propositionis 25 partis I.{non-deductive reference}
2d02 essentia 2d02 essentia [notes] [geomap]
DEFINITION II. I consider as belonging to the essence of a thing that, which being given, the thing is necessarily given also, and, which being removed, the thing is necessarily removed also; in other words, that without which the thing, and which itself without the thing, can neither be nor be conceived. II. Ad essentiam alicujus rei id pertinere dico quo dato res necessario ponitur et quo sublato res necessario tollitur; vel [mng eqv] id sine quo res et vice versa id quod sine re nec esse nec concipi potest.
2d03 idea 2d03 idea [notes] [geomap]
DEFINITION III. By idea, I mean the mental conception which is formed by the mind as a thinking thing. III. Per ideam intelligo mentis conceptum quem mens format propterea quod res est cogitans.
Explanation.-I say conception rather than perception, because the word perception seems to imply that the mind is passive in respect to the object; whereas conception seems to express an activity of the mind. EXPLICATIO: Dico potius conceptum quam perceptionem quia perceptionis nomen indicare videtur mentem ab objecto pati. At conceptus actionem mentis exprimere videtur.
2d04 idea (cognitia) adaequata 2d04 idea (cognitia) adaequata [notes] [geomap]
DEFINITION IV. By an adequate idea, I mean an idea which, in so far as it is considered in itself, without relation to the object, has all the properties or intrinsic marks of a true idea. IV. Per ideam adaequatam intelligo ideam quae quatenus in se sine relatione ad objectum consideratur, omnes verae ideae proprietates sive [mng eqv]  denominationes intrinsecas habet.
Explanation.-I say intrinsic, in order to exclude that mark which is extrinsic, namely, the agreement between the idea and its object (ideatum). EXPLICATIO: Dico intrinsecas ut illam secludam quae extrinseca est nempe convenientiam ideae cum suo ideato.
2d05 duratio 2d05 duratio [notes] [geomap]
DEFINITION V. Duration is the indefinite continuance of existing. V. Duratio est indefinita existendi continuatio.
Explanation.-I say indefinite, because it cannot be determined through the existence itself of the existing thing, or by its efficient cause, which necessarily gives the existence of the thing, but does not take it away. EXPLICATIO: Dico indefinitam quia per ipsam rei existentis naturam determinari nequaquam potest neque etiam a causa efficiente quae scilicet rei existentiam necessario ponit, non autem tollit.
2d06 perfectio 2d06 perfectio [notes] [geomap]
DEFINITION VI. Reality and perfection I use as synonymous terms. VI. Per realitatem et perfectionem idem intelligo.
2d07 (res) singularis, particularis 2d07 (res) singularis, particularis [notes] [geomap]
DEFINITION VII. By particular things, I mean things which are finite and have a conditioned existence; but if several individual things concur in one action, so as to be all simultaneously the effect of one cause, I consider them all, so far, as one particular thing. VII. Per res singulares intelligo res quae finitae sunt et determinatam habent existentiam. Quod si plura individua in una actione ita concurrant ut omnia simul unius effectus sint causa, eadem omnia eatenus ut unam rem singularem considero.
AXIOMS AXIOMATA
2a1.1 Hominis essentia non involvit existentiam 2a1.1 Hominis essentia non involvit existentiam [geomap]
I. The essence of man does not involve necessary existence, that is, it may, in the order of nature, come to pass that this or that man does or does not exist. I. Hominis essentia non involvit necessariam existentiam hoc est [mng-eqv] ex naturae ordine tam fieri potest ut hic et ille homo existat quam ut non existat.
2a1.2 Homo cogitat 2a1.2 Homo cogitat [geomap]
II. Man thinks. II. Homo cogitat.
2a1.3 Modi cogitandi idea rei 2a1.3 Modi cogitandi idea rei [geomap]
III. Modes of thinking, such as love, desire, or any other of the passions, do not take place, unless there be in the same individual an idea of the thing loved, desired, &c. But the idea can exist without the presence of any other mode of thinking. III. Modi cogitandi ut amor, cupiditas vel [excl non-exh] quicunque nomine affectus animi insigniuntur, non dantur nisi in eodem individuo detur idea rei amat, desiderat etc. At idea dari potest quamvis nullus alius detur cogitandi modus.
2a1.4 affici sentimus 2a1.4 affici sentimus [geomap]
IV. We perceive that our body is affected in many ways. IV. Nos corpus quoddam multis modis affici sentimus.
2a1.5 sentimus corpora cogitandi modos 2a1.5 sentimus corpora cogitandi modos [geomap]
V. We feel and perceive no particular things, save bodies and modes of thought. N.B. The Postulates are given after the conclusion of Prop. xiii. V. Nullas res singulares praeter corpora et cogitandi  modos sentimus nec percipimus. Postulata vide post 13 propositionem {non-deductive reference}.
PROPOSITIONS PROPOSITIONES
2p01 Deus res cogitans 2p01 Deus res cogitans [geomap]
PROP. I. Thought is an attribute of God, or God is a thinking thing. PROPOSITIO I: Cogitatio attributum Dei est sive [mng eqv]  Deus est res cogitans.
Proof.-Particular thoughts, or this and that thought, are modes which, in a certain conditioned manner, express the nature of God (Pt. i., Prop. xxv., Coroll.). God therefore possesses the attribute (Pt. i., Def. v.) of which the concept is involved in all particular thoughts, which latter are conceived thereby. Thought, therefore, is one of the infinite attributes of God, which express God's eternal and infinite essence (Pt. i., Def. vi.). In other words, God is a thinking thing. Q.E.D. DEMONSTRATIO: Singulares cogitationes sive [mng eqv]  haec et illa cogitatio modi sunt qui Dei naturam certo et determinato modo exprimunt (per corollarium propositionis 25 partis I {1p25}). Competit ergo Deo (per definitionem 5 partis I {1d05}) attributum cujus conceptum singulares omnes cogitationes involvunt, per quod etiam concipiuntur. Est igitur cogitatio unum ex infinitis Dei attributis quod Dei aeternam et infinitam essentiam exprimit (vide definitionem 6 partis I {1d06}) sive [mng eqv]  Deus est res cogitans. Q.E.D.
2p01s possumus ens cogitans infinitum concipere 2p01s possumus ens cogitans infinitum concipere
Note.-This proposition is also evident from the fact, that we are able to conceive an infinite thinking being. For, in proportion as a thinking being is conceived as thinking more thoughts, so is it conceived as containing more reality or perfection. Therefore a being, which can think an infinite number of things in an infinite number of ways, is, necessarily, in respect of thinking, infinite. As, therefore, from the consideration of thought alone, we conceive an infinite being, thought is necessarily (Pt. i., Deff. iv. and vi.) one of the infinite attributes of God, as we were desirous of showing. SCHOLIUM: Patet etiam hic propositio ex hoc quod nos possumus ens cogitans infinitum concipere. Nam quo plura ens cogitans potest cogitare, eo plus realitatis sive perfectionis idem continere concipimus; ergo ens quod infinita infinitis modis cogitare potest, est necessario virtute cogitandi infinitum. Cum itaque ad solam cogitationem attendendo Ens infinitum concipiamus, est necessario (per definitiones 4 et 6 partis I) cogitatio unum ex infinitis Dei attributis, ut volebamus.
2p02 Deus res extensa 2p02 Deus res extensa [geomap]
PROP. II. Extension is an attribute of God, or God is an extended thing. PROPOSITIO II: Extensio attributum Dei est sive [mng eqv]  Deus est res extensa.
Proof.-The proof of this proposition is similar to that of the last. DEMONSTRATIO: Hujus eodem modo procedit ac demonstratio praecedentis propositionis. [using singulares modi naturam exprimunt {1p25}  {1d05} involvunt concipiuntur infinitis  aeternam essentiam {1d06}]
2p03 Deo sequuntur 2p03 Deo sequuntur [geomap]
PROP. III. In God there is necessarily the idea not only of his essence, but also of all things which necessarily follow from his essence. PROPOSITIO III: In Deo datur necessario idea tam ejus essentiae quam omnium quae ex ipsius essentia necessario sequuntur.
Proof.-God (by the first Prop. of this Part) can think an infinite number of things in infinite ways, or (what is the same thing, by Prop. xvi., Part i.) can form the idea of his essence, and of all things which necessarily follow therefrom. Now all that is in the power of God necessarily is (Pt. i., Prop. xxxv.). Therefore, such an idea as we are considering necessarily is, and in God alone. Q.E.D. (Part i., Prop. xv.) DEMONSTRATIO: Deus enim (per propositionem 1 hujus {2p01}) infinita infinitis modis cogitare sive [prf eqv]  (quod idem est per propositionem 16 partis I {1p16}) ideam suae essentiae et omnium quae necessario ex ea sequuntur, formare potest. Atqui omne id quod in Dei potestate est, necessario est (per propositionem 35 partis I {1p35}); ergo datur necessario talis idea et (per propositionem 15 partis I {1p15}) non nisi in Deo. Q.E.D.
2p03s Deus non rex 2p03s Deus non rex
Note.-The multitude understand by the power of God the free will of God, and the right over all things that exist, which latter are accordingly generally considered as contingent. For it is said that God has the power to destroy all things, and to reduce them to nothing. Further, the power of God is very often likened to the power of kings. But this doctrine we have refuted (Pt. i., Prop. xxxii., Corolls. i. and ii.), and we have shown (Part i., Prop. xvi.) that God acts by the same necessity, as that by which he understands himself; in other words, as it follows from the necessity of the divine nature (as all admit), that God understands himself, so also does it follow by the same necessity, that God performs infinite acts in infinite ways. We further showed (Part i., Prop. xxxiv.), that God's power is identical with God's essence in action; therefore it is as impossible for us to conceive God as not acting, as to conceive him as non-existent. If we might pursue the subject further, I could point out, that the power which is commonly attributed to God is not only human (as showing that God is conceived by the multitude as a man, or in the likeness of a man), but involves a negation of power. However, I am unwilling to go over the same ground so often. I would only beg the reader again and again, to turn over frequently in his mind what I have said in Part I from Prop. xvi. to the end. No one will be able to follow my meaning, unless he is scrupulously careful not to confound the power of God with the human power and right of kings. SCHOLIUM: Vulgus per Dei potentiam intelligit Dei liberam voluntatem et jus in omnia quae sunt quque propterea communiter ut contingentia considerantur. Deum enim potestatem omnia destruendi habere dicunt et in nihilum redigendi. Dei porro potentiam cum potentia regum spissime comparant. Sed hoc in corollario I et II propositionis 32 partis I refutavimus et propositione 16 partis I ostendimus Deum eadem necessitate agere qua seipsum intelligit hoc est sicuti ex necessitate divinae naturae sequitur (sicut omnes uno ore statuunt) ut Deus seipsum intelligat, eadem etiam necessitate sequitur ut Deus infinita infinitis modis agat. Deinde propositione 34 partis I ostendimus Dei potentiam nihil esse praeterquam Dei actuosam essentiam adeoque tam nobis impossibile est concipere Deum non agere quam Deum non esse. Porro si haec ulterius persequi liberet, possem hic etiam ostendere potentiam illam quam vulgus Deo affingit, non tantum humanam esse (quod ostendit Deum hominem vel instar hominis a vulgo concipi) sed etiam impotentiam involvere. Sed nolo de eadem re toties sermonem instituere. Lectorem solummodo iterum atque iterum rogo ut quae in prima parte ex propositione 16 usque ad finem de hac re dicta sunt, semel atque iterum perpendat. Nam nemo ea quae volo percipere recte poterit nisi magnopere caveat ne Dei potentiam cum humana regum potentia vel jure confundat.
2p04 Idea Dei unica 2p04 Idea Dei unica [geomap]
PROP. IV. The idea of God, from which an infinite number of things follow in infinite ways, can only be one. PROPOSITIO IV: Idea  Dei ex qua infinita infinitis modis sequuntur, unica tantum esse potest.
Proof.-Infinite intellect comprehends nothing save the attributes of God and his modifications [Lat: affectiones] (Part i., Prop. xxx.). Now God is one (Part i., Prop. xiv., Coroll.). Therefore the idea of God, wherefrom an infinite number of things follow in infinite ways, can only be one. Q.E.D. DEMONSTRATIO: Intellectus infinitus nihil praeter Dei attributa ejusque affectiones comprehendit (per propositionem 30 partis I {1p30}). Atqui Deus est unicus (per corollarium I propositionis 14 partis I {1p14}). Ergo idea Dei ex qua infinita infinitis modis sequuntur, unica tantum esse potest. Q.E.D.
2p05 Esse formale idearum 2p05 Esse formale idearum [geomap]
PROP. V. The actual being of ideas owns God as its cause, only in so far as he is considered as a thinking thing, not in so far as he is unfolded in any other attribute; that is, the ideas both of the attributes of God and of particular things do not own as their efficient cause their objects (ideata) or the things perceived, but God himself in so far as he is a thinking thing. PROPOSITIO V: Esse formale idearum Deum quatenus tantum ut res cogitans consideratur, pro causa agnoscit et non quatenus alio attributo explicatur. Hoc est tam Dei attributorum quam rerum singularium ideae non ipsa ideata sive [mng eqv]  res perceptas pro causa efficiente agnoscunt sed ipsum Deum quatenus est res cogitans.
Proof.-This proposition is evident from Prop. iii. of this Part. We there drew the conclusion, that God can form the idea of his essence, and of all things which follow necessarily therefrom, solely because he is a thinking thing, and not because he is the object of his own idea. Wherefore the actual being of ideas owns for cause God, in so far as he is a thinking thing. It may be differently proved as follows: the actual being of ideas is (obviously) a mode of thought, that is (Part i., Prop. xxv., Coroll.) a mode which expresses in a certain manner the nature of God, in so far as he is a thinking thing, and therefore (Part i., Prop. x.) involves the conception of no other attribute of God, and consequently (by Part i., Ax. iv.) is not the effect of any attribute save thought. Therefore the actual being of ideas owns God as its cause, in so far as he is considered as a thinking thing, &c. Q.E.D. DEMONSTRATIO: Patet quidem ex propositione 3 hujus  {2p03}. Ibi enim concludebamus Deum ideam suae essentiae et omnium quae ex ea necessario sequuntur, formare posse ex hoc solo nempe quod Deus est res cogitans et non ex eo quod sit suae ideae objectum. Quare esse formale idearum Deum quatenus est res cogitans, pro causa agnoscit. Sed aliter hoc modo demonstratur. Esse  formale idearum modus est cogitandi (ut per se notum) hoc est (per corollarium propositionis 25 partis I {1p25}) modus qui Dei naturam quatenus est res cogitans, certo modo exprimit adeoque (per propositionem 10 partis I {1p10}) nullius alterius attributi Dei conceptum involvit et consequenter (per axioma 4 partis I {1a04}) nullius alterius attributi nisi cogitationis est effectus adeoque Esse  formale idearum Deum quatenus tantum ut res cogitans consideratur etc. Q.E.D.
2p06 modi Deum causa attributo 2p06 modi Deum causa attributo [geomap]
PROP. VI. The modes of any given attribute are caused by God, in so far as he is considered through the attribute of which they are modes, and not in so far as he is considered through any other attribute. PROPOSITIO VI: Cujuscunque attributi  modi Deum quatenus tantum sub illo attributo cujus modi sunt et non quatenus sub ullo alio consideratur, pro causa habent.
Proof.-Each attribute is conceived through itself, without any other (Part i., Prop. x.); wherefore the modes of each attribute involve the conception of that attribute, but not of any other. Thus (Part i., Ax. iv.) they are caused by God, only in so far as he is considered through the attribute whose modes they are, and not in so far as he is considered through any other. Q.E.D. DEMONSTRATIO: Unumquodque enim attributum per se absque alio concipitur (per propositionem 10 partis I) {1p10}. Quare uniuscujusque attributi modi conceptum sui attributi, non autem alterius involvunt adeoque (per axioma 4 partis I) {1a04} Deum quatenus tantum sub illo attributo cujus modi sunt et non quatenus sub ullo alio consideratur, pro causa habent. Q.E.D.
2p06c res ideatae ex suis attributis 2p06c res ideatae ex suis attributis [geomap]
Corollary.-Hence the actual being of things which are not modes of thought, does not follow from the divine nature, because that nature has prior knowledge of the things. Things represented in ideas follow, and are derived from their particular attribute, in the same manner, and with the same necessity as ideas follow (according to what we have shown) from the attribute of thought. COROLLARIUM {2p06}: Hinc sequitur quod esse formale rerum quae modi non sunt cogitandi, non sequitur ideo ex divina natura quia res prius cognovit sed eodem modo eademque necessitate res ideatae ex suis attributis consequuntur et concluduntur ac ideas ex attributo cogitationis consequi ostendimus.
2p07 ordo et connexio 2p07 ordo et connexio [geomap]
PROP. VII. The order and connection of ideas is the same as the order and connection of things. PROPOSITIO VII: ordo et connexio idearum idem est ac ordo et connexio rerum.
Proof.-This proposition is evident from Part i., Ax. iv. For the idea of everything that is caused depends on a knowledge of the cause, whereof it is an effect. DEMONSTRATIO: Patet ex axiomate 4 partis I. {1a04} Nam cujuscunque causati idea a cognitione causae cujus est effectus, dependet.
2p07c formaliter objective 2p07c formaliter objective [geomap]
Corollary.-Hence God's power of thinking is equal to his realized power of action-that is, whatsoever follows from the infinite nature of God in the world of extension (formaliter), follows without exception in the same order and connection from the idea of God in the world of thought (objective). COROLLARIUM {2p07}: Hinc sequitur quod Dei cogitandi potentia qualis est ipsius actualiae agendi potentiae. Hoc est quicquid ex infinita Dei natura sequitur formaliter, id omne ex Dei idea eodem ordine eademque connexione sequitur in Deo objective.
2p07s substantia cogitans et substantia extensa una 2p07s substantia cogitans et substantia extensa una
Note.-Before going any further, I wish to recall to mind what has been pointed out above-namely, that whatsoever can be perceived by the infinite intellect as constituting the essence of substance, belongs altogether only to one substance: consequently, substance thinking and substance extended are one and the same substance, comprehended now through one attribute, now through the other. So, also, a mode of extension and the idea of that mode are one and the same thing, though expressed in two ways. This truth seems to have been dimly recognized by those Jews who maintained that God, God's intellect, and the things understood by God are identical. For instance, a circle existing in nature, and the idea of a circle existing, which is also in God, are one and the same thing displayed through different attributes. Thus, whether we conceive nature under the attribute of extension, or under the attribute of thought, or under any other attribute, we shall find the same order, or one and the same chain of causes-that is, the same things following in either case.
I said that God is the cause of an idea-for instance, of the idea of a circle,-in so far as he is a thinking thing; and of a circle, in so far as he is an extended thing, simply because the actual being of the idea of a circle can only be perceived as a proximate cause through another mode of thinking, and that again through another, and so on to infinity; so that, so long as we consider things as modes of thinking, we must explain the order of the whole of nature, or the whole chain of causes, through the attribute of thought only. And, in so far as we consider things as modes of extension, we must explain the order of the whole of nature through the attributes of extension only; and so on, in the case of the other attributes. Wherefore of things as they are in themselves God is really the cause, inasmuch as he consists of infinite attributes. I cannot for the present explain my meaning more clearly.
SCHOLIUM: Hic antequam ulterius pergamus, revocandum nobis in memoriam est id quod supra ostendimus nempe quod quicquid ab infinito intellectu percipi potest tanquam  substantiae essentiam constituens, id omne ad unicam tantum substantiam pertinet et consequenter quod substantia cogitans et substantia extensa una eademque est substantia quae jam sub hoc jam sub illo attributo comprehenditur. Sic etiam modus extensionis et idea illius modi una eademque est res sed duobus modis expressa, quod quidam Hebrorum quasi per nebulam vidisse videntur, qui scilicet statuunt Deum, Dei intellectum resque ab ipso intellectas unum et idem esse. Exempli gratia circulus in natura existens et idea circuli existentis quae etiam in Deo est, una eademque est res quae per diversa attributa explicatur et ideo sive naturam sub attributo extensionis sive sub attributo cogitationis sive sub alio quocunque concipiamus, unum eundemque ordinem sive unam eandemque causarum connexionem hoc est easdem res invicem sequi reperiemus. Nec ulla alia de causa dixi quod Deus sit causa ideae exempli gratia circuli quatenus tantum est res cogitans et circuli quatenus tantum est res extensa nisi quia esse formale ideae circuli non nisi per alium cogitandi modum tanquam causam proximam et ille iterum per alium et sic in infinitum, potest percipi ita ut quamdiu res ut cogitandi modi considerantur, ordinem totius naturae sive causarum connexionem per solum cogitationis attributum explicare debemus et quatenus ut modi extensionis considerantur, ordo etiam totius naturae per solum extensionis attributum explicari debet et idem de aliis attributis intelligo. Quare rerum ut in se sunt, Deus revera est causa quatenus infinitis constat attributis nec impraesentiarum haec clarius possum explicare.
2p08 rerum non existentium 2p08 rerum non existentium [geomap]
PROP. VIII. The ideas of particular things, or of modes, that do not exist, must be comprehended in the infinite idea of God, in the same way as the formal essences of particular things or modes are contained in the attributes of God. PROPOSITIO VIII: ideae rerum singularium sive [mng eqv] modorum non existentium ita debent comprehendi in Dei infinita idea ac rerum singularium sive [mng eqv]  modorum essentiae formales in Dei attributis continentur.
Proof.-This proposition is evident from the last; it is understood more clearly from the preceding note. DEMONSTRATIO: Haec propositio patet ex praecedenti {2p07} sed intelligitur clarius ex praecedenti scholio {non-deductive reference}.
2p08c rerum non existentium ideae non existunt 2p08c  rerum non existentium ideae non existunt [geomap]
Corollary.-Hence, so long as particular things do not exist, except in so far as they are comprehended in the attributes of God, their representations in thought or ideas do not exist, except in so far as the infinite idea of God exists; and when particular things are said to exist, not only in so far as they are involved in the attributes of God, but also in so far as they are said to continue, their ideas will also involve existence, through which they are said to continue. COROLLARIUM: Hinc sequitur quod quamdiu res singulares non existunt nisi quatenus in Dei attributis comprehenduntur, earum esse  objectivum sive[mng eqv] ideae non existunt nisi quatenus infinita Dei idea existit et ubi res singulares dicuntur existere non tantum quatenus in Dei attributis comprehenduntur sed quatenus etiam durare dicuntur, earum ideae etiam existentiam per quam durare dicuntur, involvent.
2p08s nempe E et D existere 2p08s nempe E et D existere
Note.-If anyone desires an example to throw more light on this question, I shall, I fear, not be able to give him any, which adequately explains the thing of which I here speak, inasmuch as it is unique; however, I will endeavour to illustrate it as far as possible. The nature of a circle is such that if any number of straight lines intersect within it, the rectangles formed by their segments will be equal to one another; thus, infinite equal rectangles are contained in a circle. Yet none of these rectangles can be said to exist, except in so far as the circle exists; nor can the idea of any of these rectangles be said to exist, except in so far as they are comprehended in the idea of the circle. Let us grant that, from this infinite number of rectangles, two only exist. The ideas of these two not only exist, in so far as they are contained in the idea of the circle, but also as they involve the existence of those rectangles; wherefore they are distinguished from the remaining ideas of the remaining rectangles. SCHOLIUM: Si quis ad uberiorem hujus rei explicationem exemplum desideret, nullum sane dare potero quod rem de qua hic loquor, utpote unicam adaequate explicet; conabor tamen rem ut fieri potest, illustrare. Nempe circulus talis est naturae ut omnium linearum rectarum in eodem sese invicem secantium rectangula sub segmentis sint inter se qualia; quare in circulo infinita inter se qualia rectangula continentur : attamen nullum eorum potest dici existere nisi quatenus circulus existit nec etiam alicujus horum rectangulorum idea potest dici existere nisi quatenus in circuli idea comprehenditur. Concipiantur jam ex infinitis illis duo tantum nempe E et D existere. Sane eorum etiam ideae jam non tantum existunt quatenus solummodo in circuli idea comprehenduntur sed etiam quatenus illorum rectangulorum existentiam involvunt, quo fit ut a reliquis reliquorum rectangulorum ideis distinguantur.
2p09 Idea rei singularis causa 2p09 Idea rei singularis causa  [geomap]
PROP. IX. The idea of an individual thing actually existing is caused by God, not in so far as he is infinite, but in so far as he is considered as affected by another idea of a thing actually existing, of which he is the cause, in so far as he is affected by a third idea, and so on to infinity. PROPOSITIO IX: Idea rei singularis actu  existentis  Deum pro causa habet non quatenus infinitus est sed quatenus alia rei singularis actu  existentis idea affectus consideratur cujus etiam Deus est causa quatenus alia tertia affectus est et sic in infinitum.
Proof.-The idea of an individual thing actually existing is an individual mode of thinking, and is distinct from other modes (by the Corollary and note to Prop. viii. of this part); thus (by Prop. vi. of this part) it is caused by God, in so far only as he is a thinking thing. But not (by Prop. xxviii. of Part i.) in so far as he is a thing thinking absolutely, only in so far as he is considered as affected by another mode of thinking; and he is the cause of this latter, as being affected by a third, and so on to infinity. Now, the order and connection of ideas is (by Prop. vii. of this book) the same as the order and connection of causes. Therefore of a given individual idea another individual idea, or God, in so far as he is considered as modified by that idea, is the cause; and of this second idea God is the cause, in so far as he is affected by another idea, and so on to infinity. Q.E.D. DEMONSTRATIO: Idea rei singularis actu  existentis modus singularis cogitandi est et a reliquis distinctus (per corollarium {2p08c} et scholium {non-deductive reference} propositionis 8 hujus ) adeoque (per propositionem 6 hujus {2p06}) Deum quatenus est tantum res cogitans, pro causa habet. At non (per propositionem 28 partis I {1p28}) quatenus est res absolute cogitans sed quatenus alio cogitandi modo affectus consideratur et hujus etiam Deus est causa quatenus alio cogitandi modo affectus est et sic in infinitum. Atqui ordo et connexio idearum (per propositionem 7 hujus {2p07}) idem est ac ordo et connexio causarum; ergo unius singularis ideae alia idea sive [mng eqv]  Deus quatenus alia idea affectus consideratur, est causa et hujus etiam quatenus alia affectus est et sic in infinitum. Q.E.D.
2p09c  Quicquid in objecto contingit 2p09c  Quicquid in objecto contingit [geomap]
Corollary.-Whatsoever takes place in the individual object of any idea, the knowledge thereof is in God, in so far as he has the idea of that object only. COROLLARIUM {2p09}: Quicquid in singulari cujuscunque ideae objecto contingit, ejus datur in Deo cognitio quatenus tantum ejusdem objecti ideam habet.
Proof.-Whatsoever takes place in the object of any idea, its idea is in God (by Prop. iii. of this part), not in so far as he is infinite, but in so far as he is considered as affected by another idea of an individual thing (by the last Prop.); but (by Prop. vii. of this part) the order and connection of ideas is the same as the order and connection of things. The knowledge, therefore, of that which takes place in any individual object will be in God, in so far as he has the idea of that object only. Q.E.D. DEMONSTRATIO: Quicquid in objecto cujuscunque ideae contingit, ejus datur in Deo idea (per propositionem 3 hujus {2p03}) non quatenus infinitus est sed quatenus alia rei singularis idea affectus consideratur (per praecedentem propositionem {{2p09}) sed (per propositionem 7 hujus {2p07}) ordo et connexio idearum idem est ac ordo et connexio rerum; erit ergo cognitio ejus quod in singulari aliquo objecto contingit, in Deo quatenus tantum ejusdem objecti habet ideam. Q.E.D.
2p10 hominis substanti formam 2p10 hominis  substantiae formam [geomap]
PROP. X. The being of substance does not appertain to the essence of man-in other words, substance does not constitute the actual being[2] of man. [2] "Forma" PROPOSITIO X: Ad essentiam hominis non pertinet esse  substantiae sive [mng eqv]  substantia formam hominis non constituit.
Proof.-The being of substance involves necessary existence (Part i., Prop. vii.). If, therefore, the being of substance appertains to the essence of man, substance being granted, man would necessarily be granted also (II. Def. ii.), and, consequently, man would necessarily exist, which is absurd (II. Ax. i.). Therefore, &c. Q.E.D. DEMONSTRATIO: Esse enim  substantiae involvit necessariam existentiam (per propositionem 7 partis I {1p07}). Si igitur ad hominis essentiam pertineret esse substantiae, data ergo substantia, daretur necessario homo (per definitionem 2 hujus {2d02}) et consequenter homo necessario existeret, quod (per axioma 1 hujus {2a1.1}) est absurdum. Ergo etc. Q.E.D.
2p10s1 Demonstratur ex propositione 5 partis I 2p10s1 Demonstratur ex propositione 5 partis I
Note.-This proposition may also be proved from I.v., in which it is shown that there cannot be two substances of the same nature; for as there may be many men, the being of substance is not that which constitutes the actual being of man. Again, the proposition is evident from the other properties of substance-namely, that substance is in its nature infinite, immutable, indivisible, &c., as anyone may see for himself. SCHOLIUM: Demonstratur etiam hic propositio ex propositione 5 partis I nempe quod duae ejusdem naturae  substantiae non dentur. Cum autem plures homines existere possint, ergo id quod hominis formam constituit, non est esse substanti. Patet praeterea haec propositio ex reliquis  substantiae proprietatibus videlicet quod substantia sit sua natura infinita, immutabilis, indivisibilis etc. ut facile unusquisque videre potest.
2p10c essentiam hominis modificationibus 2p10c essentiam hominis modificationibus [geomap]
Corollary.-Hence it follows, that the essence of man is constituted by certain modifications [Lat: affectiones] of the attributes of God. COROLLARIUM {2p10}: Hinc sequitur essentiam hominis constitui a certis Dei attributorum modificationibus.
Proof. For (by the last Prop.) the being of substance does not belong to the essence of man. That essence therefore (by i. 15) is something which is in God, and which without God can neither be nor be conceived as a modification [Lat: affectiones] (i. 25. Coroll.) in other words, as a mode which expresses God's nature in a certain conditioned manner. DEMONSTRATIO: Nam esse  substantiae (per propositionem praecedentem {2p10}) ad essentiam hominis non pertinet. Est ergo (per propositionem 15 partis I {1p15}) aliquid quod in Deo est et quod sine Deo nec esse nec concipi potest sive [prf eqv]  (per corollarium propositionis 25 partis I {1p25}) affectio sive [prf eqv]  modus qui Dei naturam certo et determinato modo exprimit.
2p10s2 essentia concipere II. Def. ii. 2p10s2 essentia concipere II. Def. ii.
Note.-Everyone must surely admit, that nothing can be or be conceived without God. All men agree that God is the one and only cause of all things, both of their essence and of their existence; that is, God is not only the cause of things in respect to their being made (secundum fieri), but also in respect to their being (secundum esse).
At the same time many assert, that that, without which a thing cannot be nor be conceived, belongs to the essence of that thing; wherefore they believe that either the nature of God appertains to the essence of created things, or else that created things can be or be conceived without God; or else, as is more probably the case, they hold inconsistent doctrines. I think the cause for such confusion is mainly, that they do not keep to the proper order of philosophic thinking. The nature of God, which should be reflected on first, inasmuch as it is prior both in the order of knowledge and the order of nature, they have taken to be last in the order of knowledge, and have put into the first place what they call the objects of sensation; hence, while they are considering natural phenomena, they give no attention at all to the divine nature, and, when afterwards they apply their mind to the study of the divine nature, they are quite unable to bear in mind the first hypotheses, with which they have overlaid the knowledge of natural phenomena, inasmuch as such hypotheses are no help towards understanding the divine nature. So that it is hardly to be wondered at, that these persons contradict themselves freely.
However, I pass over this point. My intention here was only to give a reason for not saying, that that, without which a thing cannot be or be conceived, belongs to the essence of that thing: individual things cannot be or be conceived without God, yet God does not appertain to their essence. I said that "I considered as belonging to the essence of a thing that, which being given, the thing is necessarily given also, and which being removed, the thing is necessarily removed also; or that without which the thing, and which itself without the thing can neither be nor be conceived." (II. Def. ii.)
SCHOLIUM: Omnes sane concedere debent nihil sine Deo esse neque concipi posse. Nam apud omnes in confesso est quod Deus omnium rerum tam earum essentiae quam earum existenti unica est causa hoc est Deus non tantum est causa rerum secundum fieri ut aiunt sed etiam secundum esse. At interim plerique id ad essentiam alicujus rei pertinere dicunt sine quo res nec esse nec concipi potest adeoque vel naturam Dei ad essentiam rerum creatarum pertinere vel res creatas sine Deo vel esse vel concipi posse credunt vel quod certius est, sibi non satis constant. Cujus rei causam fuisse credo quod ordinem philosophandi non tenuerint. Nam naturam divinam quam ante omnia contemplari debebant quia tam cognitione quam natura prior est, ordine cognitionis ultimam et res quae sensuum objecta vocantur, omnibus priores esse crediderunt; unde factum est ut dum res naturales contemplati sunt, de nulla re minus cogitaverint quam de divina natura et cum postea animum ad divinam naturam contemplandum appulerint, de nulla re minus cogitare potuerint quam de primis suis figmentis quibus rerum naturalium cognitionem superstruxerant; utpote quae ad cognitionem divinae naturae nihil juvare poterant adeoque nihil mirum si sibi passim contradixerint. Sed hoc mitto. Nam meum intentum hic tantum fuit causam reddere cur non dixerim id ad essentiam alicujus rei pertinere sine quo res nec esse nec concipi potest; nimirum quia res singulares non possunt sine Deo esse nec concipi et tamen Deus ad earum essentiam non pertinet sed id necessario essentiam alicujus rei constituere dixi quo dato, res ponitur et quo sublato, res tollitur vel id sine quo res et vice versa id quod sine re nec esse nec concipi potest.
2p11 mentis humanae 2p11 mentis humanae [geomap]
PROP. XI. The first element, which constitutes the actual being of the human mind, is the idea of some particular thing actually existing. PROPOSITIO XI: Primum quod actuale mentis humanae esse constituit, nihil aliud est quam idea  rei alicujus singularis actu existentis.
Proof.-The essence of man (by the Coroll. of the last Prop.) is constituted by certain modes of the attributes of God, namely (by II. Ax. ii.), by the modes of thinking, of all which (by II. Ax. iii.) the idea is prior in nature, and, when the idea is given, the other modes (namely, those of which the idea is prior in nature) must be in the same individual (by the same Axiom). Therefore an idea is the first element constituting the human mind. But not the idea of a non-existent thing, for then (II. viii. Coroll.) the idea itself cannot be said to exist; it must therefore be the idea of something actually existing. But not of an infinite thing. For an infinite thing (I. xxi., xxii.), must always necessarily exist; this would (by II. Ax. i.) involve an absurdity. Therefore the first element, which constitutes the actual being of the human mind, is the idea of something actually existing. Q.E.D. DEMONSTRATIO: Essentia hominis (per corollarium praecedentis propositionis) a certis Dei attributorum  modis constituitur nempe (per axioma 2 hujus {2a1.2}) a modis cogitandi quorum omnium (per axioma 3 hujus {2a1.3}) idea natura prior est et ea data reliqui modi (quibus scilicet idea natura prior est) in eodem debent esse individuo (per axioma 3 hujus {2a1.3}). Atque adeo idea primum est quod humanae mentis esse constituit. At non idea rei non existentis. Nam tum (per corollarium propositionis 8 hujus {2p08}) ipsa idea non potest dici existere; erit ergo idea rei actu existentis. At non rei infinitae. res namque infinita (per propositiones 21 et 22 partis I {1p[21} {1p22}) debet semper necessario existere; atqui hoc (per axioma 1 hujus {2a1.1}) est absurdum; ergo primum quod esse humanae mentis actuale constituit, est idea rei singularis actu existentis. Q.E.D.
2p11c mens partem infiniti intellectus Dei 2p11c mens partem infiniti intellectus Dei [geomap]
Corollary.-Hence it follows, that the human mind is part of the infinite intellect of God; thus when we say, that the human mind perceives this or that, we make the assertion, that God has this or that idea, not in so far as he is infinite, but in so far as he is displayed through the nature of the human mind, or in so far as he constitutes the essence of the human mind; and when we say that God has this or that idea, not only in so far as he constitutes the essence of the human mind, but also in so far as he, simultaneously with the human mind, has the further idea of another thing, we assert that the human mind perceives a thing in part or inadequately. COROLLARIUM {2p11}: Hinc sequitur mentem humanam partem esse infiniti intellectus Dei ac proinde cum dicimus mentem humanam hoc vel illud percipere, nihil aliud dicimus quam quod Deus non quatenus infinitus est sed quatenus per naturam humanae mentis explicatur sive [mng eqv] quatenus humanae mentis essentiam constituit, hanc vel illam habet ideam et cum dicimus Deum hanc vel  illam ideam habere non tantum quatenus naturam humanae mentis constituit sed quatenus simul cum mente humana alterius rei etiam habet ideam, tum dicimus mentem humanam rem ex partesive sive [mng eqv] inadaequate percipere.
2p11s rogo 2p11s rogo
Note.-Here, I doubt not, readers will come to a stand, and will call to mind many things which will cause them to hesitate; I therefore beg them to accompany me slowly, step by step, and not to pronounce on my statements, till they have read to the end. SCHOLIUM: Hic sine dubio lectores hrebunt multaque comminiscentur quae moram injiciant et hac de causa ipsos rogo ut lento gradu mecum pergant nec de his judicium ferant donec omnia perlegerint.
2p12 objecto ideae contingit, debet percipi 2p12 objecto ideae contingit, debet percipi [geomap]
PROP. XII. Whatsoever comes to pass in the object of the idea, which constitutes the human mind, must be perceived by the human mind, or there will necessarily be an idea in the human mind of the said occurrence. That is, if the object of the idea constituting the human mind be a body, nothing can take place in that body without being perceived by the mind. PROPOSITIO XII: Quicquid in objecto ideae humanam mentem constituentis contingit, id ab humana mente debet percipi sive [mng eqv]  ejus rei dabitur in mente necessario idea hoc est [mng eqv] si objectum ideae humanam mentem constituentis sit corpus, nihil in eo corpore poterit contingere quod a mente non percipiatur.
Proof.-Whatsoever comes to pass in the object of any idea, the knowledge thereof is necessarily in God (II. ix. Coroll.), in so far as he is considered as affected by the idea of the said object, that is (II. xi.), in so far as he constitutes the mind of anything. Therefore, whatsoever takes place in the object constituting the idea of the human mind, the knowledge thereof is necessarily in God, in so far as he constitutes the essence of the human mind; that is (by II. xi. Coroll.) the knowledge of the said thing will necessarily be in the mind, in other words the mind perceives it. DEMONSTRATIO: Quicquid enim in objecto cujuscunque ideae contingit, ejus rei datur necessario in Deo cognitio (per corollarium propositionis 9 hujus {2p09}) quatenus ejusdem objecti idea affectus consideraturhoc est (per propositionem 11 hujus {2p11}) quatenus mentem alicujus rei constituit. Quicquid igitur in objecto ideae humanam mentem constituentis contingit, ejus datur necessario in Deo cognitio quatenus naturam humanae mentis constituit hoc est (per corollarium propositionis 11 hujus {2p11c}) ejus rei cognitio erit necessario in mente sive [mng eqv]  mens id percipit. Q.E.D.
2p12s II. vii. 2p12s II. vii.
Note.-This proposition is also evident, and is more clearly to be understood from II. vii., which see. SCHOLIUM: Haec propositio patet etiam et clarius intelligitur ex scholio propositionis 7 hujus, quod vide.
2p13 corpus objectum mentem 2p13 corpus objectum mentem [geomap]
PROP. XIII. The object of the idea constituting the human mind is the body, in other words a certain mode of extension which actually exists, and nothing else. PROPOSITIO XIII: Objectum ideae humanam mentem constituentis est corpus sive [a kind of]  certus extensionis modus actu existens et nihil aliud.
Proof.-If indeed the body were not the object of the human mind, the ideas of the modifications [Lat: affectiones] of the body would not be in God (II. ix. Coroll.) in virtue of his constituting our mind, but in virtue of his constituting the mind of something else; that is (II. xi. Coroll.) the ideas of the modifications [Lat: affectiones] of the body would not be in our mind: now (by II. Ax. iv.) we do possess the idea of the modifications [Lat: affectiones] of the body. Therefore the object of the idea constituting the human mind is the body, and the body as it actually exists (II. xi.). Further, if there were any other object of the idea constituting the mind besides body, then, as nothing can exist from which some effect does not follow (I. xxxvi.) there would necessarily have to be in our mind an idea, which would be the effect of that other object (II. xi.); but (I. Ax. v.) there is no such idea. Wherefore the object of our mind is the body as it exists, and nothing else. Q.E.D. DEMONSTRATIO: Si enim corpus non esset humanae mentis objectum, ideae affectionum corporis non essent in Deo (per corollarium propositionis 9 hujus {2p09}) quatenus mentem nostramsed quatenus alterius rei mentem constitueret hoc est (per corollarium propositionis 11 hujus {2p11c}) ideae affectionum corporis non essent in nostra mente; atqui (per axioma 4 hujus {2a1.4}) ideas affectionum corporis habemus. Ergo objectum ideae humanam mentem constituentis est corpus idque (per propositionem 11 hujus {2p11}) actu existens. Deinde si praeter corpus etiam aliud esset mentis objectum, cum nihil (per propositionem 36 partis I {1p36}) existat ex quo aliquis effectus non sequatur, deberet (per propositionem 12 hujus {2p12}) necessario alicujus ejus effectus idea in mente nostra dari; atqui (per axioma 5 hujus {2a1.5}) nulla ejus idea datur. Ergo objectum nostrae mentis est corpus existens et nihil aliud. Q.E.D.
2p13c ipsum sentimus existere 2p13c ipsum sentimus existere [geomap]
Corrollary: From this follows that the human consists of mind and body and that the human body exists exactly as we perceive it COROLLARIUM: Hinc sequitur hominem mente et corpore constare et corpus humanum prout ipsum sentimus existere.
2p13s mentis et corporis unionem, praestantiorem realitatis 2p13s mentis et corporis unionem, praestantiorem realitatis
Note.-We thus comprehend, not only that the human mind is united to the body, but also the nature of the union between mind and body. However, no one will be able to grasp this adequately or distinctly, unless he first has adequate knowledge of the nature of our body. The propositions we have advanced hitherto have been entirely general, applying not more to men than to other individual things, all of which, though in different degrees, are animated.[3] For of everything there is necessarily an idea in God, of which God is the cause, in the same way as there is an idea of the human body; thus whatever we have asserted of the idea of the human body must necessarily also be asserted of the idea of everything else. Still, on the other hand, we cannot deny that ideas, like objects, differ one from the other, one being more excellent than another and containing more reality, just as the object of one idea is more excellent than the object of another idea, and contains more reality.
[3] "Animata"
Wherefore, in order to determine, wherein the human mind differs from other things, and wherein it surpasses them, it is necessary for us to know the nature of its object, that is, of the human body. What this nature is, I am not able here to explain, nor is it necessary for the proof of what I advance, that I should do so. I will only say generally, that in proportion as any given body is more fitted than others for doing many actions or receiving many impressions at once, so also is the mind, of which it is the object, more fitted than others for forming many simultaneous perceptions; and the more the actions of the body depend on itself alone, and the fewer other bodies concur with it in action, the more fitted is the mind of which it is the object for distinct comprehension. We may thus recognize the superiority of one mind over others, and may further see the cause, why we have only a very confused knowledge of our body, and also many kindred questions, which I will, in the following propositions, deduce from what has been advanced. Wherefore I have thought it worth while to explain and prove more strictly my present statements. In order to do so, I must premise a few propositions concerning the nature of bodies.
SCHOLIUM: Ex his non tantum intelligimus mentem humanam unitam esse corpori sed etiam quid per mentis et corporis unionem intelligendum sit. Verum ipsam adaequate sive distincte intelligere nemo poterit nisi prius nostri corporis naturam adaequate cognoscat. Nam ea quae hucusque ostendimus, admodum communia sunt nec magis ad homines quam ad reliqua individua pertinent, quae omnia quamvis diversis gradibus animata tamen sunt. Nam cujuscunque rei datur necessario in Deo idea cujus Deus est causa eodem modo ac humani corporis ideae atque adeo quicquid de idea humani corporis diximus, id de cujuscunque rei idea necessario dicendum est. Attamen nec etiam negare possumus ideas inter se ut ipsa objecta differre unamque alia praestantiorem esse plusque realitatis continere prout objectum unius objecto alterius praestantius est plusque realitatis continet ac propterea ad determinandum quid mens humana reliquis intersit quidque reliquis praestet, necesse nobis est ejus objecti ut diximus hoc est corporis humani naturam cognoscere. Eam autem hic explicare nec possum nec id ad ea quae demonstrare volo, necesse est. Hoc tamen in genere dico quo corpus aliquod reliquis aptius est ad plura simul agendum vel patiendum, eo ejus mens reliquis aptior est ad plura simul percipiendum et quo unius corporis actiones magis ab ipso solo pendent et quo minus alia corpora cum eodem in agendo concurrunt, eo ejus mens aptior est ad distincte intelligendum. Atque ex his praestantiam unius mentis prae aliis cognoscere possumus, deinde causam etiam videre cur nostri corporis non nisi admodum confusam habeamus cognitionem et alia plura quae in sequentibus ex his deducam. Qua de causa operae pretium esse duxi haec ipsa accuratius explicare et demonstrare, ad quod necesse est pauca de natura corporum praemittere.
2a2.1 corpora moventur quiescunt 2a2.1 corpora moventur quiescunt [geomap]
AXIOM I. All bodies are either in motion or at rest. AXIOMA I: Omnia corpora vel [excl exh] moventur vel quiescunt.
2a2.2 tardius celerius 2a2.2 tardius celerius [geomap]
AXIOM II. Every body is moved sometimes more slowly, sometimes more quickly. AXIOMA II: Unumquodque corpus jam tardius jam celerius movetur.
2L01 Corpora non substanti distinguuntur 2L01 Corpora non  substantiae distinguuntur [geomap]
LEMMA I. Bodies are distinguished from one another in respect of motion and rest, quickness and slowness, and not in respect of substance. LEMMA I: corpora ratione motus et quietis, celeritatis et tarditatis et non ratione  substantiae ab invicem distinguuntur.
Proof.-The first part of this proposition is, I take it, self-evident. That bodies are not distinguished in respect of substance, is plain both from I. v. and I. viii. It is brought out still more clearly from I. xv, note. DEMONSTRATIO: Primam partem hujus per se notam suppono. At quod ratione  substantiae non distinguantur corpora, patet tam ex propositione 5 {1p05} quam 8 {1p08} partis I sed clarius ex iis quae in scholio propositionis 15 partis {non-deductive reference} I dicta sunt.
2L02 corpora conveniunt 2L02 corpora conveniunt [geomap]
LEMMA II. All bodies agree in certain respects. LEMMA II: Omnia corpora in quibusdam conveniunt.
Proof.-All bodies agree in the fact, that they involve the conception of one and the same attribute (II., Def. i.). Further, in the fact that they may be moved less or more quickly, and may be absolutely in motion or at rest. DEMONSTRATIO: In his enim omnia corpora conveniunt quod unius ejusdemque attributi conceptum involvunt (per definitionem 1 hujus {2d01}), deinde quod jam tardius jam celerius et absolute jam moveri jam quiescere possunt.
2L03 corpus motum determinari ab alio 2L03 corpus motum determinari ab alio [geomap]
LEMMA III. A body in motion or at rest must be determined to motion or rest by another body, which other body has been determined to motion or rest by a third body, and that third again by a fourth, and so on to infinity. LEMMA III: corpus motum vel [excl exh] quiescens ad motum vel [excl exh] quietem determinari debuit ab alio corpore quod etiam ad motum vel [excl exh] quietem determinatum fuit ab alio et illud iterum ab alio et sic in infinitum.
Proof.-Bodies are individual things (II., Def. i.), which (Lemma I.) are distinguished one from the other in respect to motion and rest; thus (I. xxviii.) each must necessarily be determined to motion or rest by another individual thing, namely (II. vi.), by another body, which other body is also (Ax. i.) in motion or at rest. And this body again can only have been set in motion or caused to rest by being determined by a third body to motion or rest. This third body again by a fourth, and so on to infinity. Q.E.D. DEMONSTRATIO: corpora (per definitionem 1 hujus {2d01}) res singulares sunt quae (per lemma 1 {2L01}) ratione motus et quietis ab invicem distinguuntur adeoque (per propositionem 28 partis I {1p28}) unumquodque ad motum vel [excl exh] quietem necessario determinari debuit ab alia re singulari nempe (per propositionem 6 hujus {2p06}) ab alio corpore quod (per axioma 1 {2a2.1}) etiam vel [excl exh] movetur vel quiescit. At hoc etiam (per eandem rationem) moveri vel [excl exh] quiescere non potuit nisi ab alio ad motum vel [excl exh] quietem determinatum fuisset et hoc iterum (per eandem rationem) ab alio et sic in infinitum. Q.E.D.
2L03c corpus motum tamdiu moveri 2L03c corpus motum tamdiu moveri [geomap]
Corollary.-Hence it follows, that a body in motion keeps in motion, until it is determined to a state of rest by some other body; and a body at rest remains so, until it is determined to a state of motion by some other body. This is indeed self-evident. For when I suppose, for instance, that a given body, A, is at rest, and do not take into consideration other bodies in motion, I cannot affirm anything concerning the body A, except that it is at rest. If it afterwards comes to pass that A is in motion, this cannot have resulted from its having been at rest, for no other consequence could have been involved than its remaining at rest. If, on the other hand, A be given in motion, we shall, so long as we only consider A, be unable to affirm anything concerning it, except that it is in motion. If A is subsequently found to be at rest, this rest cannot be the result of A's previous motion, for such motion can only have led to continued motion; the state of rest therefore must have resulted from something, which was not in A, namely, from an external cause determining A to a state of rest. COROLLARIUM {2L03}: Hinc sequitur corpus motum tamdiu moveri donec ab alio corpore ad quiescendum determinetur et corpus quiescens tamdiu etiam quiescere donec ab alio ad motum determinetur. Quod etiam per se notum est. Nam cum suppono corpus exempli gratia A quiescere nec ad alia corpora mota attendo, nihil de corpore A dicere potero nisi quod quiescat. Quod si postea contingat ut corpus A moveatur, id sane evenire non potuit ex eo quod quiescebat; ex eo enim nil aliud sequi poterat quam ut corpus A quiesceret. Si contra supponatur A moveri, quotiescunque ad A tantum attendimus, nihil de eodem affirmare poterimus nisi quod moveatur. Quod si postea contingat ut A quiescat, id sane evenire etiam non potuit ex motu quem habebat; ex motu enim nihil aliud sequi poterat quam ut A moveretur : contingit itaque a re quae non erat in A nempe a causa externa a qua ad quiescendum determinatum fuit.
2a3.1 corporis affecti afficientis 2a3.1 corporis affecti afficientis [geomap]
Axiom I.-All modes, wherein one body is affected by another body, follow simultaneously from the nature of the body affected and the body affecting; so that one and the same body may be moved in different modes, according to the difference in the nature of the bodies moving it; on the other hand, different bodies may be moved in different modes by one and the same body. AXIOMA I: Omnes modi quibus corpus aliquod ab alio afficitur corpore, ex natura corporis affecti et simul ex natura corporis afficientis sequuntur ita ut unum idemque corpus diversimode moveatur pro diversitate naturae corporum moventium et contra ut diversa corpora ab uno eodemque corpore diversimode moveantur.
2a3.2 angulus line motus reflectionis 2a3.2 angulus line motus reflectionis [geomap]
Axiom II.-When a body in motion impinges on another body at rest, which it is unable to move, it recoils, in order to continue its motion, and the angle made by the line of motion in the recoil and the plane of the body at rest, whereon the moving body has impinged, will be equal to the angle formed by the line of motion of incidence and the same plane. AXIOMA II: Cum corpus motum alterius quiescenti quod dimovere nequit, impingit, reflectitur ut moveri pergat et angulus line motus reflectionis cum plano corporis quiescentis cui impegit, qualis erit angulo quem linea motus incidenti cum eodem plano efficit.
So far we have been speaking only of the most simple bodies, which are only distinguished one from the other by motion and rest, quickness and slowness. We now pass on to compound bodies. Atque haec de corporibus simplicissimis quae scilicet solo motu et quiete, celeritate et tarditate ab invicem distinguuntur : jam ad composita ascendamus.
2d08 (corpora) unita 2d08 (corpora) unita [notes] [geomap]
Definition.-When any given bodies of the same or different magnitude are compelled by other bodies to remain in contact, or if they be moved at the same or different rates of speed, so that their mutual movements should preserve among themselves a certain fixed relation, we say that such bodies are in union, and that together they compose one body or individual, which is distinguished from other bodies by the fact of this union. DEFINITIO: Cum corpora aliquot ejusdem aut [excl exh] diversae magnitudinis a reliquis ita coercentur ut invicem incumbant vel [excl non-exh] si eodem aut [excl exh] diversis celeritatis gradibus moventur ut motus suos invicem certa quadam ratione communicent, illa corpora invicem unita dicemus et omnia simul unum corpus sive [mng eqv]  individuum componere quod a reliquis per hanc corporum unionem distinguitur.
2a3.3 dura mollia fluida 2a3.3 dura mollia fluida [geomap]
Axiom III.-In proportion as the parts of an individual, or a compound body, are in contact over a greater or less superficies, they will with greater or less difficulty admit of being moved from their position; consequently the individual will, with greater or less difficulty, be brought to assume another form. Those bodies, whose parts are in contact over large superficies, are called hard; those, whose parts are in contact over small superficies, are called soft; those, whose parts are in motion among one another, are called fluid. AXIOMA III: Quo partes individui vel [excl exh] corporis compositi secundum majores vel [excl non-exh] minores superficies sibi invicem incumbunt, eo difficilius vel [excl non-exh] facilius cogi possunt ut situm suum mutent et consequenter eo difficilius vel [excl non-exh] facilius effici potest ut ipsum individuum aliam figuram induat. Atque hinc corpora quorum partes secundum magnas superficies invicem incumbunt, dura, quorum autem partes secundum parvas, mollia et quorum denique partes inter se moventur, fluida vocabo.
2L04 alia succedant 2L04 alia succedant [geomap]
LEMMA IV. If from a body or individual, compounded of several bodies, certain bodies be separated, and if, at the same time, an equal number of other bodies of the same nature take their place, the individual will preserve its nature as before, without any change in its actuality (forma). LEMMA IV: Si corporis sive [mng eqv]  individui quod ex pluribus corporibus componitur, quaedam corpora segregentur et simul totidem alia ejusdem naturae eorum loco succedant, retinebit individuum suam naturam uti antea absque ulla ejus formae mutatione.
Proof.-Bodies (Lemma i.) are not distinguished in respect of substance: that which constitutes the actuality (formam) of an individual consists (by the last Def.) in a union of bodies; but this union, although there is a continual change of bodies, will (by our hypothesis) be maintained; the individual, therefore, will retain its nature as before, both in respect of substance and in respect of mode. Q.E.D. DEMONSTRATIO: corpora enim (per lemma 1 {2L01}) ratione  substantiae non distinguuntur; id autem quod formam individui constituit, in corporum unione (per definitionem praecedentem {2d08}) consistit; atqui haec (per hypothesin) tametsi corporum continua fiat mutatio, retinetur : retinebit ergo individuum tam ratione  substantiae quam modi suam naturam uti ante. Q.E.D.
2L05 invicem motus et quietis rationem 2L05 invicem motus et quietis rationem [geomap]
LEMMA V. If the parts composing an individual become greater or less, but in such proportion, that they all preserve the same mutual relations of motion and rest, the individual will still preserve its original nature, and its actuality will not be changed. LEMMA V : Si partes individuum componentes majores minoresve evadant, ea tamen proportione ut omnes eandem ut antea ad invicem motus et quietis rationem servent, retinebit itidem individuum suam naturam ut antea absque ulla formae mutatione.
Proof.-The same as for the last Lemma. DEMONSTRATIO: Hujus eadem est ac praecedentis lemmatis {2L04}.
2L06 qua antea ratione communicare 2L06 qua antea ratione communicare [geomap]
LEMMA VI. If certain bodies composing an individual be compelled to change the motion, which they have in one direction, for motion in another direction, but in such a manner, that they be able to continue their motions and their mutual communication in the same relations as before, the individual will retain its own nature without any change of its actuality. LEMMA VI: Si corpora quaedam individuum componentia motum quem versus unam partem habent, aliam versus flectere cogantur at ita ut motus suos continuare possint atque invicem eadem qua antea ratione communicare, retinebit itidem individuum suam naturam absque ulla formae mutatione.
Proof.-This proposition is self-evident, for the individual is supposed to retain all that, which, in its definition, we spoke of as its actual being. DEMONSTRATIO: Per se patet. Id enim omne retinere supponitur quod in ejusdem definitione formam ipsius constituere diximus.
2L07 motum retineat antea reliquis communicet 2L07 motum retineat antea reliquis communicet [geomap]
LEMMA VII. Furthermore, the individual thus composed preserves its nature, whether it be, as a whole, in motion or at rest, whether it be moved in this or that direction; so long as each part retains its motion, and preserves its communication with other parts as before. LEMMA VII: Retinet praeterea individuum sic compositum suam naturam sive [non-excl exh triple]  id secundum totum moveatur  sive [excl exh triple] quiescat  sive [non-excl exh triple] versus hanc sive versus illam partem moveatur dummodo unaquque pars motum suum retineat eumque uti antea reliquis communicet.
Proof.-This proposition is evident from the definition of an individual prefixed to Lemma iv. DEMONSTRATIO: Patet ex ipsius definitione {2d08}, quam vide ante lemma 4.
2L07s aliud pluribus individuis compositum tertium 2L07s aliud pluribus individuis compositum tertium
 Note.-We thus see, how a composite individual may be affected in many different ways, and preserve its nature notwithstanding. Thus far we have conceived an individual as composed of bodies only distinguished one from the other in respect of motion and rest, speed and slowness; that is, of bodies of the most simple character. If, however, we now conceive another individual composed of several individuals of diverse natures, we shall find that the number of ways in which it can be affected, without losing its nature, will be greatly multiplied. Each of its parts would consist of several bodies, and therefore (by Lemma vi.) each part would admit, without change to its nature, of quicker or slower motion, and would consequently be able to transmit its motions more quickly or more slowly to the remaining parts. If we further conceive a third kind of individuals composed of individuals of this second kind, we shall find that they may be affected in a still greater number of ways without changing their actuality. We may easily proceed thus to infinity, and conceive the whole of nature as one individual, whose parts, that is, all bodies, vary in infinite ways, without any change in the individual as a whole. I should feel bound to explain and demonstrate this point at more length, if I were writing a special treatise on body. But I have already said that such is not my object; I have only touched on the question, because it enables me to prove easily that which I have in view. SCHOLIUM: His itaque videmus qua ratione individuum compositum possit multis modis affici, ejus nihilominus natura servata. Atque hucusque individuum concepimus quod non nisi ex corporibus quae solo motu et quiete, celeritate et tarditate inter se distinguuntur hoc est quod ex corporibus simplicissimis componitur. Quod si jam aliud concipiamus ex pluribus diversae naturae individuis compositum, idem pluribus aliis modis posse affici reperiemus, ipsius nihilominus natura servata. Nam quandoquidem ejus unaquque pars ex pluribus corporibus est composita, poterit ergo (per lemma praecedens) unaquque pars absque ulla ipsius naturae mutatione jam tardius jam celerius moveri et consequenter motus suos citius vel tardius reliquis communicare. Quod si praeterea tertium individuorum genus ex his secundis compositum concipiamus, idem multis aliis modis affici posse reperiemus absque ulla ejus form mutatione. Et si sic porro in infinitum pergamus, facile concipiemus totam naturam unum esse Individuum cujus partes hoc est omnia corpora infinitis modis variant absque ulla totius Individui mutatione. Atque haec, si animus fuisset de corpore ex professo agere, prolixius explicare et demonstrare debuissem. Sed jam dixi me aliud velle nec alia de causa haec adferre quam quia ex ipsis ea quae demonstrare constitui, facile possum deducere.
POSTULATES POSTULATA
2post01 plurimis individuis 2post01 plurimis individuis [geomap]
I. The human body is composed of a number of individual parts, of diverse nature, each one of which is in itself extremely complex.  I. Corpus humanum componitur ex plurimis (diversae naturae) individuis quorum unumquodque valde compositum est.
2post02 fluida mollia dura 2post02 fluida mollia dura [geomap]
II. Of the individual parts composing the human body some are fluid, some soft, some hard. II. Individuorum ex quibus corpus humanum componitur quaedam fluida, quaedam mollia et quaedam denique dura sunt.
2post03 externis plurimis modis afficitur 2post03 externis plurimis modis afficitur [geomap]
III. The individual parts composing the human body, and consequently the human body itself, are affected in a variety of ways by external bodies. III. Individua corpus humanum componentia et consequenter ipsum humanum corpus a corporibus externis plurimis modis afficitur.
2post04 regeneratur 2post04 regeneratur [geomap]
IV. The human body stands in need for its preservation of a number of other bodies, by which it is continually, so to speak, regenerated. IV. Corpus humanum indiget ut conservetur plurimis aliis corporibus a quibus continuo quasi regeneratur.
2post05 in aliam mollem imprimit 2post05 in aliam mollem imprimit [geomap]
V. When the fluid part of the human body is determined by an external body to impinge often on another soft part, it changes the surface of the latter, and, as it were, leaves the impression thereupon of the external body which impels it. V. Cum corporis humani pars fluida a corpore externo determinatur ut in aliam mollem spe impingat, ejus planum mutat et veluti quaedam corporis externi impellentis vestigia eidem imprimit.
2post06 corpora externa movere 2post06 corpora externa movere [geomap]
VI. The human body can move external bodies, and arrange them in a variety of ways. VI. Corpus humanum potest corpora externa plurimis modis movere plurimisque modis disponere.
2p14 Mens plurima percipiendum 2p14 Mens plurima percipiendum [geomap]
PROP. XIV. The human mind is capable of perceiving a great number of things, and is so in proportion as its body is capable of receiving a great number of impressions. PROPOSITIO XIV: Mens humana apta est ad plurima percipiendum et eo aptior quo ejus corpus pluribus modis disponi potest.
Proof.-The human body (by Post. iii. and vi.) is affected in very many ways by external bodies, and is capable in very many ways of affecting external bodies. But (II. xii.) the human mind must perceive all that takes place in the human body; the human mind is, therefore, capable of perceiving a great number of things, and is so in proportion, &c. Q.E.D. DEMONSTRATIO: Corpus enim humanum (per postulata 3 {2post03} et 6 {2post06}) plurimis modis a corporibus externis afficitur disponiturque ad corpora externa plurimis modis afficiendum. At omnia quae in corpore humano contingunt (per propositionem 12 hujus {2p12}) mens humana percipere debet; est ergo mens humana apta ad plurima percipiendum et eo aptior etc. Q.E.D.
2p15 Idea mentis composita 2p15 Idea mentis composita [geomap]
PROP. XV. The idea, which constitutes the actual being of the human mind, is not simple, but compounded of a great number of ideas. PROPOSITIO XV: Idea quae esse  formale humanae mentis constituit non est simplex sed ex plurimis ideis composita.
Proof.-The idea constituting the actual being of the human mind is the idea of the body (II. xiii.), which (Post. i.) is composed of a great number of complex individual parts. But there is necessarily in God the idea of each individual part whereof the body is composed (II. viii. Coroll.); therefore (II. vii.), the idea of the human body is composed of these numerous ideas of its component parts. Q.E.D. DEMONSTRATIO: Idea quae esse  formale humanae mentis constituit, est idea corporis (per propositionem 13 hujus {2post01}) ex plurimis valde compositis individuis componitur. At cujuscunque individui corpus componentis datur necessario (per corollarium propositionis 8 hujus {2p08}) in Deo idea; ergo (per propositionem 7 hujus {2p07}) idea corporis humani ex plurimis hisce partium componentium ideis est composita. Q.E.D.
2p16 Idea afficitur corporis humani et externi 2p16 Idea afficitur corporis humani et externi [geomap]
PROP. XVI. The idea of every way in which the human body is affected by external bodies, must involve the nature of the human body, and also the nature of the external body. PROPOSITIO XVI : Idea cujuscunque modi quo corpus humanum a corporibus externis afficitur, involvere debet naturam corporis humani et simul naturam corporis externi.
Proof.-All the ways in which any given body is affected, follow from the nature of the body affected, and also from the nature of the affecting body (by Ax. i., after the Coroll. of Lemma iii.), wherefore their idea also necessarily (by I. Ax. iv.) involves the nature of both bodies; therefore, the idea of every way in which the human body is affected by external bodies, involves the nature of the human body and of the external body. Q.E.D. DEMONSTRATIO: Omnes enim modi quibus corpus aliquod afficitur ex natura corporis affecti et simul ex natura corporis afficientis sequuntur (per axioma 1  post corollarium lemmatis 3) {2a3.1}: quare eorum idea (per axioma 4 partis I {1a04}) utriusque corporis naturam necessario involvet adeoque idea  cujuscunque modi quo corpus humanum a corpore externo afficitur, corporis humani et corporis externi naturam involvit. Q.E.D.
2p16c1 plurimorum corporum naturam 2p16c1 plurimorum corporum naturam [geomap]
Corollary I.-Hence it follows, first, that the human mind perceives the nature of a variety of bodies, together with the nature of its own. COROLLARIUM {2p16} I: Hinc sequitur primo mentem humanam plurimorum corporum naturam una cum sui corporis natura percipere.
2p16c2 magis nostri corporis 2p16c2 magis nostri corporis [geomap]
Corollary II.-It follows, secondly, that the ideas, which we have of external bodies, indicate rather the constitution of our own body than the nature of external bodies. I have amply illustrated this in the Appendix to Part I. COROLLARIUM {2p16} II: Sequitur secundo quod ideae quas corporum externorum habemus, magis nostri corporis constitutionem quam corporum externorum naturam indicant; quod in appendice partis prim multis exemplis explicui.
2p17 existens vel ut sibi praesens 2p17 existens vel ut sibi praesens [geomap]
PROP. XVII. If the human body is affected in a manner which involves the nature of any external body, the human mind will regard the said external body as actually existing, or as present to itself, until the human body be affected in such a way, as to exclude the existence or the presence of the said external body. PROPOSITIO XVII: Si humanum corpus affectum est modo qui naturam corporis alicujus externi involvit, mens humana idem corpus externum ut actu existens vel [mng eqv] ut sibi praesens contemplabitur donec corpus afficiatur affectu qui ejusdem corporis existentiam vel [mng eqv] praesentiam secludat.
Proof.-This proposition is self-evident, for so long as the human body continues to be thus affected, so long will the human mind (II. xii.) regard this modification [Lat: affectiones] of the body-that is (by the last Prop.), it will have the idea as (in the way of) actually existing, and this idea involves the nature of the external body. In other words, it will have the idea which does not exclude, but postulates the existence or presence of the nature of the external body; therefore the mind (by II. xvi., Coroll. i.) will regard the external body as actually existing, until it is affected, &c. Q.E.D. DEMONSTRATIO: Patet. Nam quamdiu corpus humanum sic affectum est tamdiu mens humana (per propositionem 12 hujus {2p12}) hanc corporis affectionem contemplabitur hoc est (per propositionem praecedentem) ideam habebit modi actu existentis quae naturam corporis externi involvit hoc est ideam quae existentiam vel [mng eqv] praesentiam naturae corporis externi non secludit sed ponit adeoque mens (per corollarium I praecedentis {2p16c1}) corpus externum ut actu existens vel [mng eqv] ut praesens contemplabitur donec afficiatur etc. Q.E.D.
2p17c quamvis non existant nec praesentia 2p17c quamvis non existant nec praesentia [geomap]
Corollary.-The mind is able to regard as present external bodies, by which the human body has once been affected, even though they be no longer in existence or present. COROLLARIUM: Mens corpora externa a quibus corpus humanum semel affectum fuit, quamvis non existant nec praesentia sint, contemplari tamen poterit velut  praesentia essent.
Proof.-When external bodies determine the fluid parts of the human body, so that they often impinge on the softer parts, they change the surface of the last named (Post. v.); hence (Ax. ii., after the Coroll. of Lemma iii.) they are refracted therefrom in a different manner from that which they followed before such change; and, further, when afterwards they impinge on the new surfaces by their own spontaneous movement, they will be refracted in the same manner, as though they had been impelled towards those surfaces by external bodies; consequently, they will, while they continue to be thus refracted, affect the human body in the same manner, whereof the mind (II. xii.) will again take cognizance-that is (II. xvii.), the mind will again regard the external body as present, and will do so, as often as the fluid parts of the human body impinge on the aforesaid surfaces by their own spontaneous motion. Wherefore, although the external bodies, by which the human body has once been affected, be no longer in existence, the mind will nevertheless regard them as present, as often as this action of the body is repeated. Q.E.D. DEMONSTRATIO: Dum corpora externa corporis humani partes fluidas ita determinant ut in molliores spe impingant, earum plana (per postulatum 5 {2post05}) mutant, unde fit (vide axioma 2 post corollarium lemmatis 3 {2a3.2}) ut inde alio modo reflectantur quam antea solebant et ut etiam postea iisdem novis planis spontaneo suo motu occurrendo eodem modo reflectantur ac cum a corporibus externis versus illa plana impulsae sunt et consequenter ut corpus humanum dum sic reflex moveri pergunt, eodem modo afficiant, de quo mens (per propositionem 12 hujus {2p12}) iterum cogitabit hoc est (per propositionem 17 hujus {2p17}) mens iterum corpus externum ut praesens contemplabitur et hoc toties quoties corporis humani partes fluid spontaneo suo motu iisdem planis occurrent. Quare quamvis corpora externa a quibus corpus humanum affectum semel fuit, non existant, mens tamen eadem toties ut praesentia contemplabitur quoties haec corporis actio repetetur. Q.E.D.
2p17s Videmus itaque non sunt veluti praesentia 2p17s Videmus itaque non sunt veluti praesentia
Note.-We thus see how it comes about, as is often the case, that we regard as present many things which are not. It is possible that the same result may be brought about by other causes; but I think it suffices for me here to have indicated one possible explanation, just as well as if I had pointed out the true cause. Indeed, I do not think I am very far from the truth, for all my assumptions are based on postulates, which rest, almost without exception, on experience, that cannot be controverted by those who have shown, as we have, that the human body, as we feel it, exists (Coroll. after II. xiii.). Furthermore (II. vii. Coroll., II. xvi. Coroll. ii.), we clearly understand what is the difference between the idea, say, of Peter, which constitutes the essence of Peter's mind, and the idea of the said Peter, which is in another man, say, Paul. The former directly answers to the essence of Peter's own body, and only implies existence so long as Peter exists; the latter indicates rather the disposition of Paul's body than the nature of Peter, and, therefore, while this disposition of Paul's body lasts, Paul's mind will regard Peter as present to itself, even though he no longer exists. Further, to retain the usual phraseology, the modifications [Lat: affectiones] of the human body, of which the ideas represent external bodies as present to us, we will call the images of things, though they do not recall the figure of things. When the mind regards bodies in this fashion, we say that it imagines. I will here draw attention to the fact, in order to indicate where error lies, that the imaginations of the mind, looked at in themselves, do not contain error. The mind does not err in the mere act of imagining, but only in so far as it is regarded as being without the idea, which excludes the existence of such things as it imagines to be present to it. If the mind, while imagining non-existent things as present to it, is at the same time conscious that they do not really exist, this power of imagination must be set down to the efficacy of its nature, and not to a fault, especially if this faculty of imagination depend solely on its own nature-that is (I. Def. vii.), if this faculty of imagination be free. SCHOLIUM: Videmus itaque qui fieri potest ut ea quae non sunt veluti praesentia contemplemur, ut spe fit. Et fieri potest ut hoc aliis de causis contingat sed mihi hic sufficit ostendisse unam per quam rem sic possim explicare ac si ipsam per veram causam ostendissem nec tamen credo me a vera longe aberrare quandoquidem omnia illa quae sumpsi postulata, vix quicquam continent quod non constet experientia de qua nobis non licet dubitare postquam ostendimus corpus humanum prout ipsum sentimus, existere (vide corollarium post propositionem 13 hujus). praeterea (ex corollario praecedentis et corollario II propositionis 16 hujus) clare intelligimus quaenam sit differentia inter ideam exempli gratia Petri quae essentiam mentis ipsius Petri constituit et inter ideam ipsius Petri quae in alio homine, puta in Paulo, est. Illa enim essentiam corporis ipsius Petri directe explicat nec existentiam involvit nisi quamdiu Petrus existit; haec autem magis constitutionem corporis Pauli quam Petri naturam indicat et ideo durante illa corporis Pauli constitutione mens Pauli quamvis Petrus non existat, ipsum tamen ut sibi praesentem contemplabitur. Porro ut verba usitata retineamus, corporis humani affectiones quarum ideae corpora externa velut nobis praesentia repraesentant, rerum imagines vocabimus tametsi rerum figuras non referunt. Et cum mens hac ratione contemplatur corpora, eandem imaginari dicemus. Atque hic ut quid sit error indicare incipiam, notetis velim mentis imaginationes in se spectatas nihil erroris continere sive mentem ex eo quod imaginatur, non errare sed tantum quatenus consideratur carere idea quae existentiam illarum rerum quas sibi praesentes imaginatur, secludat. Nam si mens dum res non existentes ut sibi praesentes imaginatur, simul sciret res illas revera non existere, hanc sane imaginandi potentiam virtuti suae naturae, non vitio tribueret praesertim si haec imaginandi facultas a sola sua natura penderet hoc est (per definitionem 7 partis I) si haec mentis imaginandi facultas libera esset.
2p18 pluribus corporibus simul 2p18 pluribus corporibus simul [geomap]
PROP. XVIII. If the human body has once been affected by two or more bodies at the same time, when the mind afterwards imagines any of them, it will straightway remember the others also. PROPOSITIO XVIII: Si corpus humanum a duobus vel pluribus corporibus simul affectum fuerit semel, ubi mens postea eorum aliquod imaginabitur, statim et aliorum recordabitur.
Proof.-The mind (II. xvii. Coroll.) imagines any given body, because the human body is affected and rearranged by the impressions from an external body, in the same manner as it is affected when certain of its parts are operated on by the said external body; but (by our hypothesis) the body was then so disposed, that the mind imagined two bodies at once; therefore, it will also in the second case imagine two bodies at once, and the mind, when it imagines one, will straightway remember the other. Q.E.D. DEMONSTRATIO: Mens (per corollarium praecedentis {2p17c}) corpus aliquod ea de causa imaginatur quia scilicet humanum corpus a corporis externi vestigiis eodem modo afficitur disponiturque ac affectum est cum quaedam ejus partes ab ipso corpore externo fuerunt impuls sed (per hypothesin) corpus tum ita fuit dispositum ut mens duo simul corpora imaginaretur; ergo jam etiam duo simul imaginabitur atque mens ubi alterutrum imaginabitur, statim et alterius recordabitur. Q.E.D.
2p18s memoria 2p18s memoria
Note.-We now clearly see what memory is. It is simply a certain association of ideas involving the nature of things outside the human body, which association arises in the mind according to the order and association of the modifications [Lat: affectiones] (affectiones) of the human body. I say, first, it is an association of those ideas only, which involve the nature of things outside the human body: not of ideas which answer to the nature of the said things: ideas of the modifications [Lat: affectiones] of the human body are, strictly speaking (II. xvi.), those which involve the nature both of the human body and of external bodies. I say, secondly, that this association arises according to the order and association of the modifications [Lat: affectiones] of the human body, in order to distinguish it from that association of ideas, which arises from the order of the intellect, whereby the mind perceives things through their primary causes, and which is in all men the same. And hence we can further clearly understand, why the mind from the thought of one thing, should straightway arrive at the thought of another thing, which has no similarity with the first; for instance, from the thought of the word pomum (an apple), a Roman would straightway arrive at the thought of the fruit apple, which has no similitude with the articulate sound in question, nor anything in common with it, except that the body of the man has often been affected by these two things; that is, that the man has often heard the word pomum, while he was looking at the fruit; similarly every man will go on from one thought to another, according as his habit has ordered the images of things in his body. For a soldier, for instance, when he sees the tracks of a horse in sand, will at once pass from the thought of a horse to the thought of a horseman, and thence to the thought of war, &c.; while a countryman will proceed from the thought of a horse to the thought of a plough, a field, &c. Thus every man will follow this or that train of thought, according as he has been in the habit of conjoining and associating the images of things in this or that manner. SCHOLIUM: Hinc clare intelligimus quid sit memoria. Est enim nihil aliud quam quaedam concatenatio idearum naturam rerum quae extra corpus humanum sunt involventium quae in mente fit secundum ordinem et concatenationem affectionum corporis humani. Dico primo concatenationem esse illarum tantum idearum quae naturam rerum quae extra corpus humanum sunt, involvunt, non autem idearum quae earundem rerum naturam explicant. Sunt enim revera (per propositionem 16 hujus) ideae affectionum corporis humani quae tam hujus quam corporum externorum naturam involvunt. Dico secundo hanc concatenationem fieri secundum ordinem et concatenationem affectionum corporis humani ut ipsam distinguerem a concatenatione idearum quae fit secundum ordinem intellectus quo res per primas suas causas mens percipit et qui in omnibus hominibus idem est. Atque hinc porro clare intelligimus cur mens ex cogitatione unius rei statim in alterius rei cogitationem incidat quae nullam cum priore habet similitudinem; ut exempli gratia ex cogitatione vocis pomi homo romanus statim in cogitationem fructus incidet qui nullam cum articulato illo sono habet similitudinem nec aliquid commune nisi quod ejusdem hominis corpus ab his duobus affectum spe fuit hoc est quod ipse homo spe vocem pomum audivit dum ipsum fructum videret et sic unusquisque ex una in aliam cogitationem incidet prout rerum imagines uniuscujusque consuetudo in corpore ordinavit. Nam miles exempli gratia visis in arena equi vestigiis statim ex cogitatione equi in cogitationem equitis et inde in cogitationem belli etc. incidet. At rusticus ex cogitatione equi in cogitationem aratri, agri etc. incidet et sic unusquisque prout rerum imagines consuevit hoc vel alio modo jungere et concatenare, ex una in hanc vel aliam incidet cogitationem.
2p19 Mens nisi per affectionum 2p19 Mens nisi per affectionum [geomap]
PROP. XIX. The human mind has no knowledge of the body, and does not know it to exist, save through the ideas of the modifications [Lat: affectiones] whereby the body is affected. PROPOSITIO XIX: Mens humana ipsum humanum corpus non cognoscit nec ipsum existere scit nisi per ideas affectionum quibus corpus afficitur.
Proof.-The human mind is the very idea or knowledge of the human body (II. xiii.), which (II. ix.) is in God, in so far as he is regarded as affected by another idea of a particular thing actually existing: or, inasmuch as (Post. iv.) the human body stands in need of very many bodies whereby it is, as it were, continually regenerated; and the order and connection of ideas is the same as the order and connection of causes (II. vii.); this idea will therefore be in God, in so far as he is regarded as affected by the ideas of very many particular things. Thus God has the idea of the human body, or knows the human body, in so far as he is affected by very many other ideas, and not in so far as he constitutes the nature of the human mind; that is (by II. xi. Coroll.), the human mind does not know the human body. But the ideas of the modifications [Lat: affectiones] of body are in God, in so far as he constitutes the nature of the human mind, or the human mind perceives those modifications [Lat: affectiones] (II. xii.), and consequently (II. xvi.) the human body itself, and as actually existing; therefore the mind perceives thus far only the human body. Q.E.D. DEMONSTRATIO: Mens enim humana est ipsa idea sive [mng eqv]   cognitio corporis humani (per propositionem 13 hujus {2p09}) in Deo quidem est quatenus alia rei singularis idea affectus consideraturvel [mng eqv] quia (per postulatum 4 {2post04}) corpus humanum plurimis corporibus indiget a quibus continuo quasi regeneratur et ordo et connexio idearum idem est (per propositionem 7 hujus {2p07}) ac ordo et connexio causarum, erit haec idea in Deo quatenus plurimarum rerum singularium ideis affectus consideratur. Deus itaque ideam corporis humani habet sive [mng eqv]   corpus humanum cognoscit quatenus plurimis aliis ideis affectus est et non quatenus naturam humanae mentis constituit hoc est [hence] (per corollarium propositionis 11 hujus {2p11}) mens humana corpus humanum non cognoscit. At ideae affectionum corporis in Deo sunt quatenus humanae mentis naturam constituit sive [mng eqv]   mens humana easdem affectiones percipit (per propositionem 12 hujus {2p12}) et consequenter (per propositionem 16 hujus {2p16}) ipsum corpus humanum idque (per propositionem 17 hujus {2p17}) ut actu existens; percipit ergo eatenus tantum mens humana ipsum humanum corpus. Q.E.D.
2p20 Mentis humanae datur etiam in Deo idea 2p20 Mentis humanae datur etiam in Deo idea [geomap]
PROP. XX. The idea or knowledge of the human mind is also in God, following in God in the same manner, and being referred to God in the same manner, as the idea or knowledge of the human body. PROPOSITIO XX: Mentis humanae datur etiam in Deo idea sive [mng eqv]   cognitio quae in Deo eodem modo sequitur et ad Deum eodem modo refertur ac idea sive [mng eqv] cognitio corporis humani.
Proof.-Thought is an attribute of God (II. i.); therefore (II. iii.) there must necessarily be in God the idea both of thought itself and of all its modifications [Lat: affectiones], consequently also of the human mind (II. xi.). Further, this idea or knowledge of the mind does not follow from God, in so far as he is infinite, but in so far as he is affected by another idea of an individual thing (II. ix.). But (II. vii.) the order and connection of ideas is the same as the order and connection of causes; therefore this idea or knowledge of the mind is in God and is referred to God, in the same manner as the idea or knowledge of the body. Q.E.D. DEMONSTRATIO: Cogitatio attributum Dei est (per propositionem 1 hujus {2p01}) adeoque (per propositionem 3 hujus {2p03}) tam ejus quam omnium ejus affectionum et consequenter (per propositionem 11 hujus {2p11}) mentis etiam humanae debet necessario in Deo dari idea. Deinde haec mentis idea sive [mng eqv] cognitio non sequitur in Deo dari quatenus infinitus sed quatenus alia rei singularis idea affectus est(per propositionem 9 hujus {2p09}). Sed ordo et connexio idearum idem est ac ordo et connexio causarum (per propositionem 7 hujus {2p07}); sequitur ergo haec mentis idea sive [mng eqv]   cognitio in Deo et ad Deum eodem modo refertur ac idea sive [mng eqv] cognitio corporis. Q.E.D.
2p21 mentis idea menti mens corpori 2p21 mentis idea menti mens corpori [geomap]
PROP. XXI. This idea of the mind is united to the mind in the same way as the mind is united to the body. PROPOSITIO XXI: Haec mentis idea eodem modo unita est menti ac ipsa mens unita est corpori.
Proof.-That the mind is united to the body we have shown from the fact, that the body is the object of the mind (II. xii. and xiii.); and so for the same reason the idea of the mind must be united with its object, that is, with the mind in the same manner as the mind is united to the body. Q.E.D. DEMONSTRATIO: Mentem unitam esse corpori ex eo ostendimus quod scilicet corpus mentis sit objectum (vide propositiones 12 {2p12} et 13 {2p13} hujus) adeoque per eandem illam rationem idea mentis cum suo objecto hoc est cum ipsa mente eodem modo unita esse debet ac ipsa mens unita est corpori. Q.E.D.
2p21s mentem et corpus unum 2p21s mentem et corpus unum
Note.-This proposition is comprehended much more clearly from what we have said in the note to II. vii. We there showed that the idea of body and body, that is, mind and body (II. xiii.), are one and the same individual conceived now under the attribute of thought, now under the attribute of extension; wherefore the idea of the mind and the mind itself are one and the same thing, which is conceived under one and the same attribute, namely, thought. The idea of the mind, I repeat, and the mind itself are in God by the same necessity and follow from him from the same power of thinking. Strictly speaking, the idea of the mind, that is, the idea of an idea, is nothing but the distinctive quality (forma) of the idea in so far as it is conceived as a mode of thought without reference to the object; if a man knows anything, he, by that very fact, knows that he knows it, and at the same time knows that he knows that he knows it, and so on to infinity. But I will treat of this hereafter. SCHOLIUM: Haec propositio longe clarius intelligitur ex dictis in scholio propositionis 7 hujus; ibi enim ostendimus corporis ideam et corpus hoc est (per propositionem 13 hujus) mentem et corpus unum et idem esse individuum quod jam sub cogitationis jam sub extensionis attributo concipitur; quare mentis idea et ipsa mens una eademque est res quae sub uno eodemque attributo nempe cogitationis concipitur. Mentis inquam idea et ipsa mens in Deo eadem necessitate ex eadem cogitandi potentia sequuntur dari. Nam revera idea mentis hoc est idea ideae nihil aliud est quam forma ideae quatenus haec ut modus cogitandi absque relatione ad objectum consideratur; simulac enim quis aliquid scit, eo ipso scit se id scire et simul scit se scire quod scit et sic in infinitum. Sed de his postea.
2p22 Mens corporis affectiones etiam affectionum ideas 2p22 Mens corporis affectiones etiam affectionum ideas [geomap]
PROP. XXII. The human mind perceives not only the modifications [Lat: affectiones] of the body, but also the ideas of such modifications [Lat: affectiones]. PROPOSITIO XXII: Mens humana non tantum corporis affectiones sed etiam harum affectionum ideas percipit.
Proof.-The ideas of the ideas of modifications [Lat: affectiones] follow in God in the same manner, and are referred to God in the same manner, as the ideas of the said modifications [Lat: affectiones]. This is proved in the same way as II. xx. But the ideas of the modifications [Lat: affectiones] of the body are in the human mind (II. xii.), that is, in God, in so far as he constitutes the essence of the human mind; therefore the ideas of these ideas will be in God, in so far as he has the knowledge or idea of the human mind, that is (II. xxi.), they will be in the human mind itself, which therefore perceives not only the modifications [Lat: affectiones] of the body, but also the ideas of such modifications [Lat: affectiones]. Q.E.D. DEMONSTRATIO: Affectionum idearum ideae in Deo eodem modo sequuntur et ad Deum eodem modo referuntur ac ipsae affectionum ide; quod eodem modo demonstratur ac propositio 20 {2p20} hujus. At ideae affectionum corporis in mente humana sunt (per propositionem 12 hujus {2p12}) hoc est (per corollarium propositionis 11 hujus {2p11}) in Deo quatenus humanae mentis essentiam constituit; ergo harum idearum ideae in Deo erunt quatenus humanae mentis cognitionem sive [mng eqv]   ideam habet hoc est (per propositionem 21 hujus {2p21}) in ipsa mente humana quae propterea non tantum corporis affectiones sed earum etiam ideas percipit. Q.E.D.
2p23 Mens se non cognoscit nisi 2p23 Mens se non cognoscit nisi [geomap]
PROP. XXIII. The mind does not know itself, except in so far as it perceives the ideas of the modifications [Lat: affectiones] of the body. PROPOSITIO XXIII: Mens se ipsam non cognoscit nisi quatenus corporis affectionum ideas percipit.
Proof.-The idea or knowledge of the mind (II. xx.) follows in God in the same manner, and is referred to God in the same manner, as the idea or knowledge of the body. But since (II. xix.) the human mind does not know the human body itself, that is (II. xi. Coroll.), since the knowledge of the human body is not referred to God, in so far as he constitutes the nature of the human mind; therefore, neither is the knowledge of the mind referred to God, in so far as he constitutes the essence of the human mind; therefore (by the same Coroll. II. xi.), the human mind thus far has no knowledge of itself. Further the ideas of the modifications [Lat: affectiones], whereby the body is affected, involve the nature of the human body itself (II. xvi.), that is (II. xiii.), they agree with the nature of the mind; wherefore the knowledge of these ideas necessarily involves knowledge of the mind; but (by the last Prop.) the knowledge of these ideas is in the human mind itself; wherefore the human mind thus far only has knowledge of itself. Q.E.D. DEMONSTRATIO: Mentis idea sive [mng eqv]   cognitio (per propositionem 20 hujus {2p20}) in Deo eodem modo sequitur et ad Deum eodem modo refertur ac corporis idea sive [mng eqv]  cognitio. At quoniam (per propositionem 19 hujus {2p19}) mens humana ipsum humanum corpus non cognoscit hoc est (per corollarium propositionis 11 hujus {2p11}) quoniam cognitio corporis humani ad Deum non refertur quatenus humanae mentis naturam constituit; ergo nec cognitio mentis ad Deum refertur quatenus essentiam mentis humanae constituitatque adeo (per idem corollarium propositionis 11 hujus {2p11}) mens humana eatenus se ipsam non cognoscit. Deinde affectionum quibus corpus afficitur ideae naturam ipsius corporis humani involvunt (per propositionem 16 hujus {2p16}) hoc est (per propositionem 13 hujus) conveniunt; quare harum idearum cognitio cognitionem mentis necessario involvet; at (per propositionem praecedentem) harum idearum cognitio in ipsa humana mente est; ergo mens humana eatenus tantum se ipsam novit. Q.E.D.
2p24 Mens partium corpus non involvit 2p24 Mens partium corpus non involvit [geomap]
PROP. XXIV. The human mind does not involve an adequate knowledge of the parts composing the human body. PROPOSITIO XXIV: Mens humana partium corpus humanum componentium adaequatam cognitionem non involvit.
Proof.-The parts composing the human body do not belong to the essence of that body, except in so far as they communicate their motions to one another in a certain fixed relation (Def. after Lemma iii.), not in so far as they can be regarded as individuals without relation to the human body. The parts of the human body are highly complex individuals (Post. i.), whose parts (Lemma iv.) can be separated from the human body without in any way destroying the nature and distinctive quality of the latter, and they can communicate their motions (Ax. i., after Lemma iii.) to other bodies in another relation; therefore (II. iii.) the idea or knowledge of each part will be in God, inasmuch (II. ix.) as he is regarded as affected by another idea of a particular thing, which particular thing is prior in the order of nature to the aforesaid part (II. vii.). We may affirm the same thing of each part of each individual composing the human body; therefore, the knowledge of each part composing the human body is in God, in so far as he is affected by very many ideas of things, and not in so far as he has the idea of the human body only, in other words, the idea which constitutes the nature of the human mind (II. xiii); therefore (II. xi. Coroll.), the human mind does not involve an adequate knowledge of the human body. Q.E.D. DEMONSTRATIO: Partes corpus humanum componentes ad essentiam ipsius corporis non pertinent nisi quatenus motus suos certa quadam ratione invicem communicant (vide definitionem post corollarium lemmatis 3 {2d08}) et non quatenus ut individua absque relatione ad humanum corpus considerari possunt. Sunt enim partes humani corporis (per postulatum 1 {2post01}) valde composita individua quorum partes (per lemma 4 {2L04}) a corpore humano, servata omnino ejusdem natura et forma, segregari possunt motusque suos (vide axioma 1 post lemma 3 {2a3.1}) aliis corporibus alia ratione communicare adeoque (per propositionem 3 hujus {2p03}) cujuscunque partis idea sive [mng eqv]  cognitio in Deo erit et quidem (per propositionem 9 hujus {2p09}) quatenus affectus consideratur alia idea rei singularis, quae res singularis ipsa parte ordine naturae prior est (per propositionem 7 hujus {2p07}). Quod idem praeterea etiam de quacunque parte ipsius individui corpus humanum componentis est dicendum adeoque cujuscunque partis corpus humanum componentis cognitio in Deo est quatenus plurimis rerum ideis affectus est et non quatenus corporis humani tantum habet ideam hoc est (per propositionem 13 hujus {2p13}) ideam quae humanae mentis naturam constituit atque adeo (per corollarium propositionis 11 hujus {2p11c}) humana mens partium corpus humanum componentium adaequatam cognitionem non involvit. Q.E.D.
2p25 corporis externi cognitionem non involvit 2p25 corporis externi cognitionem non involvit [geomap]
PROP. XXV. The idea of each modification [Lat: affectiones] of the human body does not involve an adequate knowledge of the external body. PROPOSITIO XXV: Idea cujuscunque affectionis corporis humani adaequatam corporis externi cognitionem non involvit.
Proof.-We have shown that the idea of a modification [Lat: affectiones] of the human body involves the nature of an external body, in so far as that external body conditions the human body in a given manner. But, in so far as the external body is an individual, which has no reference to the human body, the knowledge or idea thereof is in God (II. ix.), in so far as God is regarded as affected by the idea of a further thing, which (II. vii.) is naturally prior to the said external body. Wherefore an adequate knowledge of the external body is not in God, in so far as he has the idea of the modification [Lat: affectiones] of the human body; in other words, the idea of the modification [Lat: affectiones] of the human body does not involve an adequate knowledge of the external body. Q.E.D. DEMONSTRATIO: ideam affectionis corporis humani eatenus corporis externi naturam involvere ostendimus (vide propositionem 16 hujus {2p16}) quatenus externum ipsum humanum corpus certo quodam modo determinat. At quatenus externum corpus individuum est quod ad corpus humanum non refertur, ejus idea sive [mng eqv]  cognitio in Deo  est (per propositionem 9 hujus {2p09}) quatenus Deus affectus consideratur alterius rei idea quae (per propositionem 7 hujus {2p07}) ipso corpore externo prior est natura. Quare corporis externi adaequata cognitio in Deo non est quatenus ideam affectionis humani corporis habet sive [mng eqv]  idea affectionis corporis humani adaequatam corporis externi cognitionem non involvit. Q.E.D.
2p26 mens percipit per ideas affectionum 2p26 mens percipit per ideas affectionum [geomap]
PROP. XXVI. The human mind does not perceive any external body as actually existing, except through the ideas of the modifications [Lat: affectiones] of its own body. PROPOSITIO XXVI: Mens humana nullum corpus externum ut actu existens percipit nisi per ideas affectionum sui corporis.
Proof.-If the human body is in no way affected by a given external body, then (II. vii.) neither is the idea of the human body, in other words, the human mind, affected in any way by the idea of the existence of the said external body, nor does it in any manner perceive its existence. But, in so far as the human body is affected in any way by a given external body, thus far (II. xvi. and Coroll.) it perceives that external body. Q.E.D. DEMONSTRATIO: Si a corpore aliquo externo corpus humanum nullo modo affectum est, ergo (per propositionem 7 hujus {2p07}) nec idea corporis humani hoc est (per propositionem 13 hujus {2p13}) nec mens humana idea existentiae illius corporis ullo etiam modo affecta est sive [prf eqv]  existentiam illius corporis externi ullo modo percipit. At quatenus corpus humanum a corpore aliquo externo aliquo modo afficitur eatenus (per propositionem 16 hujus  {2p16} cum corollario I ejusdem {2p16c1}) corpus externum percipit. Q.E.D.
2p26c corpus imaginatur cognitionem non habet 2p26c corpus imaginatur cognitionem non habet [geomap]
Corollary.-In so far as the human mind imagines an external body, it has not an adequate knowledge thereof. COROLLARIUM {2p26}: quatenus mens humana corpus externum imaginatur eatenus adaequatam ejus cognitionem non habet.
Proof.-When the human mind regards external bodies through the ideas of the modifications [Lat: affectiones] of its own body, we say that it imagines (see II. xvii. note); now the mind (by II. xvi) can only imagine external bodies as actually existing. Therefore (by II. xxv.), in so far as the mind imagines external bodies, it has not an adequate knowledge of them. Q.E.D. DEMONSTRATIO: Cum mens humana per ideas affectionum sui corporis corpora externa contemplatur, eandem tum imaginari dicimus (vide scholium propositionis 17 hujus {non-deductive reference}) nec mens alia ratione (per propositionem praecedentem {2p26}) corpora externa ut actu existentia imaginari potest. Atque adeo (per propositionem 25 hujus {2p25}) quatenus mens corpora externa imaginatur, eorum adaequatam cognitionem non habet. Q.E.D.
2p27 Idea affectionis corporis cognitionem non involvit 2p27 Idea affectionis corporis cognitionem non involvit [geomap]
PROP. XXVII. The idea of each modification [Lat: affectiones] of the human body does not involve an adequate knowledge of the human body itself. PROPOSITIO XXVII: Idea cujuscunque affectionis corporis humani adaequatam ipsius humani corporis cognitionem non involvit.
Proof.-Every idea of a modification [Lat: affectiones] of the human body involves the nature of the human body, in so far as the human body is regarded as affected in a given manner (II. xvi.). But, inasmuch as the human body is an individual which may be affected in many other ways, the idea of the said modification [Lat: affectiones], &c. Q.E.D. DEMONSTRATIO: Quaelibet idea cujuscunque affectionis humani corporis eatenus naturam corporis humani involvit quatenus ipsum humanum corpus certo quodam modo affici consideratur (vide propositionem 16 hujus {2p16}). At quatenus corpus humanum individuum est quod multis aliis modis affici potest, ejus idea etc. Vide demonstrationem propositionis 25 hujus {2p25}.
2p28 ideae affectionum corporis ad mentem referuntur non clarae 2p28 ideae affectionum corporis ad mentem referuntur non clarae [geomap]
PROP. XXVIII. The ideas of the modifications [Lat: affectiones] of the human body, in so far as they have reference only to the human mind, are not clear and distinct, but confused. PROPOSITIO XXVIII: Ideae affectionum corporis humani quatenus ad humanam mentem tantum referuntur, non sunt clarae et distinctae sed confusae.
Proof.-The ideas of the modifications [Lat: affectiones] of the human body involve the nature both of the human body and of external bodies (II. xvi.); they must involve the nature not only of the human body but also of its parts; for the modifications [Lat: affectiones] are modes (Post. iii.), whereby the parts of the human body, and, consequently, the human body as a whole are affected. But (by II. xxiv., xxv.) the adequate knowledge of external bodies, as also of the parts composing the human body, is not in God, in so far as he is regarded as affected by the human mind, but in so far as he is regarded as affected by other ideas. These ideas of modifications [Lat: affectiones], in so far as they are referred to the human mind alone, are as consequences without premisses, in other words, confused ideas. Q.E.D. DEMONSTRATIO: Ideae enim affectionum corporis humani tam corporum externorum quam ipsius humani corporis naturam involvunt (per propositionem 16 hujus {2p16}) nec tantum corporis humani sed ejus etiam partium naturam involvere debent; affectiones namque modi sunt (per postulatum 3 {2post3}) quibus partes corporis humani et consequenter totum corpus afficitur. At (per propositiones 24 {2p24} et 25 hujus {2p25}) corporum externorum adaequata cognitio ut et partium corpus humanum componentium in Deo non est quatenus humana mente sed quatenus aliis ideis affectus consideratur. Sunt ergo hae affectionum ideae quatenus ad solam humanam mentem referuntur, veluti consequenti absque praemissis hoc est [mng eqv] (ut per se notum) ideae confusae. Q.E.D.
2p28s Idea naturam mentis humanae non clara 2p28s Idea naturam mentis humanae non clara
Note.-The idea which constitutes the nature of the human mind is, in the same manner, proved not to be, when considered in itself alone, clear and distinct; as also is the case with the idea of the human mind, and the ideas of the ideas of the modifications [Lat: affectiones] of the human body, in so far as they are referred to the mind only, as everyone may easily see. SCHOLIUM: Idea quae naturam mentis humanae constituit, demonstratur eodem modo non esse, in se sola considerata, clara et distincta, ut etiam idea mentis humanae et ideae idearum affectionum corporis humani quatenus ad solam mentem referuntur, quod unusquisque facile videre potest.
2p29 Idea ideae affectionis cognitionem non involvit 2p29 Idea ideae affectionis cognitionem non involvit [geomap]
PROP. XXIX. The idea of the idea of each modification [Lat: affectiones] of the human body does not involve an adequate knowledge of the human mind. PROPOSITIO XXIX: Idea ideae cujuscunque affectionis corporis humani adaequatam humanae mentis cognitionem non involvit.
Proof.-The idea of a modification [Lat: affectiones] of the human body (II. xxvii.) does not involve an adequate knowledge of the said body, in other words, does not adequately express its nature; that is (II. xiii.) it does not agree with the nature of the mind adequately; therefore (I. Ax. vi) the idea of this idea does not adequately express the nature of the human mind, or does not involve an adequate knowledge thereof. DEMONSTRATIO: Idea enim affectionis corporis humani (per propositionem 27 hujus {2p27}) adaequatam ipsius corporis cognitionem non involvit sive [mng eqv]  ejus naturam adaequate non exprimit hoc est [mng eqv]  per propositionem 13 hujus {2p23}) cum natura mentis non convenit adaequate adeoque [mng eqv] (per axioma 6 partis I {1a06}) hujus ideae idea adaequate humanae mentis naturam non exprimit sive [mng eqv]  adaequatam ejus cognitionem non involvit. Q.E.D.
2p29c mentem confusam tantum cognitionem 2p29c mentem confusam tantum cognitionem [geomap]
Corollary.-Hence it follows that the human mind, when it perceives things after the common order of nature, has not an adequate but only a confused and fragmentary knowledge of itself, of its own body, and of external bodies. For the mind does not know itself, except in so far as it perceives the ideas of the modifications [Lat: affectiones] of body (II. xxiii.). It only perceives its own body (II. xix.) through the ideas of the modifications [Lat: affectiones], and only perceives external bodies through the same means; thus, in so far as it has such ideas of modification [Lat: affectiones], it has not an adequate knowledge of itself (II. xxix.), nor of its own body (II. xxvii.), nor of external bodies (II. xxv.), but only a fragmentary and confused knowledge thereof (II. xxviii. and note). Q.E.D. COROLLARIUM: Hinc sequitur mentem humanam quoties ex communi naturae ordine res percipit, nec sui ipsius nec sui corporis nec corporum externorum adaequatam sed confusam tantum et mutilatam habere cognitionem. Nam mens se ipsam non cognoscit nisi quatenus ideas affectionum corporis percipit (per propositionem 23 hujus {2p23}). Corpus autem suum (per propositionem 19 hujus {2p19}) non percipit nisi per ipsas affectionum ideas per quas etiam tantum (per propositionem 26 hujus {2p26}) corpora externa percipit atque adeo quatenus eas habet, nec sui ipsius (per propositionem 29 hujus {2p29}) nec sui corporis (per propositionem 27 hujus {2p27}) nec corporum externorum (per propositionem 25 hujus {2p25}) habet adaequatam cognitionem sed tantum (per propositionem 28 hujus {2p28} cum ejus scholio {non-deductive reference}) mutilatam et confusam. Q.E.D.
2p29s rerum nempe fortuito occursu 2p29s rerum nempe fortuito occursu
Note.-I say expressly, that the mind has not an adequate but only a confused knowledge of itself, its own body, and of external bodies, whenever it perceives things after the common order of nature; that is, whenever it is determined from without, namely, by the fortuitous play of circumstance, to regard this or that; not at such times as it is determined from within, that is, by the fact of regarding several things at once, to understand their points of agreement, difference, and contrast. Whenever it is determined in anywise from within, it regards things clearly and distinctly, as I will show below. SCHOLIUM: Dico expresse quod mens nec sui ipsius nec sui corporis nec corporum externorum adaequatam sed confusam tantum et mutilatam cognitionem habeat quoties ex communi naturae ordine res percipit hoc est quoties externe, ex rerum nempe fortuito occursu, determinatur ad hoc vel illud contemplandum et non quoties interne, ex eo scilicet quod res plures simul contemplatur, determinatur ad earundem convenientias, differentias et oppugnantias intelligendum; quoties enim hoc vel alio modo interne disponitur, tum res clare et distincte contemplatur, ut infra ostendam.
2p30 duratione inadaequatam cognitionem 2p30 duratione inadaequatam cognitionem [geomap]
PROP. XXX. We can only have a very inadequate knowledge of the duration of our body. PROPOSITIO XXX: Nos de duratione nostri corporis nullam nisi admodum inadaequatam cognitionem habere possumus.
Proof.-The duration of our body does not depend on its essence (II. Ax. i.), nor on the absolute nature of God (I. xxi.). But (I. xxviii.) it is conditioned to exist and operate by causes, which in their turn are conditioned to exist and operate in a fixed and definite relation by other causes, these last again being conditioned by others, and so on to infinity. The duration of our body therefore depends on the common order of nature, or the constitution of things. Now, however a thing may be constituted, the adequate knowledge of that thing is in God, in so far as he has the ideas of all things, and not in so far as he has the idea of the human body only. (II. ix. Coroll.) Wherefore the knowledge of the duration of our body is in God very inadequate, in so far as he is only regarded as constituting the nature of the human mind; that is (II. xi. Coroll.), this knowledge is very inadequate to our mind. Q.E.D. DEMONSTRATIO: Nostri corporis duratio ab ejus essentia non dependet (per axioma 1 hujus {2a1.1}) nec etiam ab absoluta Dei natura (per propositionem 21 partis I {1p25}). Sed (per propositionem 28 partis I {1p28}) ad existendum et operandum determinatura talibus causis quae etiam ab aliis determinatae sunt ad existendum et operandum certa ac determinata ratione et hae iterum ab aliis et sic in infinitum. Nostri igitur corporis duratio a communi naturae ordine et rerum constitutione pendet. Qua autem ratione constitut sint, ejus rei adaequata cognitio datur in Deo quatenus earum omnium ideas et non quatenus tantum humani corporis ideam habet (per corollarium propositionis 9 hujus {2p09c}); quare cognitio durationis nostri corporis est in Deo admodum inadaequata quatenus tantum naturam mentis humanae constituere consideratur hoc est (per corollarium propositionis 11 hujus {2p11c}) haec cognitio est in nostra mente admodum inadaequata. Q.E.D.
2p31 duratione rerum extra nos inadaequatam cognitionem 2p31 duratione rerum extra nos inadaequatam cognitionem [geomap]
PROP. XXmaps/2p31c omnes res contingentes et corruptibiles.html XI. We can only have a very inadequate knowledge of the duration of particular things external to ourselves. PROPOSITIO XXXI: Nos de duratione rerum  singularium quae extra nos sunt, nullam nisi admodum inadaequatam cognitionem habere  possumus.
Proof.-Every particular thing, like the human body, must be conditioned by another particular thing to exist and operate in a fixed and definite relation; this other particular thing must likewise be conditioned by a third, and so on to infinity. (I. xxviii.) As we have shown in the foregoing proposition, from this common property of particular things, we have only a very inadequate knowledge of the duration of our body; we must draw a similar conclusion with regard to the duration of particular things, namely, that we can only have a very inadequate knowledge of the duration thereof. Q.E.D. DEMONSTRATIO: Unaquque enim res singularis sicuti humanum corpus ab alia re singulari determinari debet ad existendum et operandum certa ac determinata ratione et haec iterum ab alia et sic in infinitum(per propositionem 28 partis I {1p28}). Cum autem ex hac communi rerum singularium proprietate in praecedenti propositione demonstraverimus nos de duratione nostri corporis non nisi admodum inadaequatam cognitionem habere, ergo hoc idem de rerum singularium duratione erit concludendum quod scilicet ejus non nisi admodum inadaequatam cognitionem habere possumus. Q.E.D.
2p31c omnes res contingentes et corruptibiles 2p31c omnes res contingentes et corruptibiles [geomap]
Corollary.-Hence it follows that all particular things are contingent and perishable. For we can have no adequate idea of their duration (by the last Prop.), and this is what we must understand by the contingency and perishableness of things. (I. xxxiii., Note i.) For (I. xxix.), except in this sense, nothing is contingent. COROLLARIUM {2p31}: Hinc sequitur omnes res particulares contingentes et corruptibiles esse. Nam de earum duratione nullam adaequatam cognitionem habere possumus (per propositionem praecedentem {2p31}) et hoc est id quod per rerum contingentiam et corruptionis possibilitatem nobis est intelligendum (vide scholium I propositionis 33 partis I {non-deductive reference}). Nam (per propositionem 29 partis I {1p29}) praeter hoc nullum datur contingens.
2p32 ideae Deum referuntur verae 2p32 ideae Deum referuntur verae [geomap]
PROP. XXXII. All ideas, in so far as they are referred to God, are true. PROPOSITIO XXXII: Omnes ideae quatenus ad Deum referuntur, verae sunt.
Proof.-All ideas which are in God agree in every respect with their objects (II. vii. Coroll.), therefore (I. Ax. vi.) they are all true. Q.E.D. DEMONSTRATIO: Omnes enim ideae quae in Deo sunt, cum suis ideatis omnino conveniunt (per corollarium propositionis 7 hujus {2p07}) adeoque (per axioma 6 partis I {1a06}) omnes verae sunt. Q.E.D.
2p33 Nihil positivum falsae 2p33 Nihil positivum falsae [geomap]
PROP. XXXIII. There is nothing positive in ideas, which causes them to be called false. PROPOSITIO XXXIII: Nihil in ideis positivum est propter quod falsae dicuntur.
Proof.-If this be denied, conceive, if possible, a positive mode of thinking, which should constitute the distinctive quality of falsehood. Such a mode of thinking cannot be in God (II. xxxii.); external to God it cannot be or be conceived (I. xv.). Therefore there is nothing positive in ideas which causes them to be called false. Q.E.D. DEMONSTRATIO: Si negas, concipe si fieri potest, modum positivum cogitandi qui formam erroris sive [mng eqv]  falsitatis constituat. Hic cogitandi modus non potest esse in Deo (per propositionem praecedentem {2p32}); extra Deum autem etiam nec esse nec concipi potest (per propositionem 15 partis I {1p15}). Atque adeo nihil potest dari positivum in ideis propter quod falsae dicuntur. Q.E.D.
2p34 absoluta sive adaequata et perfecta vera 2p34 absoluta sive adaequata et perfecta vera [geomap]
PROP. XXXIV. Every idea, which in us is absolute or adequate and perfect, is true. PROPOSITIO XXXIV: Omnis idea quae in nobis est absoluta sive [prf eqv]  adaequata et [prf eqv] perfecta, vera est.
Proof.-When we say that an idea in us is adequate and perfect, we say, in other words (II. xi. Coroll.), that the idea is adequate and perfect in God, in so far as he constitutes the essence of our mind; consequently (II. xxxii.), we say that such an idea is true. Q.E.D. DEMONSTRATIO: Cum dicimus dari in nobis ideam adaequatam et perfectam, nihil aliud dicimus (per corollarium propositionis 11 hujus {2p11}) quam quod in Deo quatenus nostrae mentis essentiam constituit, detur idea adaequata et perfecta et consequenter (per propositionem 32 hujus {2p32}) nihil aliud dicimus quam quod talis idea sit vera. Q.E.D.
2p35 Falsitas consistit privatione 2p35 Falsitas consistit privatione [geomap]
PROP. XXXV. Falsity consists in the privation of knowledge, which inadequate, fragmentary, or confused ideas involve. PROPOSITIO XXXV: Falsitas consistit in cognitionis privatione quam ideae inadaequatae sive [mng eqv]  mutilatae et confusae involvunt.
Proof.-There is nothing positive in ideas, which causes them to be called false (II. xxxiii.); but falsity cannot consist in absolute privation (for minds, not bodies, are said to err and to be mistaken), neither can it consist in absolute ignorance, for ignorance and error are not identical; wherefore it consists in the privation of knowledge, which inadequate, fragmentary, or confused ideas involve. Q.E.D. DEMONSTRATIO: Nihil in ideis positivum datur quod falsitatis formam constituat (per propositionem 33 hujus {2p33}); at falsitas in absoluta privatione consistere nequit (mentes enim, non corpora errare nec falli dicuntur) neque etiam in absoluta ignorantia; diversa enim sunt ignorare et errare; quare in cognitionis privatione quam rerum inadaequata cognitio sive [mng eqv]  ideae inadaequatae et confusae involvunt, consistit. Q.E.D.
2p35s exemplum liberos 2p35s exemplum liberos
Note.-In the note to II. xvii. I explained how error consists in the privation of knowledge, but in order to throw more light on the subject I will give an example. For instance, men are mistaken in thinking themselves free; their opinion is made up of consciousness of their own actions, and ignorance of the causes by which they are conditioned. Their idea of freedom, therefore, is simply their ignorance of any cause for their operations. As for their saying that human actions depend on the will, this is a mere phrase without any idea to correspond thereto. What the will is, and how it moves the body, they none of them know; those who boast of such knowledge, and feign dwellings and habitations for the soul, are wont to provoke either laughter or disgust. So, again, when we look at the sun, we imagine that it is distant from us about two hundred feet; this error does not lie solely in this fancy, but in the fact that, while we thus imagine, we do not know the sun's true distance or the cause of the fancy. For although we afterwards learn, that the sun is distant from us more than six hundred of the earth's diameters, we none the less shall fancy it to be near; for we do not imagine the sun as near us, because we are ignorant of its true distance, but because the modification [Lat: affectiones] of our body involves the essence of the sun, in so far as our said body is affected thereby. SCHOLIUM: In scholio propositionis 17 hujus partis explicui qua ratione error in cognitionis privatione consistit sed ad uberiorem hujus rei explicationem exemplum dabo nempe falluntur homines quod se liberos esse putant, quae opinio in hoc solo consistit quod suarum actionum sint conscii et ignari causarum a quibus determinantur. Haec ergo est eorum libertatis idea quod suarum actionum nullam cognoscant causam. Nam quod aiunt humanas actiones a voluntate pendere, verba sunt quorum nullam habent ideam. Quid enim voluntas sit et quomodo moveat corpus, ignorant omnes; qui aliud jactant et animae sedes et habitacula fingunt, vel risum vel nauseam movere solent. Sic cum solem intuemur, eum ducentos circiter pedes a nobis distare imaginamur, qui error in hac sola imaginatione non consistit sed in eo quod dum ipsum sic imaginamur, veram ejus distantiam et hujus imaginationis causam ignoramus. Nam tametsi postea cognoscamus eundem ultra 600 terr diametros a nobis distare, ipsum nihilominus prope adesse imaginabimur; non enim solem adeo propinquum imaginamur propterea quod veram ejus distantiam ignoramus sed propterea quod affectio nostri corporis essentiam solis involvit quatenus ipsum corpus ab eodem afficitur.
2p36 ideae inadaequatae et confusae eadem necessitate 2p36 ideae inadaequatae et confusae eadem necessitate [geomap]
PROP. XXXVI. Inadequate and confused ideas follow by the same necessity, as adequate or clear and distinct ideas. PROPOSITIO XXXVI: Ideae inadaequatae et confusae eadem necessitate consequuntur ac adaequatae sive [mng eqv]  clarae  ac distinctae ideae.
Proof.-All ideas are in God (I. xv.), and in so far as they are referred to God are true (II. xxxii.) and (II. vii. Coroll.) adequate; therefore there are no ideas confused or inadequate, except in respect to a particular mind (cf. II. xxiv. and xxviii.); therefore all ideas, whether adequate or inadequate, follow by the same necessity (II. vi.). Q.E.D. DEMONSTRATIO: Ideae omnes in Deo sunt (per propositionem 15 partis I {1p15}) et quatenus ad  Deum referuntur, sunt verae (per propositionem 32 hujus {2p32}) et (per corollarium propositionis 7 hujus) adaequatae adeoque nullae inadaequatae nec confusae sunt nisi quatenus ad singularem alicujus mentem referuntur (qua de re vide propositiones 24 {2p24} et 28 {2p28} hujus) adeoque omnes tam adaequatae quam inadaequatae eadem necessitate (per corollarium propositionis 6 hujus {2p06c}) consequuntur. Q.E.D.
2p37 commune nullius essentiam 2p37 commune nullius essentiam [geomap]
PROP. XXXVII. That which is common to all (cf. Lemma II., above), and which is equally in a part and in the whole, does not constitute the essence of any particular thing. PROPOSITIO XXXVII: Id quod omnibus commune (de his vide supra lemma 2) quodque que in parte ac in toto est, nullius rei singularis essentiam constituit.
Proof.-If this be denied, conceive, if possible, that it constitutes the essence of some particular thing; for instance, the essence of B. Then (II. Def. ii.) it cannot without B either exist or be conceived; but this is against our hypothesis. Therefore it does not appertain to B's essence, nor does it constitute the essence of any particular thing. Q.E.D. DEMONSTRATIO: Si negas, concipe si fieri potest, id essentiam alicujus rei singularis constituere nempe essentiam B. Ergo (per definitionem 2 hujus {2d02}) id sine B non poterit esse neque concipi; atqui hoc est contra hypothesin : ergo id ad essentiam B non pertinet nec alterius rei singularis essentiam constituit. Q.E.D.
2p38 omnibus communia non concipi nisi adaequate 2p38 omnibus communia non concipi nisi adaequate [geomap]
PROP. XXXVIII. Those things, which are common to all, and which are equally in a part and in the whole, cannot be conceived except adequately. PROPOSITIO XXXVIII: Illa quae omnibus communia quaeque que in parte ac in toto sunt, non possunt concipi nisi adaequate.
Proof.-Let A be something, which is common to all bodies, and which is equally present in the part of any given body and in the whole. I say A cannot be conceived except adequately. For the idea thereof in God will necessarily be adequate (II. vii. Coroll.), both in so far as God has the idea of the human body, and also in so far as he has the idea of the modifications [Lat: affectiones] of the human body, which (II. xvi., xxv., xxvii.) involve in part the nature of the human body and the nature of external bodies; that is (II. xii., xiii.), the idea in God will necessarily be adequate, both in so far as he constitutes the human mind, and in so far as he has the ideas, which are in the human mind. Therefore the mind (II. xi. Coroll.) necessarily perceives adequately, and has this adequate perception, both in so far as it perceives itself, and in so far as it perceives its own or any external body, nor can A be conceived in any other manner. Q.E.D. DEMONSTRATIO: Sit A aliquid quod omnibus corporibus commune quodque que in parte cujuscunque corporis ac in toto est. Dico A non posse concipi nisi adaequate. Nam ejus idea (per corollarium propositionis 7 hujus {2p07c}) erit necessario in Deo adaequata tam quatenus ideam corporis humani quam quatenus ideas habet ejusdem affectionum quae (per propositiones 16 {2p16}, 25 {2p25} et 27 {2p27} hujus) tam corporis humani quam corporum externorum naturam ex parte involvunt hoc est (per propositiones 12 {2p12} et 13 {2p13} necessario in Deo adaequata quatenus mentem humanam constituit  sive [excl non-exh] quatenus ideas habet quae in mente humana sunt; mens igitur (per corollarium propositionis 11 {2p11c} hujus) A necessario adaequate percipit idque tam quatenus se quam quatenus suum vel [excl exh] quodcunque externum corpus percipit nec A alio modo potest concipi. Q.E.D.
2p38c dari quasdam ideas omnibus communes 2p38c dari quasdam ideas omnibus communes [geomap]
Corollary-Hence it follows that there are certain ideas or notions common to all men; for (by Lemma ii.) all bodies agree in certain respects, which (by the foregoing Prop.) must be adequately or clearly and distinctly perceived by all.  COROLLARIUM {2p38}: Hinc sequitur dari quasdam ideas sive [mng eqv]   notiones omnibus hominibus communes. Nam (per lemma 2 {2L02}) omnia corpora in quibusdam conveniunt, quae (per propositionem praecedentem {2p38}) ab omnibus debent adaequate sive [mng eqv]   clare et distincte percipi.
2p39 corpori humano corporibus externis commune in mente adaequata 2p39 corpori humano corporibus externis commune in mente adaequata [geomap]
PROP. XXXIX. That, which is common to and a property of the human body and such other bodies as are wont to affect the human body, and which is present equally in each part of either, or in the whole, will be represented by an adequate idea in the mind. PROPOSITIO XXXIX: Id quod corpori humano et quibusdam corporibus externis a quibus corpus humanum affici solet, commune est et proprium quodque in cujuscunque horum parte que ac in toto est, ejus etiam idea erit in mente adaequata.
Proof.-If A be that, which is common to and a property of the human body and external bodies, and equally present in the human body and in the said external bodies, in each part of each external body and in the whole, there will be an adequate idea of A in God (II. vii. Coroll.), both in so far as he has the idea of the human body, and in so far as he has the ideas of the given external bodies. Let it now be granted, that the human body is affected by an external body through that, which it has in common therewith, namely, A; the idea of this modification [Lat: affectiones] will involve the property A (II. xvi.), and therefore (II. vii. Coroll.) the idea of this modification [Lat: affectiones], in so far as it involves the property A, will be adequate in God, in so far as God is affected by the idea of the human body; that is (II. xiii.), in so far as he constitutes the nature of the human mind; therefore (II. xi. Coroll.) this idea is also adequate in the human mind. Q.E.D. DEMONSTRATIO: Sit A id quod corpori humano et quibusdam corporibus externis commune est et proprium quodque que in humano corpore ac in iisdem corporibus externis et quod denique que in cujuscunque corporis externi parte ac in toto est. Ipsius A dabitur in Deo idea adaequata (per corollarium propositionis 7 hujus {2p07c}) tam quatenus ideam corporis humani quam quatenus positorum corporum externorum ideas habet. Ponatur jam humanum corpus a corpore externo affici per id quod cum eo habet commune hoc est ab A; hujus affectionis idea proprietatem A involvet (per propositionem 16 hujus {2p16}) atque adeo (per idem corollarium propositionis 7 hujus {2p07c}) idea hujus affectionis quatenus proprietatem A involvit, erit in Deo adaequata quatenus idea corporis humani affectus est hoc est (per propositionem 13 hujus) quatenus mentis humanae naturam constituit adeoque (per corollarium propositionis 11 {2p11c} hujus) haec idea est etiam in mente humana adaequata. Q.E.D.
2p39c plura adaequate percipiendum plura communia 2p39c plura adaequate percipiendum plura communia [geomap]
 Corollary.-Hence it follows that the mind is fitted to perceive adequately more things, in proportion as its body has more in common with other bodies. COROLLARIUM {2p39}: Hinc sequitur quod mens eo aptior est ad plura adaequate percipiendum quo ejus corpus plura habet cum aliis corporibus communia.
2p40 sequuntur adaequatae etiam 2p40 sequuntur adaequatae etiam [geomap]
PROP. XL. Whatsoever ideas in the mind follow from ideas which are therein adequate, are also themselves adequate. PROPOSITIO XL: Quaecunque ideae in mente sequuntur ex ideis quae in ipsa sunt adaequatae, sunt etiam adaequatae.
Proof.-This proposition is self-evident. For when we say that an idea in the human mind follows from ideas which are therein adequate, we say, in other words (II. xi. Coroll.), that an idea is in the divine intellect, whereof God is the cause, not in so far as he is infinite, nor in so far as he is affected by the ideas of very many particular things, but only in so far as he constitutes the essence of the human mind. DEMONSTRATIO: Patet. Nam cum dicimus in mente humana ideam sequi ex ideis quae in ipsa sunt adaequatae, nihil aliud dicimus (per corollarium propositionis 11 hujus {2p11}) quam quod in ipso divino intellectu detur idea cujus Deus est causa, non quatenus infinitus est nec quatenus plurimarum rerum singularium ideis affectus est sed quatenus tantum humanae mentis essentiam constituit.
2p40s1 aliae causae 2p40s1 aliae causae
Note I.-I have thus set forth the cause of those notions, which are common to all men, and which form the basis of our ratiocination. But there are other causes of certain axioms or notions, which it would be to the purpose to set forth by this method of ours; for it would thus appear what notions are more useful than others, and what notions have scarcely any use at all. Furthermore, we should see what notions are common to all men, and what notions are only clear and distinct to those who are unshackled by prejudice, and we should detect those which are ill-founded. Again we should discern whence the notions called secondary derived their origin, and consequently the axioms on which they are founded, and other points of interest connected with these questions. But I have decided to pass over the subject here, partly because I have set it aside for another treatise, partly because I am afraid of wearying the reader by too great prolixity. Nevertheless, in order not to omit anything necessary to be known, I will briefly set down the causes, whence are derived the terms styled transcendental, such as Being, Thing, Something. These terms arose from the fact, that the human body, being limited, is only capable of distinctly forming a certain number of images (what an image is I explained in the II. xvii. note) within itself at the same time; if this number be exceeded, the images will begin to be confused; if this number of images, of which the body is capable of forming distinctly within itself, be largely exceeded, all will become entirely confused one with another. This being so, it is evident (from II. Prop. xvii. Coroll., and xviii.) that the human mind can distinctly imagine as many things simultaneously, as its body can form images simultaneously. When the images become quite confused in the body, the mind also imagines all bodies confusedly without any distinction, and will comprehend them, as it were, under one attribute, namely, under the attribute of Being, Thing, &c. The same conclusion can be drawn from the fact that images are not always equally vivid, and from other analogous causes, which there is no need to explain here; for the purpose which we have in view it is sufficient for us to consider one only. All may be reduced to this, that these terms represent ideas in the highest degree confused. From similar causes arise those notions, which we call general, such as man, horse, dog, &c. They arise, to wit, from the fact that so many images, for instance, of men, are formed simultaneously in the human body, that the powers of imagination break down, not indeed utterly, but to the extent of the mind losing count of small differences between individuals (e.g. colour, size, &c.) and their definite number, and only distinctly imagining that, in which all the individuals, in so far as the body is affected by them, agree; for that is the point, in which each of the said individuals chiefly affected the body; this the mind expresses by the name man, and this it predicates of an infinite number of particular individuals. For, as we have said, it is unable to imagine the definite number of individuals. We must, however, bear in mind, that these general notions are not formed by all men in the same way, but vary in each individual according as the point varies, whereby the body has been most often affected and which the mind most easily imagines or remembers. For instance, those who have most often regarded with admiration the stature of man, will by the name of man understand an animal of erect stature; those who have been accustomed to regard some other attribute, will form a different general image of man, for instance, that man is a laughing animal, a two-footed animal without feathers, a rational animal, and thus, in other cases, everyone will form general images of things according to the habit of his body.
It is thus not to be wondered at, that among philosophers, who seek to explain things in nature merely by the images formed of them, so many controversies should have arisen.
SCHOLIUM I: His causam notionum quae communes vocantur quaeque ratiocinii nostri fundamenta sunt, explicui. Sed ali quorundam axiomatum sive notionum causae dantur quas hac nostra methodo explicare e re foret; ex iis namque constaret quaenam notiones prae reliquis utiliores, quaenam vero vix ullius usus essent. Deinde quaenam communes et quaenam iis tantum qui praejudiciis non laborant, clarae  et distinctae et quaenam denique male fundat sint. praeterea constaret unde notiones illae quas secundas vocant et consequenter axiomata quae in iisdem fundantur suam duxerunt originem et alia quae circa haec aliquando meditatus sum. Sed quoniam haec alii dicavi tractatui et etiam ne propter nimiam hujus rei prolixitatem fastidium crearem, hac re hic supersedere decrevi. Attamen ne quid horum omittam quod scitu necessarium sit, causas breviter addam ex quibus termini transcendentales dicti suam duxerunt originem ut Ens, Res, Aliquid. Hi termini ex hoc oriuntur quod scilicet humanum corpus quandoquidem limitatum est, tantum est capax certi imaginum numeri (quid imago sit explicui in scholio propositionis 17 hujus) in se distincte simul formandi, qui si excedatur, hae imagines confundi incipient et si hic imaginum numerus quarum corpus est capax ut eas in se simul distincte formet, longe excedatur, omnes inter se plane confundentur. Cum hoc ita se habeat, patet ex corollario propositionis 17 et propositione 18 hujus quod mens humana tot corpora distincte simul imaginari poterit quot in ipsius corpore imagines possunt simul formari. At ubi imagines in corpore plane confunduntur, mens etiam omnia corpora confuse sine ulla distinctione imaginabitur et quasi sub uno attributo comprehendet nempe sub attributo entis, rei etc. Potest hoc etiam ex eo deduci quod imagines non semper que vigeant et ex aliis causis his analogis quas hic explicare non est opus nam ad nostrum ad quem collimamus scopum, unam tantum sufficit considerare. Nam omnes huc redeunt quod hi termini ideas significent summo gradu confusas. Ex similibus deinde causis ort sunt notiones illae quas universales vocant ut Homo, Equus, Canis etc. videlicet quia in corpore humano tot imagines exempli gratia hominum formantur simul ut vim imaginandi, non quidem penitus sed eo usque tamen superent ut singulorum parvas differentias (videlicet uniuscujusque colorem, magnitudinem etc.) eorumque determinatum numerum mens imaginari nequeat et id tantum in quo omnes quatenus corpus ab iisdem afficitur, conveniunt, distincte imaginetur nam ab eo corpus maxime scilicet ab unoquoque singulari affectum fuit atque hoc nomine hominis exprimit hocque de infinitis singularibus praedicat. Nam singularium determinatum numerum ut diximus imaginari nequit. Sed notandum has notiones non ab omnibus eodem modo formari sed apud unumquemque variare pro ratione rei a qua corpus affectum spius fuit quamque facilius mens imaginatur vel recordatur. Exempli gratia qui spius cum admiratione hominum staturam contemplati sunt, sub nomine hominis intelligent animal erect statur; qui vero aliud assueti sunt contemplari, aliam hominum communem imaginem formabunt nempe hominem esse animal risibile, animal bipes sine plumis, animal rationale et sic de reliquis unusquisque pro dispositione sui corporis rerum universales imagines formabit. Quare non mirum est quod inter philosophos qui res naturales per solas rerum imagines explicare voluerunt, tot sint ort controversi.
2p40s2 percipere 1 sensus mutilate 2 signis 3 notiones communes 2p40s2 percipere 1 sensus mutilate 2 signis 3 notiones communes
Note II.-From all that has been said above it is clear, that we, in many cases, perceive and form our general notions:-(1.) From particular things represented to our intellect fragmentarily, confusedly, and without order through our senses (II. xxix. Coroll.); I have settled to call such perceptions by the name of knowledge from the mere suggestions of experience.[4]
[4] A Baconian phrase. Nov. Org. Aph. 100. [Pollock, p. 126, n.]
(2.) From symbols, e.g., from the fact of having read or heard certain words we remember things and form certain ideas concerning them, similar to those through which we imagine things (II. xviii. note). I shall call both these ways of regarding things knowledge of the first kind, opinion, or imagination. (3.) From the fact that we have notions common to all men, and adequate ideas of the properties of things (II. xxxviii. Coroll., xxxix. and Coroll. and xl.); this I call reason and knowledge of the second kind. Besides these two kinds of knowledge, there is, as I will hereafter show, a third kind of knowledge, which we will call intuition. This kind of knowledge proceeds from an adequate idea of the absolute essence of certain attributes of God to the adequate knowledge of the essence of things. I will illustrate all three kinds of knowledge by a single example. Three numbers are given for finding a fourth, which shall be to the third as the second is to the first. Tradesmen without hesitation multiply the second by the third, and divide the product by the first; either because they have not forgotten the rule which they received from a master without any proof, or because they have often made trial of it with simple numbers, or by virtue of the proof of the nineteenth proposition of the seventh book of Euclid, namely, in virtue of the general property of proportionals.
But with very simple numbers there is no need of this. For instance, one, two, three, being given, everyone can see that the fourth proportional is six; and this is much clearer, because we infer the fourth number from an intuitive grasping of the ratio, which the first bears to the second.
SCHOLIUM II: Ex omnibus supra dictis clare apparet nos multa percipere et notiones universales formare I ex singularibus nobis per sensus mutilate, confuse et sine ordine ad intellectum repraesentatis (vide corollarium propositionis 29 hujus) et ideo tales perceptiones cognitionem ab experientia vaga vocare consuevi. II ex signis exempli gratia ex eo quod auditis aut lectis quibusdam verbis rerum recordemur et earum quasdam ideas formemus similes iis per quas res imaginamur (vide scholium propositionis 18 hujus). Utrumque hunc res contemplandi modum cognitionem primi generis, opinionem vel imaginationem in posterum vocabo. III denique ex eo quod notiones communes rerumque proprietatum ideas adaequatas habemus (vide corollarium propositionis 38 et propositionem 39 cum ejus corollario et propositionem 40 hujus) atque hunc rationem et secundi generis cognitionem vocabo. praeter haec duo cognitionis genera datur, ut in sequentibus ostendam, aliud tertium quod scientiam intuitivam vocabimus. Atque hoc cognoscendi genus procedit ab adaequata idea essentiae formalis quorundam Dei attributorum ad adaequatam cognitionem essentiae rerum. Haec omnia unius rei exemplo explicabo. Dantur exempli gratia tres numeri ad quartum obtinendum qui sit ad tertium ut secundus ad primum. Non dubitant mercatores secundum in tertium ducere et productum per primum dividere quia scilicet ea quae a magistro absque ulla demonstratione audiverunt, nondum tradiderunt oblivioni vel quia id spe in numeris simplicissimis experti sunt vel ex vi demonstrationis propositionis 19 libri 7 Euclidis nempe ex communi proprietate proportionalium. At in numeris simplicissimis nihil horum opus est. Exempli gratia datis numeris 1, 2, 3, nemo non videt quartum numerum proportionalem esse 6 atque hoc multo clarius quia ex ipsa ratione quam primum ad secundum habere uno intuitu videmus, ipsum quartum concludimus.
2p41 primi generis falsitatis, secundi tertii vera 2p41 primi generis falsitatis, secundi tertii vera [geomap]
PROP. XLI. Knowledge of the first kind is the only source of falsity, knowledge of the second and third kinds is necessarily true. PROPOSITIO XLI: Cognitio primi generis unica est falsitatis causa, secundi autem et tertii est necessario vera.
Proof.-To knowledge of the first kind we have (in the foregoing note) assigned all those ideas, which are inadequate and confused; therefore this kind of knowledge is the only source of falsity (II. xxxv.). Furthermore, we assigned to the second and third kinds of knowledge those ideas which are adequate; therefore these kinds are necessarily true (II. xxxiv.). Q.E.D. DEMONSTRATIO: Ad primi generis cognitionem illas omnes ideas diximus in praecedenti scholio {non-deductive reference} pertinere quae sunt inadaequatae et confusae atque adeo (per propositionem 35 hujus {2p35}) haec cognitio unica est falsitatis causa. Deinde ad cognitionem secundi et tertii illas pertinere diximus quae sunt adaequatae adeoque (per propositionem 34 hujus {2p34}) est necessario vera. Q.E.D.
2p42 Secundi  tertii non primi verum falso distinguere. 2p42 Secundi  tertii non primi verum falso distinguere [geomap]
PROP. XLII. Knowledge of the second and third kinds, not knowledge of the first kind, teaches us to distinguish the true from the false. PROPOSITIO XLII: Secundi et tertii et non primi generis cognitio docet nos verum a falso distinguere.
Proof.-This proposition is self-evident. He, who knows how to distinguish between true and false, must have an adequate idea of true and false. That is (II. xl., note ii.), he must know the true and the false by the second or third kind of knowledge. DEMONSTRATIO: Haec propositio per se patet. Qui enim inter verum et falsum scit distinguere, debet adaequatam veri et falsi habere ideam hoc est (per II scholium propositionis 40 hujus {non-deductive reference}) verum et falsum secundo aut [non-excl non-exh] tertio cognitionis genere cognoscere.
2p43 veram habet simul scit 2p43 veram habet simul scit [geomap]
PROP. XLIII. He, who has a true idea, simultaneously knows that he has a true idea, and cannot doubt of the truth of the thing perceived. PROPOSITIO XLIII: Qui veram habet ideam, simul scit se veram habere ideam nec de rei veritate potest dubitare.
Proof.-A true idea in us is an idea which is adequate in God, in so far as he is displayed through the nature of the human mind (II. xi. Coroll.). Let us suppose that there is in God, in so far as he is displayed through the human mind, an adequate idea, A. The idea of this idea must also necessarily be in God, and be referred to him in the same way as the idea A (by II. xx., whereof the proof is of universal application). But the idea A is supposed to be referred to God, in so far as he is displayed through the human mind; therefore, the idea of the idea A must be referred to God in the same manner; that is (by II. xi. Coroll.), the adequate idea of the idea A will be in the mind, which has the adequate idea A; therefore he, who has an adequate idea or knows a thing truly (II. xxxiv.), must at the same time have an adequate idea or true knowledge of his knowledge; that is, obviously, he must be assured. Q.E.D. DEMONSTRATIO: Idea vera in nobis est illa quae in Deo quatenus per naturam mentis humanae explicatur, est adaequata (per corollarium propositionis 11 hujus {2p11c}). Ponamus itaque dari in Deo quatenus per naturam mentis humanae explicatur, ideam adaequatam A. Hujus ideae debet necessario dari etiam in Deo idea quae ad Deum eodem modo refertur ac idea A (per propositionem 20 hujus {2p20} cujus demonstratio universalis est). At idea A ad Deum referri supponitur quatenus per naturam mentis humanae explicatur; ergo etiam idea ideae A ad Deum eodem modo debet referri hoc est (per idem corollarium propositionis 11 hujus {2p11c}) haec adaequata idea ideae A erit in ipsa mente quae ideam adaequatam A habet adeoque qui adaequatam habet ideam sive [prf eqv]  (per propositionem 34 hujus {2p34}) qui vere rem cognoscit, debet simul suae cognitionis adaequatam habere ideam sive [prf eqv]  veram cognitionem hoc est (ut per se manifestum) debet simul esse certus. Q.E.D.
2p43s praecedentem propositionem manifestam 2p43s praecedentem propositionem manifestam
Note.-I explained in the note to II. xxi. what is meant by the idea of an idea; but we may remark that the foregoing proposition is in itself sufficiently plain. No one, who has a true idea, is ignorant that a true idea involves the highest certainty. For to have a true idea is only another expression for knowing a thing perfectly, or as well as possible. No one, indeed, can doubt of this, unless he thinks that an idea is something lifeless, like a picture on a panel, and not a mode of thinking-namely, the very act of understanding. And who, I ask, can know that he understands anything, unless he do first understand it? In other words, who can know that he is sure of a thing, unless he be first sure of that thing? Further, what can there be more clear, and more certain, than a true idea as a standard of truth? Even as light displays both itself and darkness, so is truth a standard both of itself and of falsity.
I think I have thus sufficiently answered these questions-namely, if a true idea is distinguished from a false idea, only in so far as it is said to agree with its object, a true idea has no more reality or perfection than a false idea (since the two are only distinguished by an extrinsic mark); consequently, neither will a man who has a true idea have any advantage over him who has only false ideas. Further, how comes it that men have false ideas? Lastly, how can anyone be sure, that he has ideas which agree with their objects? These questions, I repeat, I have, in my opinion, sufficiently answered. The difference between a true idea and a false idea is plain: from what was said in II. xxxv., the former is related to the latter as being is to not-being. The causes of falsity I have set forth very clearly in II. xix. and II. xxxv. with the note. From what is there stated, the difference between a man who has true ideas, and a man who has only false ideas, is made apparent. As for the last question-as to how a man can be sure that he has ideas that agree with their objects, I have just pointed out, with abundant clearness, that his knowledge arises from the simple fact, that he has an idea which corresponds with its object-in other words, that truth is its own standard. We may add that our mind, in so far as it perceives things truly, is part of the infinite intellect of God (II. xi. Coroll.); therefore, the clear and distinct ideas of the mind are as necessarily true as the ideas of God.
SCHOLIUM: In scholio propositionis 21 hujus partis explicui quid sit idea ideae sed notandum praecedentem propositionem per se satis esse manifestam. Nam nemo qui veram habet ideam, ignorat veram ideam summam certitudinem involvere; veram namque habere ideam nihil aliud significat quam perfecte sive optime rem cognoscere nec sane aliquis de hac re dubitare potest nisi putet ideam quid mutum instar picturae in tabula et non modum cogitandi esse nempe ipsum intelligere et quaeso quis scire potest se rem aliquam intelligere nisi prius rem intelligat? hoc est quis potest scire se de aliqua re certum esse nisi prius de ea re certus sit? Deinde quid idea vera clarius et certius dari potest quod norma sit veritatis? Sane sicut lux seipsam et tenebras manifestat, sic veritas norma sui et falsi est. Atque his me ad has qustiones respondisse puto nempe si idea vera quatenus tantum dicitur cum suo ideato convenire, a falsa distinguitur, nihil ergo realitatis aut perfectionis idea vera habet prae falsa (quandoquidem per solam denominationem extrinsecam distinguuntur) et consequenter neque etiam homo qui veras prae illo qui falsas tantum ideas habet? Deinde unde fit ut homines falsas habeant ideas? Et denique unde aliquis certo scire potest se ideas habere quae cum suis ideatis conveniant? Ad has inquam qustiones me jam respondisse puto. Nam quod ad differentiam inter ideam veram et falsam attinet, constat ex propositione 35 hujus illam ad hanc sese habere ut ens ad non-ens. Falsitatis autem causas a propositione 19 usque ad 35 cum ejus scholio clarissime ostendi. Ex quibus etiam apparet quid homo qui veras habet ideas, homini qui non nisi falsas habet, intersit. Quod denique ultimum attinet nempe undenam homo scire potest se habere ideam quae cum suo ideato conveniat, id modo satis superque ostendi ex hoc solo oriri quod ideam habet quae cum suo ideato convenit sive quod veritas sui sit norma. His adde quod mens nostra quatenus res vere percipit, pars est infiniti Dei intellectus (per corollarium propositionis 11 hujus) adeoque tam necesse est ut mentis clarae  et distinctae ideae verae sint ac Dei ide.
2p44 natura rationis necessarias 2p44 natura rationis necessarias [geomap]
PROP. XLIV. It is not in the nature of reason to regard things as contingent, but as necessary. PROPOSITIO XLIV: De natura rationis non est res ut contingentes sed ut necessarias contemplari.
Proof.-It is in the nature of reason to perceive things truly (II. xli.), namely (I. Ax. vi.), as they are in themselves-that is (I. xxix.), not as contingent, but as necessary. Q.E.D. DEMONSTRATIO: De natura rationis est res vere percipere (per propositionem 41 hujus {2p41}) nempe (per axioma 6 partis I {1a06}) ut in se sunt hoc est (per propositionem 29 partis I {1p29}) non ut contingentes sed ut necessarias. Q.E.D.
2p44c1 sola imaginatione contingentes 2p44c1 sola imaginatione contingentes [geomap]
 Corollary I.-Hence it follows, that it is only through our imagination that we consider things, whether in respect to the future or the past, as contingent. COROLLARIUM {2p44} I: Hinc sequitur a sola imaginatione pendere quod res tam respectu praeteriti quam [excl non-exh] futuri ut contingentes contemplemur.
2p44s ratione hoc fiat 2p44s ratione hoc fiat
Note.-How this way of looking at things arises, I will briefly explain. We have shown above (II. xvii. and Coroll.) that the mind always regards things as present to itself, even though they be not in existence, until some causes arise which exclude their existence and presence. Further (II. xviii.), we showed that, if the human body has once been affected by two external bodies simultaneously, the mind, when it afterwards imagines one of the said external bodies, will straightway remember the other-that is, it will regard both as present to itself, unless there arise causes which exclude their existence and presence. Further, no one doubts that we imagine time, from the fact that we imagine bodies to be moved some more slowly than others, some more quickly, some at equal speed. Thus, let us suppose that a child yesterday saw Peter for the first time in the morning, Paul at noon, and Simon in the evening; then, that today he again sees Peter in the morning. It is evident, from II. Prop. xviii., that, as soon as he sees the morning light, he will imagine that the sun will traverse the same parts of the sky, as it did when he saw it on the preceding day; in other words, he will imagine a complete day, and, together with his imagination of the morning, he will imagine Peter; with noon, he will imagine Paul; and with evening, he will imagine Simon-that is, he will imagine the existence of Paul and Simon in relation to a future time; on the other hand, if he sees Simon in the evening, he will refer Peter and Paul to a past time, by imagining them simultaneously with the imagination of a past time. If it should at any time happen, that on some other evening the child should see James instead of Simon, he will, on the following morning, associate with his imagination of evening sometimes Simon, sometimes James, not both together: for the child is supposed to have seen, at evening, one or other of them, not both together. His imagination will therefore waver; and, with the imagination of future evenings, he will associate first one, then the other-that is, he will imagine them in the future, neither of them as certain, but both as contingent. This wavering of the imagination will be the same, if the imagination be concerned with things which we thus contemplate, standing in relation to time past or time present: consequently, we may imagine things as contingent, whether they be referred to time present, past, or future. SCHOLIUM: Qua autem ratione hoc fiat paucis explicabo. Ostendimus supra (propositione 17 hujus cum ejus corollario) mentem, quamvis res non existant, eas tamen semper ut sibi praesentes imaginari nisi causae occurrant quae earum praesentem existentiam secludant. Deinde (propositione 18 hujus) ostendimus quod si corpus humanum semel a duobus corporibus externis simul affectum fuit, ubi mens postea eorum alterutrum imaginabitur, statim et alterius recordabitur hoc est ambo ut sibi praesentia contemplabitur nisi causae occurrant quae eorum praesentem existentiam secludant. praeterea nemo dubitat quin etiam tempus imaginemur nempe ex eo quod corpora alia aliis tardius vel celerius vel que celeriter moveri imaginemur. Ponamus itaque puerum qui heri prima vice hora matutina viderit Petrum, meridiana autem Paulum et vespertina Simeonem atque hodie iterum matutina hora Petrum. Ex propositione 18 hujus patet quod simulac matutinam lucem videt, illico solem eandem cli quam die praecedenti viderit partem percurrentem sive diem integrum et simul cum tempore matutino Petrum, cum meridiano autem Paulum et cum vespertino Simeonem imaginabitur hoc est Pauli et Simeonis existentiam cum relatione ad futurum tempus imaginabitur et contra si hora vespertina Simeonem videat, Paulum et Petrum ad tempus praeteritum referet, eosdem scilicet simul cum tempore praeterito imaginando atque haec eo constantius quo spius eos eodem hoc ordine viderit. Quod si aliquando contingat ut alia quadam vespera loco Simeonis Jacobum videat, tum sequenti mane cum tempore vespertino jam Simeonem jam Jacobum, non vero ambos simul imaginabitur. Nam alterutrum tantum, non autem ambos simul tempore vespertino vidisse supponitur. Fluctuabitur itaque ejus imaginatio et cum futuro tempore vespertino jam hunc jam illum imaginabitur hoc est neutrum certo sed utrumque contingenter futurum contemplabitur. Atque haec imaginationis fluctuatio eadem erit si imaginatio rerum sit quas eodem modo cum relatione ad tempus praeteritum vel praesens contemplamur et consequenter res tam ad tempus praesens quam ad praeteritum vel futurum relatas ut contingentes imaginabimur.
2p44c2 aeternitatis specie 2p44c2 aeternitatis specie [geomap]
Corollary II.-It is in the nature of reason to perceive things under a certain form of eternity (sub quadam aeternitatis specie). COROLLARIUM  {2p44} II: De natura rationis est res sub quadam aeternitatis specie percipere.
Proof.-It is in the nature of reason to regard things, not as contingent, but as necessary (II. xliv.). Reason perceives this necessity of things (II. xli.) truly-that is (I. Ax. vi.), as it is in itself. But (I. xvi.) this necessity of things is the very necessity of the eternal nature of God; therefore, it is in the nature of reason to regard things under this form of eternity. We may add that the bases of reason are the notions (II. xxxviii.), which answer to things common to all, and which (II. xxxvii.) do not answer to the essence of any particular thing: which must therefore be conceived without any relation to time, under a certain form of eternity. DEMONSTRATIO: De natura enim rationis est res ut necessarias et non ut contingentes contemplari (per propositionem praecedentem {2p44}). Hanc autem rerum necessitatem (per propositionem 41 hujus {2p41}) vere hoc est (per axioma 6 partis I {1a06}) ut in se est, percipit. Sed (per propositionem 16 partis I {1p16}) haec rerum necessitas est ipsa Dei aeternae naturae necessitas; ergo de natura rationis est res sub hac aeternitatis specie contemplari. Adde quod fundamenta rationis notiones sint (per propositionem 38 hujus {2p38}) quae illa explicant quae omnibus communia sunt quque (per propositionem 37 hujus {2p37}) nullius rei singularis essentiam explicant quque propterea absque ulla temporis relatione sed sub quadam aeternitatis specie debent concipi. Q.E.D.
2p45 Unaquque idea Dei involvit 2p45 Unaquque idea Dei involvit [geomap]
PROP. XLV. Every idea of every body, or of every particular thing actually existing, necessarily involves the eternal and infinite essence of God. PROPOSITIO XLV: Unaquaeque cujuscunque corporis vel [mng eqv] rei singularis actu existentis idea Dei aeternam et infinitam essentiam necessario involvit.
Proof.-The idea of a particular thing actually existing necessarily involves both the existence and the essence of the said thing (II. viii.). Now particular things cannot be conceived without God (I. xv.); but, inasmuch as (II. vi.) they have God for their cause, in so far as he is regarded under the attribute of which the things in question are modes, their ideas must necessarily involve (I. Ax. iv.) the conception of the attributes of those ideas-that is (I. vi.), the eternal and infinite essence of God. Q.E.D. DEMONSTRATIO: Idea rei singularis actu existentis ipsius rei tam essentiam quam existentiam necessario involvit (per corollarium propositionis 8 hujus {2p08c}). At res singularis (per propositionem 15 partis I {1p15}) non possunt sine Deo concipi sed quia (per propositionem 6 hujus {2p06}) Deum pro causa habent quatenus sub attributo consideratur cujus res ipsae modi sunt, debent necessario earum ideae (per axioma 4 partis I {1a04}) ipsarum attributi conceptum hoc est (per definitionem 6 partis I {1d06}) Dei aeternam et infinitam essentiam involvere. Q.E.D.
2p45s per existentiam intelligo 2p45s per existentiam intelligo
Note.-By existence I do not here mean duration-that is, existence in so far as it is conceived abstractedly, and as a certain form of quantity. I am speaking of the very nature of existence, which is assigned to particular things, because they follow in infinite numbers and in infinite ways from the eternal necessity of God's nature (I. xvi.). I am speaking, I repeat, of the very existence of particular things, in so far as they are in God. For although each particular thing be conditioned by another particular thing to exist in a given way, yet the force whereby each particular thing perseveres in existing follows from the eternal necessity of God's nature (cf. I. xxiv. Coroll.). SCHOLIUM: Hic per existentiam non intelligo durationem hoc est existentiam quatenus abstracte concipitur et tanquam quaedam quantitatis species. Nam loquor de ipsa natura existenti quae rebus singularibus tribuitur propterea quod ex aeterna necessitate Dei naturae infinita infinitis modis sequuntur (vide propositionem 16 partis I). Loquor inquam de ipsa existentia rerum singularium quatenus in Deo sunt. Nam etsi unaquque ab alia re singulari determinetur ad certo modo existendum, vis tamen qua unaquque in existendo perseverat, ex aeterna necessitate naturae Dei sequitur. Qua de re vide corollarium propositionis 24 partis I.
2p46 Cognitio essentiae Dei adaequata perfecta 2p46 Cognitio essentiae Dei adaequata perfecta [geomap]
PROP. XLVI. The knowledge of the eternal and infinite essence of God which every idea involves is adequate and perfect. PROPOSITIO XLVI: Cognitio aeternae et infinitae essentiae Dei quam unaquaeque idea involvit, est adaequata et perfecta.
Proof.-The proof of the last proposition is universal; and whether a thing be considered as a part or a whole, the idea thereof, whether of the whole or of a part (by the last Prop.), will involve God's eternal and infinite essence. Wherefore, that, which gives knowledge of the eternal and infinite essence of God, is common to all, and is equally in the part and in the whole; therefore (II. xxxviii.) this knowledge will be adequate. Q.E.D. DEMONSTRATIO: Demonstratio praecedentis propositionis universalis est et sive [excl exh] res ut pars  sive [excl exh] ut totum consideretur, ejus idea sive [excl exh] totius sit  sive [excl exh] partis (per propositionem praecedentem {2p45}) Dei aeternam et infinitam essentiam involvet. Quare id quod cognitionem aeternae et infinitae essentiae Dei dat, omnibus commune et que in parte ac in toto est adeoque (per propositionem 38 hujus {2p38}) erit haec cognitio adaequata. Q.E.D.
2p47 Mens adaequatam cognitionem Dei 2p47 Mens adaequatam cognitionem Dei [geomap]
PROP. XLVII. The human mind has an adequate knowledge of the eternal and infinite essence of God. PROPOSITIO XLVII : Mens humana adaequatam habet cognitionem aeternae et infinitae essentiae Dei.
Proof.-The human mind has ideas (II. xxii.), from which (II. xxiii.) it perceives itself and its own body (II. xix.) and external bodies (II. xvi. Coroll. i. and II. xvii.) as actually existing; therefore (II. xlv. and xlvi.) it has an adequate knowledge of the eternal and infinite essence of God. Q.E.D. DEMONSTRATIO: Mens humana ideas habet (per propositionem 22 hujus {2p22}) ex quibus (per propositionem 23 hujus {2p23}) se suumque corpus (per propositionem 19 hujus) {2p19} et (per corollarium I propositionis 16 {2p16c1} et per propositionem 17 hujus  {2p17}) corpora externa ut actu existentia percipit adeoque (per propositiones 45  {2p45} et 46 hujus {2p46}) cognitionem aeternae et infinitae essentiae Dei habet adaequatam. Q.E.D.
2p47s tertium illud cognitionis genus 2p47s tertium illud cognitionis genus
Note.-Hence we see, that the infinite essence and the eternity of God are known to all. Now as all things are in God, and are conceived through God, we can from this knowledge infer many things, which we may adequately know, and we may form that third kind of knowledge of which we spoke in the note to II. xl., and of the excellence and use of which we shall have occasion to speak in Part V. Men have not so clear a knowledge of God as they have of general notions, because they are unable to imagine God as they do bodies, and also because they have associated the name God with images of things that they are in the habit of seeing, as indeed they can hardly avoid doing, being, as they are, men, and continually affected by external bodies. Many errors, in truth, can be traced to this head, namely, that we do not apply names to things rightly. For instance, when a man says that the lines drawn from the centre of a circle to its circumference are not equal, he then, at all events, assuredly attaches a meaning to the word circle different from that assigned by mathematicians. So again, when men make mistakes in calculation, they have one set of figures in their mind, and another on the paper. If we could see into their minds, they do not make a mistake; they seem to do so, because we think, that they have the same numbers in their mind as they have on the paper. If this were not so, we should not believe them to be in error, any more than I thought that a man was in error, whom I lately heard exclaiming that his entrance hall had flown into a neighbour's hen, for his meaning seemed to me sufficiently clear. Very many controversies have arisen from the fact, that men do not rightly explain their meaning, or do not rightly interpret the meaning of others. For, as a matter of fact, as they flatly contradict themselves, they assume now one side, now another, of the argument, so as to oppose the opinions, which they consider mistaken and absurd in their opponents. SCHOLIUM: Hinc videmus Dei infinitam essentiam ejusque aeternitatem omnibus esse notam. Cum autem omnia in Deo sint et per Deum concipiantur, sequitur nos ex cognitione hac plurima posse deducere quae adaequate cognoscamus atque adeo tertium illud cognitionis genus formare de quo diximus in scholio II propositionis 40 hujus partis et de cujus praestantia et utilitate in quinta parte erit nobis dicendi locus. Quod autem homines non que claram Dei ac notionum communium habeant cognitionem, inde fit quod Deum imaginari nequeant ut corpora et quod nomen "Deus" junxerunt imaginibus rerum quas videre solent; quod homines vix vitare possunt quia continuo a corporibus externis afficiuntur. Et profecto plerique errores in hoc solo consistunt quod scilicet nomina rebus non recte applicamus. Cum enim aliquis ait lineas quae ex centro circuli ad ejusdem circumferentiam ducuntur esse inquales, ille sane aliud tum saltem per circulum intelligit quam mathematici. Sic cum homines in calculo errant, alios numeros in mente, alios in charta habent. Quare si ipsorum mentem spectes, non errant sane; videntur tamen errare quia ipsos in mente putamus habere numeros qui in charta sunt. Si hoc non esset, nihil eosdem errare crederemus; ut non credidi quendam errare quem nuper audivi clamantem suum atrium volasse in gallinam vicini quia scilicet ipsius mens satis perspecta mihi videbatur. Atque hinc plerque oriuntur controversi nempe quia homines mentem suam non recte explicant vel quia alterius mentem male interpretantur. Nam revera dum sibi maxime contradicunt, vel eadem vel diversa cogitant ita ut quos in alio errores et absurda esse putant, non sint.
2p48 In mente nulla est absoluta sive libera voluntas 2p48 In mente nulla est absoluta sive libera voluntas [geomap]
PROP. XLVIII. In the mind there is no absolute or free will; but the mind is determined to wish this or that by a cause, which has also been determined by another cause, and this last by another cause, and so on to infinity. PROPOSITIO XLVIII: In mente nulla est absoluta sive [mng eqv]  libera voluntas sed mens ad hoc vel illud volendum determinatur a causa quae etiam ab alia determinata est et haec iterum ab alia et sic in infinitum.
Proof.-The mind is a fixed and definite mode of thought (II. xi.), therefore it cannot be the free cause of its actions (I. xvii. Coroll. ii.); in other words, it cannot have an absolute faculty of positive or negative volition; but (by I. xxviii.) it must be determined by a cause, which has also been determined by another cause, and this last by another, &c. Q.E.D. DEMONSTRATIO: Mens certus et determinatus modus cogitandi est (per propositionem 11 hujus {2p11}) adeoque (per corollarium II propositionis 17 partis I {1p17c2}) suarum actionum non potest esse causa libera sive [mng eqv]  absolutam facultatem volendi et nolendi habere non potest sed ad hoc vel illud volendum (per propositionem 28 partis I {1p28}) determinari debet a causa quae etiam ab alia determinata est et haec iterum ab alia etc. Q.E.D.
2p48s nullam dari facultatem absolutam intelligendi, cupiendi, amandi etc. 2p48s nullam dari facultatem absolutam intelligendi, cupiendi, amandi etc.
Note.-In the same way it is proved, that there is in the mind no absolute faculty of understanding, desiring, loving, &c. Whence it follows, that these and similar faculties are either entirely fictitious, or are merely abstract and general terms, such as we are accustomed to put together from particular things. Thus the intellect and the will stand in the same relation to this or that idea, or this or that volition, as "lapidity" to this or that stone, or as "man" to Peter and Paul. The cause which leads men to consider themselves free has been set forth in the Appendix to Part I. But, before I proceed further, I would here remark that, by the will to affirm and decide, I mean the faculty, not the desire. I mean, I repeat, the faculty, whereby the mind affirms or denies what is true or false, not the desire, wherewith the mind wishes for or turns away from any given thing. After we have proved, that these faculties of ours are general notions, which cannot be distinguished from the particular instances on which they are based, we must inquire whether volitions themselves are anything besides the ideas of things. We must inquire, I say, whether there is in the mind any affirmation or negation beyond that, which the idea, in so far as it is an idea, involves. On which subject see the following proposition, and II. Def. iii., lest the idea of pictures should suggest itself. For by ideas I do not mean images such as are formed at the back of the eye, or in the midst of the brain, but the conceptions of thought. SCHOLIUM: Eodem hoc modo demonstratur in mente nullam dari facultatem absolutam intelligendi, cupiendi, amandi etc. Unde sequitur has et similes facultates vel prorsus fictitias vel nihil esse praeter entia metaphysica vel universalia quae ex particularibus formare solemus. Adeo ut intellectus et voluntas ad hanc et illam ideam vel ad hanc et illam volitionem eodem modo sese habeant ac lapideitas ad hunc et illum lapidem vel ut homo ad Petrum et Paulum. Causam autem cur homines se liberos esse putent explicuimus in appendice partis prim. Verum antequam ulterius pergam, venit hic notandum me per voluntatem affirmandi et negandi facultatem, non autem cupiditatem intelligere; facultatem inquam intelligo qua mens quid verum quidve falsum sit, affirmat vel negat et non cupiditatem qua mens res appetit vel aversatur. At postquam demonstravimus has facultates notiones esse universales quae a singularibus ex quibus easdem formamus, non distinguuntur, inquirendum jam est an ips volitiones aliquid sint praeter ipsas rerum ideas. Inquirendum inquam est an in mente alia affirmatio et negatio detur praeter illam quam idea quatenus idea est, involvit, qua de re vide sequentem propositionem ut et demonstrationem 3 hujus ne cogitatio in picturas incidat. Non enim per ideas imagines quales in fundo oculi et si placet, in medio cerebro formantur sed cogitationis conceptus intelligo.
2p49 volitio idea involvit 2p49 volitio idea involvit [geomap]
PROP. XLIX. There is in the mind no volition or affirmation and negation, save that which an idea, inasmuch as it is an idea, involves. PROPOSITIO XLIX: In mente nulla datur volitio sive [mng eqv]  affirmatio et negatio praeter illam quam idea quatenus idea est, involvit.
Proof.-There is in the mind no absolute faculty of positive or negative volition, but only particular volitions, namely, this or that affirmation, and this or that negation. Now let us conceive a particular volition, namely, the mode of thinking whereby the mind affirms, that the three interior angles of a triangle are equal to two right angles. This affirmation involves the conception or idea of a triangle, that is, without the idea of a triangle it cannot be conceived. It is the same thing to say, that the concept A must involve the concept B, as it is to say, that A cannot be conceived without B. Further, this affirmation cannot be made (II. Ax. iii.) without the idea of a triangle. Therefore, this affirmation can neither be nor be conceived, without the idea of a triangle. Again, this idea of a triangle must involve this same affirmation, namely, that its three interior angles are equal to two right angles. Wherefore, and vice versae, this idea of a triangle can neither be nor be conceived without this affirmation, therefore, this affirmation belongs to the essence of the idea of a triangle, and is nothing besides. What we have said of this volition (inasmuch as we have selected it at random) may be said of any other volition, namely, that it is nothing but an idea. Q.E.D. DEMONSTRATIO: In mente (per propositionem praecedentem) nulla datur absoluta facultas volendi et volendi sed tantum singulares volitiones nempe haec et illa affirmatio et haec et illa negatio. Concipiamus itaque singularem aliquam volitionem nempe modum cogitandi quo mens affirmat tres angulos trianguli quales esse duobus rectis. Haec affirmatio conceptum sive [mng eqv]  ideam trianguli involvit hoc est sine idea trianguli non potest concipi. Idem enim est si dicam quod A conceptum B debeat involvere ac quod A sine B non possit concipi. Deinde haec affirmatio (per axioma 3 hujus {2a1.3}) non potest etiam sine idea trianguli esse. Haec ergo affirmatio sine idea trianguli nec esse nec concipi potest. Porro haec trianguli idea hanc eandem affirmationem involvere debet nempe quod tres ejus anguli quentur duobus rectis. Quare et vice versa haec trianguli idea sine hac affirmatione nec esse nec concipi potest adeoque (per definitionem 2 hujus {2d02}) haec affirmatio ad essentiam ideae trianguli pertinet nec aliud praeter ipsam est. Et quod de hac volitione diximus (quandoquidem eam ad libitum sumpsimus) dicendum etiam est de quacunque volitione nempe quod praeter ideam nihil sit. Q.E.D.
2p49c Voluntas intellectus idem 2p49c Voluntas intellectus idem [geomap]
Corollary.-Will and understanding are one and the same.  COROLLARIUM {2p49}: Voluntas et intellectus unum et idem sunt.
Proof.-Will and understanding are nothing beyond the individual volitions and ideas (II. xlviii. and note). But a particular volition and a particular idea are one and the same (by the foregoing Prop.); therefore, will and understanding are one and the same. Q.E.D. DEMONSTRATIO: Voluntas et intellectus nihil praeter ipsas singulares volitiones et ideas sunt (per propositionem 48 hujus {2p48} et ejusdem scholium {non-deductive reference}). At singularis volitio et idea (per propositionem praecedentem {2p49}) unum et idem sunt, ergo voluntas et intellectus unum et idem sunt. Q.E.D.
2p49s certitudinem non involvit in falsis acquiescere 2p49s certitudinem non involvit in falsis acquiescere
Note.-We have thus removed the cause which is commonly assigned for error. For we have shown above, that falsity consists solely in the privation of knowledge involved in ideas which are fragmentary and confused. Wherefore, a false idea, inasmuch as it is false, does not involve certainty. When we say, then, that a man acquiesces in what is false, and that he has no doubts on the subject, we do not say that he is certain, but only that he does not doubt, or that he acquiesces in what is false, inasmuch as there are no reasons, which should cause his imagination to waver (see II. xliv. note). Thus, although the man be assumed to acquiesce in what is false, we shall never say that he is certain. For by certainty we mean something positive (II. xliii. and note), not merely the absence of doubt.
However, in order that the foregoing proposition may be fully explained, I will draw attention to a few additional points, and I will furthermore answer the objections which may be advanced against our doctrine. Lastly, in order to remove every scruple, I have thought it worth while to point out some of the advantages, which follow therefrom. I say "some," for they will be better appreciated from what we shall set forth in the fifth part.
SCHOLIUM: His causam quae communiter erroris esse statuitur, sustulimus. Supra autem ostendimus falsitatem in sola privatione quam ideae mutilat et confusae involvunt, consistere. Quare idea falsa quatenus falsa est, certitudinem non involvit. Cum itaque dicimus hominem in falsis acquiescere nec de iis dubitare, non ideo ipsum certum esse sed tantum non dubitare dicimus vel quod in falsis acquiescit quia null causae dantur quae efficiant ut ipsius imaginatio fluctuetur. Qua de re vide scholium propositionis 44 hujus partis. Quantumvis igitur homo falsis adhrere supponatur, nunquam tamen ipsum certum esse dicemus. Nam per certitudinem quid positivum intelligimus (vide propositionem 43 hujus cum ejusdem scholio) non vero dubitationis privationem. At per certitudinis privationem falsitatem intelligimus. Sed ad uberiorem explicationem praecedentis propositionis quaedam monenda supersunt. Superest deinde ut ad objectiones quae in nostram hanc doctrinam objici possunt, respondeam et denique ut omnem amoveam scrupulum, operae pretium esse duxi hujus doctrin quasdam utilitates indicare. Quasdam inquam nam praecipu ex iis quae in quinta parte dicemus, melius intelligentur.
I begin, then, with the first point, and warn my readers to make an accurate distinction between an idea, or conception of the mind, and the images of things which we imagine. It is further necessary that they should distinguish between idea and words, whereby we signify things. These three-namely, images, words, and ideas-are by many persons either entirely confused together, or not distinguished with sufficient accuracy or care, and hence people are generally in ignorance, how absolutely necessary is a knowledge of this doctrine of the will, both for philosophic purposes and for the wise ordering of life. Those who think that ideas consist in images which are formed in us by contact with external bodies, persuade themselves that the ideas of those things, whereof we can form no mental picture, are not ideas, but only figments, which we invent by the free decree of our will; they thus regard ideas as though they were inanimate pictures on a panel, and, filled with this misconception, do not see that an idea, inasmuch as it is an idea, involves an affirmation or negation. Again, those who confuse words with ideas, or with the affirmation which an idea involves, think that they can wish something contrary to what they feel, affirm, or deny. This misconception will easily be laid aside by one, who reflects on the nature of knowledge, and seeing that it in no wise involves the conception of extension, will therefore clearly understand, that an idea (being a mode of thinking) does not consist in the image of anything, nor in words. The essence of words and images is put together by bodily motions, which in no wise involve the conception of thought.
Incipio igitur a primo lectoresque moneo ut accurate distinguant inter ideam sive mentis conceptum et inter imagines rerum quas imaginamur. Deinde necesse est ut distinguant inter ideas et verba quibus res significamus. Nam quia haec tria, imagines scilicet verba et ide, a multis vel plane confunduntur vel non satis accurate vel denique non satis caute distinguuntur, ideo hanc de voluntate doctrinam scitu prorsus necessariam tam ad speculationem quam ad vitam sapienter instituendam plane ignorarunt. Quippe qui putant ideas consistere in imaginibus quae in nobis ex corporum occur su formantur, sibi persuadent ideas illas rerum quarum similem nullam imaginem formare possumus, non esse ideas sed tantum figmenta quae ex libero voluntatis arbitrio fingimus; ideas igitur veluti picturas in tabula mutas aspiciunt et hoc praejudicio proccupati non vident ideam quatenus idea est, affirmationem aut negationem involvere. Deinde qui verba confundunt cum idea vel cum ipsa affirmatione quam idea involvit, putant se posse contra id quod sentiunt velle quando aliquid solis verbis contra id quod sentiunt affirmant aut negant. Haec autem praejudicia exuere facile is poterit qui ad naturam cogitationis attendit, quae extensionis conceptum minime involvit atque adeo clare intelliget ideam (quandoquidem modus cogitandi est) neque in rei alicujus imagine neque in verbis consistere. Verborum namque et imaginum essentia a solis motibus corporeis constituitur, qui cogitationis conceptum minime involvunt.
These few words on this subject will suffice: I will therefore pass on to consider the objections, which may be raised against our doctrine. Of these, the first is advanced by those, who think that the will has a wider scope than the understanding, and that therefore it is different therefrom. The reason for their holding the belief, that the will has wider scope than the understanding, is that they assert, that they have no need of an increase in their faculty of assent, that is of affirmation or negation, in order to assent to an infinity of things which we do not perceive, but that they have need of an increase in their faculty of understanding. The will is thus distinguished from the intellect, the latter being finite and the former infinite. Secondly, it may be objected that experience seems to teach us especially clearly, that we are able to suspend our judgment before assenting to things which we perceive; this is confirmed by the fact that no one is said to be deceived, in so far as he perceives anything, but only in so far as he assents or dissents  Atque haec pauca de his monuisse sufficiat, quare ad praedictas objectiones transeo.
Harum prima est quod constare putant voluntatem latius se extendere quam intellectum atque adeo ab eodem diversam esse. Ratio autem cur putant voluntatem latius se extendere quam intellectum est quia se experiri aiunt se non majore assentiendi sive affirmandi et negandi facultate indigere ad infinitis aliis rebus quas non percipimus, assentiendum quam jam habemus, at quidem majore facultate intelligendi. Distinguitur ergo voluntas ab intellectu quod finitus hic sit, illa autem infinita.
Secundo nobis objici potest quod experientia nihil clarius videatur docere quam quod nostrum judicium possumus suspendere ne rebus quas percipimus, assentiamur; quod hinc etiam confirmatur quod nemo dicitur decipi quatenus aliquid percipit sed tantum quatenus assentitur aut dissentitur.
For instance, he who feigns a winged horse, does not therefore admit that a winged horse exists; that is, he is not deceived, unless he admits in addition that a winged horse does exist. Nothing therefore seems to be taught more clearly by experience, than that the will or faculty of assent is free and different from the faculty of understanding. Thirdly, it may be objected that one affirmation does not apparently contain more reality than another; in other words, that we do not seem to need for affirming, that what is true is true, any greater power than for affirming, that what is false is true. We have, however, seen that one idea has more reality or perfection than another, for as objects are some more excellent than others, so also are the ideas of them some more excellent than others; this also seems to point to a difference between the understanding and the will. Fourthly, it may be objected, if man does not act from free will, what will happen if the incentives to action are equally balanced, as in the case of Buridan's ass? Will he perish of hunger and thirst? If I say that he would, I shall seem to have in my thoughts an ass or the statue of a man rather than an actual man. If I say that he would not, he would then determine his own action, and would consequently possess the faculty of going and doing whatever he liked. Other objections might also be raised, but, as I am not bound to put in evidence everything that anyone may dream, I will only set myself to the task of refuting those I have mentioned, and that as briefly as possible. Exempli gratia qui equum alatum fingit, non ideo concedit dari equum alatum hoc est non ideo decipitur nisi simul concedat dari equum alatum; nihil igitur clarius videtur docere experientia quam quod voluntas sive facultas assentiendi libera sit et a facultate intelligendi diversa.
Tertio objici potest quod una affirmatio non plus realitatis videtur continere quam alia hoc est non majore potentia indigere videmur ad affirmandum verum esse id quod verum est, quam ad aliquid quod falsum est, verum esse affirmandum; at unam ideam plus realitatis sive perfectionis quam aliam habere percipimus; quantum enim objecta alia aliis praestantiora tantum etiam eorum ideae ali aliis perfectiores sunt; ex quibus etiam constare videtur differentia inter voluntatem et intellectum.
Quarto objici potest si homo non operatur ex libertate voluntatis, quid ergo fiet si in quilibrio sit ut Buridani asina? Famene et siti peribit? Quod si concedam, viderer asinam vel hominis statuam, non hominem concipere; si autem negem, ergo seipsum determinabit et consequenter eundi facultatem et faciendi quicquid velit, habet. praeter haec alia forsan possunt objici sed quia inculcare non teneor quid unusquisque somniare potest, ad has objectiones tantum respondere curabo idque quam potero breviter.
To the first objection I answer, that I admit that the will has a wider scope than the understanding, if by the understanding be meant only clear and distinct ideas; but I deny that the will has a wider scope than the perceptions, and the faculty of forming conceptions; nor do I see why the faculty of volition should be called infinite, any more than the faculty of feeling: for, as we are able by the same faculty of volition to affirm an infinite number of things (one after the other, for we cannot affirm an infinite number simultaneously), so also can we, by the same faculty of feeling, feel or perceive (in succession) an infinite number of bodies. If it be said that there is an infinite number of things which we cannot perceive, I answer, that we cannot attain to such things by any thinking, nor, consequently, by any faculty of volition. But, it may still be urged, if God wished to bring it about that we should perceive them, he would be obliged to endow us with a greater faculty of perception, but not a greater faculty of volition than we have already. This is the same as to say that, if God wished to bring it about that we should understand an infinite number of other entities, it would be necessary for him to give us a greater understanding, but not a more universal idea of entity than that which we have already, in order to grasp such infinite entities. We have shown that will is a universal entity or idea, whereby we explain all particular volitions-in other words, that which is common to all such volitions.
As, then, our opponents maintain that this idea, common or universal to all volitions, is a faculty, it is little to be wondered at that they assert, that such a faculty extends itself into the infinite, beyond the limits of the understanding: for what is universal is predicated alike of one, of many, and of an infinite number of individuals.
Et quidem ad primam dico me concedere voluntatem latius se extendere quam intellectum si per intellectum claras tantummodo et distinctas ideas intelligant sed nego voluntatem latius se extendere quam perceptiones sive concipiendi facultatem nec sane video cur facultas volendi potius dicenda est infinita quam sentiendi facultas; sicut enim infinita (unum tamen post aliud nam infinita simul affirmare non possumus) eadem volendi facultate possumus affirmare, sic etiam infinita corpora (unum nempe post aliud) eadem sentiendi facultate possumus sentire sive percipere. Quod si dicant infinita dari quae percipere non possumus? regero nos ea ipsa nulla cogitatione et consequenter nulla volendi facultate posse assequi. At dicunt si Deus vellet efficere ut ea etiam perciperemus, majorem quidem facultatem percipiendi deberet nobis dare sed non majorem quam dedit volendi facultatem; quod idem est ac si dicerent quod si Deus velit efficere ut infinita alia entia intelligeremus, necesse quidem esset ut nobis daret majorem intellectum sed non universaliorem entis ideam quam dedit ad eadem infinita entia amplectendum. Ostendimus enim voluntatem ens esse universale sive ideam qua omnes singulares volitiones hoc est id quod iis omnibus commune est, explicamus. Cum itaque hanc omnium volitionum communem sive universalem ideam facultatem esse credant, minime mirum si hanc facultatem ultra limites intellectus in infinitum se extendere dicant. Universale enim que de uno ac de pluribus ac de infinitis individuis dicitur.
To the second objection I reply by denying, that we have a free power of suspending our judgment: for, when we say that anyone suspends his judgment, we merely mean that he sees, that he does not perceive the matter in question adequately. Suspension of judgment is, therefore, strictly speaking, a perception, and not free will. In order to illustrate the point, let us suppose a boy imagining a horse, and perceive nothing else. Inasmuch as this imagination involves the existence of the horse (II. xvii. Coroll.), and the boy does not perceive anything which would exclude the existence of the horse, he will necessarily regard the horse as present: he will not be able to doubt of its existence, although he be not certain thereof. We have daily experience of such a state of things in dreams; and I do not suppose that there is anyone, who would maintain that, while he is dreaming, he has the free power of suspending his judgment concerning the things in his dream, and bringing it about that he should not dream those things, which he dreams that he sees; yet it happens, notwithstanding, that even in dreams we suspend our judgment, namely, when we dream that we are dreaming.
Further, I grant that no one can be deceived, so far as actual perception extends-that is, I grant that the mind's imaginations, regarded in themselves, do not involve error (II. xvii. note); but I deny, that a man does not, in the act of perception, make any affirmation. For what is the perception of a winged horse, save affirming that a horse has wings? If the mind could perceive nothing else but the winged horse, it would regard the same as present to itself: it would have no reasons for doubting its existence, nor any faculty of dissent, unless the imagination of a winged horse be joined to an idea which precludes the existence of the said horse, or unless the mind perceives that the idea which it possess of a winged horse is inadequate, in which case it will either necessarily deny the existence of such a horse, or will necessarily be in doubt on the subject.
Ad secundam objectionem respondeo negando nos liberam habere potestatem judicium suspendendi. Nam cum dicimus aliquem judicium suspendere, nihil aliud dicimus quam quod videt se rem non adaequate percipere. Est igitur judicii suspensio revera perceptio et non libera voluntas. Quod ut clare intelligatur, concipiamus puerum equum alatum imaginantem nec aliud quicquam percipientem. Quandoquidem haec imaginatio equi existentiam involvit (per corollarium propositionis 17 hujus) nec puer quicquam percipit quod equi existentiam tollat, ille necessario equum ut praesentem contemplabitur nec de ejus existentia poterit dubitare quamvis de eadem non sit certus. Atque hoc quotidie in somnis experimur nec credo aliquem esse qui putet se, dum somniat, liberam habere potestatem suspendendi de iis quae somniat, judicium efficiendique ut ea quae se videre somniat, non somniet et nihilominus contingit ut etiam in somnis judicium suspendamus nempe cum somniamus nos somniare. Porro concedo neminem decipi quatenus percipit hoc est mentis imaginationes in se consideratas nihil erroris involvere concedo (vide scholium propositionis 17 hujus) sed nego hominem nihil affirmare quatenus percipit. Nam quid aliud est equum alatum percipere quam alas de equo affirmare? Si enim mens praeter equum alatum nihil aliud perciperet, eundem sibi praesentem contemplaretur nec causam haberet ullam dubitandi de ejusdem existentia nec ullam dissentiendi facultatem nisi imaginatio equi alati juncta sit ideae quae existentiam ejusdem equi tollit vel quod percipit ideam equi alati quam habet esse inadaequatam atque tum vel ejusdem equi existentiam necessario negabit vel de eadem necessario dubitabit.
I think that I have anticipated my answer to the third objection, namely, that the will is something universal which is predicated of all ideas, and that it only signifies that which is common to all ideas, namely, an affirmation, whose adequate essence must, therefore, in so far as it is thus conceived in the abstract, be in every idea, and be, in this respect alone, the same in all, not in so far as it is considered as constituting the idea's essence: for, in this respect, particular affirmations differ one from the other, as much as do ideas. For instance, the affirmation which involves the idea of a circle, differs from that which involves the idea of a triangle, as much as the idea of a circle differs from the idea of a triangle.
Further, I absolutely deny, that we are in need of an equal power of thinking, to affirm that that which is true is true, and to affirm that that which is false is true. These two affirmations, if we regard the mind, are in the same relation to one another as being and not-being; for there is nothing positive in ideas, which constitutes the actual reality of falsehood (II. xxxv. note, and xlvii. note).
We must therefore conclude, that we are easily deceived, when we confuse universals with singulars, and the entities of reason and abstractions with realities.
Atque his puto me ad tertiam etiam objectionem respondisse nempe quod voluntas universale quid sit quod de omnibus ideis praedicatur quodque id tantum significat quod omnibus ideis commune est nempe affirmationem. Cujus propterea adaequata essentia quatenus sic abstracte concipitur, debet esse in unaquaque idea et hac ratione tantum in omnibus eadem sed non quatenus consideratur essentiam ideae constituere nam eatenus singulares affirmationes que inter se differunt ac ips ide. Exempli gratia affirmatio quam idea circuli ab illa quam idea trianguli involvit que differt ac idea circuli ab idea trianguli. Deinde absolute nego nos quali cogitandi potentia indigere ad affirmandum verum esse id quod verum est quam ad affirmandum verum esse id quod falsum est. Nam hae duae affirmationes, si mentem spectes, se habent ad invicem ut ens ad non-ens; nihil enim in ideis positivum est quod falsitatis formam constituit (vide propositionem 35 hujus cum ejus scholio et scholium propositionis 47 hujus). Quare hic apprime venit notandum quam facile decipimur quando universalia cum singularibus, et entia rationis et abstracta cum realibus confundimus.
As for the fourth objection, I am quite ready to admit, that a man placed in the equilibrium described (namely, as perceiving nothing but hunger and thirst, a certain food and a certain drink, each equally distant from him) would die of hunger and thirst. If I am asked, whether such an one should not rather be considered an ass than a man; I answer, that I do not know, neither do I know how a man should be considered, who hangs himself, or how we should consider children, fools, madmen, &c.
It remains to point out the advantages of a knowledge of this doctrine as bearing on conduct, and this may be easily gathered from what has been said. The doctrine is good,
1. Inasmuch as it teaches us to act solely according to the decree of God, and to be partakers in the Divine nature, and so much the more, as we perform more perfect actions and more and more understand God. Such a doctrine not only completely tranquilizes our spirit, but also shows us where our highest happiness or blessedness is, namely, solely in the knowledge of God, whereby we are led to act only as love and piety shall bid us. We may thus clearly understand, how far astray from a true estimate of virtue are those who expect to be decorated by God with high rewards for their virtue, and their best actions, as for having endured the direst slavery; as if virtue and the service of God were not in itself happiness and perfect freedom.
Quod denique ad quartam objectionem attinet, dico me omnino concedere quod homo in tali quilibrio positus (nempe qui nihil aliud percipit quam sitim et famem, talem cibum et talem potum qui que ab eo distant) fame et siti peribit. Si me rogant an talis homo non potius asinus quam homo sit stimandus? dico me nescire ut etiam nescio quanti stimandus sit ille qui se pensilem facit et quanti stimandi sint pueri, stulti, vesani, etc.
Superest tandem indicare quantum hujus doctrin cognitio ad usum vit conferat, quod facile ex his animadvertemus. Nempe
I quatenus docet nos ex solo Dei nutu agere divinque naturae esse participes et eo magis quo perfectiores actiones agimus et quo magis magisque Deum intelligimus. Haec ergo doctrina praeterquam quod animum omnimode quietum reddit, hoc etiam habet quod nos docet in quo nostra summa felicitas sive beatitudo consistit nempe in sola Dei cognitione ex qua ad ea tantum agenda inducimur quae amor et pietas suadent. Unde clare intelligimus quantum illi a vera virtutis stimatione aberrant qui pro virtute et optimis actionibus tanquam pro summa servitute, summis prmiis a Deo decorari exspectant quasi ipsa virtus Deique servitus non esset ipsa felicitas et summa libertas.

2. Inasmuch as it teaches us, how we ought to conduct ourselves with respect to the gifts of fortune, or matters which are not in our power, and do not follow from our nature. For it shows us, that we should await and endure fortune's smiles or frowns with an equal mind, seeing that all things follow from the eternal decree of God by the same necessity, as it follows from the essence of a triangle, that the three angles are equal to two right angles.
3. This doctrine raises social life, inasmuch as it teaches us to hate no man, neither to despise, to deride, to envy, or to be angry with any. Further, as it tells us that each should be content with his own, and helpful to his neighbour, not from any womanish pity, favour, or superstition, but solely by the guidance of reason, according as the time and occasion demand, as I will show in Part III.
4. Lastly, this doctrine confers no small advantage on the commonwealth; for it teaches how citizens should be governed and led, not so as to become slaves, but so that they may freely do whatsoever things are best.
I have thus fulfilled the promise made at the beginning of this note, and I thus bring the second part of my treatise to a close. I think I have therein explained the nature and properties of the human mind at sufficient length, and, considering the difficulty of the subject, with sufficient clearness. I have laid a foundation, whereon may be raised many excellent conclusions of the highest utility and most necessary to be known, as will, in what follows, be partly made plain.
II quatenus docet quomodo circa res fortun sive quae in nostra potestate non sunt hoc est circa res quae ex nostra natura non sequuntur, nos gerere debeamus nempe utramque fortun faciem quo animo exspectare et ferre : nimirum quia omnia ab aeterno Dei decreto eadem necessitate sequuntur ac ex essentia trianguli sequitur quod tres ejus anguli sunt quales duobus rectis.
III Confert haec doctrina ad vitam socialem quatenus docet neminem odio habere, contemnere, irridere, nemini irasci, invidere. praeterea quatenus docet ut unusquisque suis sit contentus et proximo auxilio, non ex muliebri misericordia, partialitate neque superstitione sed ex solo rationis ductu prout scilicet tempus et res postulat ut in quarta parte ostendam.
IV Denique confert etiam haec doctrina non parum ad communem societatem quatenus docet qua ratione cives gubernandi sint et ducendi nempe non ut serviant sed ut libere ea quae optima sunt, agant. Atque his quae in hoc scholio agere constitueram, absolvi et eo finem huic nostrae secund parti impono in qua puto me naturam mentis humanae ejusque proprietates satis prolixe et quantum rei difficultas fert, clare explicuisse atque talia tradidisse ex quibus multa praeclara, maxime utilia et cognitu necessaria concludi possunt, ut partim ex sequentibus constabit.
Finis secund partis 
SPINOZAE ETHICA ORDINE GEOMETRICO DEMONSTRATA ET IN QUINQUE PARTES DISTINCTA PART III: ON THE ORIGIN AND NATURE OF THE EMOTIONS SPINOZAE ETHICA ORDINE GEOMETRICO DEMONSTRATA ET IN QUINQUE PARTES DISTINCTA PARS TERTIA: DE ORIGINE ET NATURA AFFECTUUM
3praef ORIGINE NATURA AFFECTUUM 3praef ORIGINE NATURA AFFECTUUM
Preface PRAEFATIO
Most writers on the emotions and on human conduct seem to be treating rather of matters outside nature than of natural phenomena following nature's general laws. They appear to conceive man to be situated in nature as a kingdom within a kingdom: for they believe that he disturbs rather than follows nature's order, that he has absolute control over his actions, and that he is determined solely by himself. They attribute human infirmities and fickleness, not to the power of nature in general, but to some mysterious flaw in the nature of man, which accordingly they bemoan, deride, despise, or, as usually happens, abuse: he, who succeeds in hitting off the weakness of the human mind more eloquently or more acutely than his fellows, is looked upon as a seer. Still there has been no lack of very excellent men (to whose toil and industry I confess myself much indebted), who have written many noteworthy things concerning the right way of life, and have given much sage advice to mankind. But no one, so far as I know, has defined the nature and strength of the emotions, and the power of the mind against them for their restraint. Plerique qui de affectibus et hominum vivendi ratione scripserunt, videntur non de rebus naturalibus quae communes naturae leges sequuntur sed de rebus quae extra naturam sunt, agere. Imo hominem in natura veluti imperium in imperio concipere videntur. Nam hominem naturae ordinem magis perturbare quam sequi ipsumque in suas actiones absolutam habere potentiam nec aliunde quam a se ipso determinari credunt. humanae deinde impotenti et inconstanti causam non communi naturae potenti sed nescio cui naturae humanae vitio tribuunt quam propterea flent, rident, contemnunt vel quod plerumque fit, detestantur et qui humanae mentis impotentiam eloquentius vel argutius carpere novit, veluti divinus habetur. Non defuerunt tamen viri praestantissimi (quorum labori et industri nos multum debere fatemur) qui de recta vivendi ratione praeclara multa scripserint et plena prudenti consilia mortalibus dederint; verum affectuum naturam et vires et quid contra mens in iisdem moderandis possit, nemo quod sciam determinavit.
I do not forget, that the illustrious Descartes, though he believed, that the mind has absolute power over its actions, strove to explain human emotions by their primary causes, and, at the same time, to point out a way, by which the mind might attain to absolute dominion over them. However, in my opinion, he accomplishes nothing beyond a display of the acuteness of his own great intellect, as I will show in the proper place. For the present I wish to revert to those, who would rather abuse or deride human emotions than understand them. Such persons will, doubtless think it strange that I should attempt to treat of human vice and folly geometrically, and should wish to set forth with rigid reasoning those matters which they cry out against as repugnant to reason, frivolous, absurd, and dreadful.  Scio equidem celeberrimum Cartesium, licet etiam crediderit mentem in suas actiones absolutam habere potentiam, affectus tamen humanos per primas suas causas explicare simulque viam ostendere studuisse qua mens in affectus absolutum habere possit imperium sed mea quidem sententia nihil praeter magni sui ingenii acumen ostendit, ut suo loco demonstrabo. Nam ad illos revertere volo qui hominum affectus et actiones detestari vel ridere malunt quam intelligere. His sine dubio mirum videbitur quod hominum vitia et ineptias more geometrico tractare aggrediar et certa ratione demonstrare velim ea quae rationi repugnare quque vana, absurda et horrenda esse clamitant.
However, such is my plan. Nothing comes to pass in nature, which can be set down to a flaw therein; for nature is always the same, and everywhere one and the same in her efficacy and power of action; that is, nature's laws and ordinances, whereby all things come to pass and change from one form to another, are everywhere and always the same; so that there should be one and the same method of understanding the nature of all things whatsoever, namely, through nature's universal laws and rules. Thus the passions of hatred, anger, envy, and so on, considered in themselves, follow from this same necessity and efficacy of nature; they answer to certain definite causes, through which they are understood, and possess certain properties as worthy of being known as the properties of anything else, whereof the contemplation in itself affords us delight. I shall, therefore, treat of the nature and strength of the emotions according to the same method, as I employed heretofore in my investigations concerning God and the mind. I shall consider human actions and desires in exactly the same manner, as though I were concerned with lines, planes, and solids.
Sed mea haec est ratio. Nihil in natura fit quod ipsius vitio possit tribui; est namque natura semper eadem et ubique una eademque ejus virtus et agendi potentia hoc est naturae leges et regul secundum quas omnia fiunt et ex unis formis in alias mutantur, sunt ubique et semper edem atque adeo una eademque etiam debet esse ratio rerum qualiumcunque naturam intelligendi nempe per leges et regulas naturae universales. Affectus itaque odii, ir, invidi etc. in se considerati ex eadem naturae necessitate et virtute consequuntur ac reliqua singularia ac proinde certas causas agnoscunt per quas intelliguntur certasque proprietates habent cognitione nostra que dignas ac proprietates cujuscunque alterius rei cujus sola contemplatione delectamur. De affectuum itaque natura et viribus ac mentis in eosdem potentia eadem methodo agam qua in praecedentibus de Deo et mente egi et humanas actiones atque appetitus considerabo perinde ac si qustio de lineis, planis aut de corporibus esset. 
DEFINITIONS DEFINITIONES [about definitions]
3d01 (causa) adaequata^inadaequata, partiale 3d01 (causa) adaequata^inadaequata, partiale  [notes] [geomap]
I. By an adequate cause, I mean a cause through which its effect can be clearly and distinctly perceived. By an inadequate or partial cause, I mean a cause through which, by itself, its effect cannot be understood. I. Causam adaequatam appello eam cujus effectus potest clare et distincte per eandem percipi. Inadaequatam autem seu [mng eqv] partialem illam voco cujus effectus per ipsam solam intelligi nequit. 
3d02 agere^patere aliquid, actio^passio NOT actu 3d02 agere^patere aliquid, actio^passio NOT actu [notes] [geomap]
II. I say that we act when anything takes place, either within us or externally to us, whereof we are the adequate cause; that is (by the foregoing definition) when through our nature something takes place within us or externally to us, which can through our nature alone be clearly and distinctly understood. On the other hand, I say that we are passive as regards something when that something takes place within us, or follows from our nature externally, we being only the partial cause. II. Nos tum agere dico cum aliquid in nobis aut [excl exh] extra nos fit cujus adaequata sumus causa hoc est (per definitionem praecedentem) cum ex nostra natura aliquid in nobis aut [excl exh] extra nos sequitur quod per eandem solam potest clare et distincte intelligi. At contra nos pati dico cum in nobis aliquid fit vel [non-excl non-exh] ex nostra natura aliquid sequitur cujus nos non nisi partialis sumus causa
3d03 affectus 3d03 affectus [notes] [geomap]
III. By emotion I mean the modifications [Lat: affectiones] of the body, whereby the active power of the said body is increased or diminished, aided or constrained, and also the ideas of such modifications [Lat: affectiones]. N.B. If we can be the adequate cause of any of these modifications [Lat: affectiones], I then call the emotion an activity, otherwise I call it a passion, or state wherein the mind is passive. III. Per affectum intelligo corporis affectiones quibus ipsius corporis agendi potentia augetur vel [excl non-exh] minuitur, juvatur vel [excl non-exh] coercetur et simul harum affectionum ideas. Si itaque alicujus harum affectionum adaequata possimus esse causa, tum per affectum actionem intelligo, alias passionem
POSTULATES POSTULATA 
3post01 multis affici modis agendi potentia 3post01 multis affici modis agendi potentia [geomap]
I. The human body can be affected in many ways, whereby its power of activity is increased or diminished, and also in other ways which do not render its power of activity either greater or less.
N.B. This postulate or axiom rests on Postulate i. and Lemmas v. and vii., which see after II. xiii.
I. Corpus humanum potest multis affici modis quibus ipsius agendi potentia augetur vel [excl non-exh] minuitur et etiam aliis qui ejusdem agendi potentiam nec majorem nec minorem reddunt. Hoc postulatum seu [mng eqv] axioma nititur postulato 1 et lemmatibus 5 et 7, quae vide post propositionem 13 partis II. 
3post02 retinere objectorum impressiones 3post02 retinere objectorum impressiones [geomap]
II. The human body can undergo many changes, and, nevertheless, retain the impressions or traces of objects (cf. II. Post. v.), and, consequently, the same images of things (see note II. xvii.). II. Corpus humanum multas pati potest mutationes et nihilominus retinere objectorum impressiones seu [mng eqv] vestigia (de quibus vide postulatum 5 partis II) et consequenter easdem rerum imagines; quarum definitionem vide in scholio propositionis 17 partis II. 
3p01 mens agit patitur ideas 3p01 mens agit patitur ideas [geomap]
PROP. I. Our mind is in certain cases active, and in certain cases passive. In so far as it has adequate ideas it is necessarily active, and in so far as it has inadequate ideas, it is necessarily passive. PROPOSITIO I: Mens nostra quaedam agit, quaedam vero patitur nempe quatenus adaequatas habet ideas eatenus quaedam necessario agit et quatenus ideas habet inadaequatas eatenus necessario quaedam patitur
Proof.-In every human mind there are some adequate ideas, and some ideas that are fragmentary and confused (II. xl. note). Those ideas which are adequate in the mind are adequate also in God, inasmuch as he constitutes the essence of the mind (II. xl. Coroll.), and those which are inadequate in the mind are likewise (by the same Coroll.) adequate in God, not inasmuch as he contains in himself the essence of the given mind alone, but as he, at the same time, contains the minds of other things. Again, from any given idea some effect must necessarily follow (I. 36); of this effect God is the adequate cause (III. Def. i.), not inasmuch as he is infinite, but inasmuch as he is conceived as affected by the given idea (II. ix.). But of that effect whereof God is the cause, inasmuch as he is affected by an idea which is adequate in a given mind, of that effect, I repeat, the mind in question is the adequate cause (II. xi. Coroll.). Therefore our mind, in so far as it has adequate ideas (III. Def. ii.), is in certain cases necessarily active; this was our first point. Again, whatsoever necessarily follows from the idea which is adequate in God, not by virtue of his possessing in himself the mind of one man only, but by virtue of his containing, together with the mind of that one man, the minds of other things also, of such an effect (II. xi. Coroll.) the mind of the given man is not an adequate, but only a partial cause; thus (III. Def. ii.) the mind, inasmuch as it has inadequate ideas, is in certain cases necessarily passive; this was our second point. Therefore our mind, &c. Q.E.D. DEMONSTRATIO: Cujuscunque humanae mentis ideae ali adaequatae sunt, ali autem mutilatae et confusae (per scholia propositionis 40 partis II {non-deductive reference}). Ideae autem quae in alicujus mente sunt adaequatae, sunt in Deo adaequatae quatenus ejusdem mentis essentiam constituit (per corollarium propositionis 11 partis II {2p11c}) et quae deinde inadaequatae sunt in mente, sunt etiam in Deo (per idem corollarium) adaequatae non quatenus ejusdem solummodo mentis essentiam sed etiam quatenus aliarum rerum mentes in se simul continet. Deinde ex data quacunque idea aliquis effectus sequi necessario debet (per propositionem 36 partis I {1p36}) cujus effectus Deus causa est adaequata (vide definitionem 1 hujus {3d01}) non quatenus infinitus est sed quatenus data illa idea affectus consideratur (vide propositionem 9 partis II {2p09}). At ejus effectus cujus Deus est causa quatenus affectus est idea quae in alicujus mente est adaequata, illa eadem mens est causa adaequata (per corollarium propositionis 11 partis II {2p11c}). Ergo mens nostra (per definitionem 2 hujus {3d02}) quatenus ideas habet adaequatas, quaedam necessario agit, quod erat primum. Deinde quicquid necessario sequitur ex idea quae in Deo est adaequata, non quatenus mentem unius hominis tantum sed quatenus aliarum rerum mentes simul cum ejusdem hominis mente in se habet, ejus (per idem corollarium propositionis 11 partis II {2p11c}) illius hominis mens non est causa adaequata sed partialis ac proinde (per definitionem 2 hujus {3d02}) mens quatenus ideas inadaequatas habet, quaedam necessario patitur. Quod erat secundum. Ergo mens nostra etc. Q.E.D. 
3p01c pluribus passionibus obnoxiam inadaequatas 3p01c pluribus passionibus obnoxiam inadaequatas [geomap]
Corollary.-Hence it follows that the mind is more or less liable to be acted upon, in proportion as it possesses inadequate ideas, and, contrariwise, is more or less active in proportion as it possesses adequate ideas. COROLLARIUM {3p01}: Hinc sequitur mentem eo pluribus passionibus esse obnoxiam quo plures ideas inadaequatas habet et contra eo plura agere quo plures habet adaequatas
3p02 Nec corpus mentem determinare potest 3p02 Nec corpus mentem determinare potest [geomap]
PROP. II. Body cannot determine mind to think, neither can mind determine body to motion or rest or any state different from these, if such there be. PROPOSITIO II: Nec corpus mentem ad cogitandum nec mens corpus ad motum neque ad quietem nec ad aliquid (si quid est) aliud determinare potest
Proof.-All modes of thinking have for their cause God, by virtue of his being a thinking thing, and not by virtue of his being displayed under any other attribute (II. vi.). That, therefore, which determines the mind to thought is a mode of thought, and not a mode of extension; that is (II. Def. i.), it is not body. This was our first point. Again, the motion and rest of a body must arise from another body, which has also been determined to a state of motion or rest by a third body, and absolutely everything which takes place in a body must spring from God, in so far as he is regarded as affected by some mode of extension, and not by some mode of thought (II. vi.); that is, it cannot spring from the mind, which is a mode of thought. This was our second point. Therefore body cannot determine mind, &c. Q.E.D. DEMONSTRATIO: Omnes cogitandi modi Deum quatenus res est cogitans et non quatenus alio attributo explicatur, pro causa habent (per propositionem 6 partis II {2p06}); id ergo quod mentem ad cogitandum determinat, modus cogitandi est et non extensionis hoc est (per definitionem 1 partis II {2d01}) non est corpus: quod erat primum. corporis deinde motus et quies ab alio oriri debet corpore quod etiam ad motum vel [excl exh] quietem determinatum fuit ab alio et absolute quicquid in corpore oritur, id a Deo oriri debuit quatenus aliquo extensionis modus et non quatenus aliquo cogitandi modo affectus consideratur (per eandem propositionem 6 partis II {2p06}) hoc est a mente quae (per propositionem 11 partis II {2p11}) modus cogitandi est, oriri non potest : quod erat secundum. Ergo nec corpus mentem etc. Q.E.D. 
3p02s scholio propositionis 7 partis II 3p02s scholio propositionis 7 partis II
Note.-This is made more clear by what was said in the note to II. vii., namely, that mind and body are one and the same thing, conceived first under the attribute of thought, secondly, under the attribute of extension. Thus it follows that the order or concatenation of things is identical, whether nature be conceived under the one attribute or the other; consequently the order of states of activity and passivity in our body is simultaneous in nature with the order of states of activity and passivity in the mind. The same conclusion is evident from the manner in which we proved II. xii.
Nevertheless, though such is the case, and though there be no further room for doubt, I can scarcely believe, until the fact is proved by experience, that men can be induced to consider the question calmly and fairly, so firmly are they convinced that it is merely at the bidding of the mind, that the body is set in motion or at rest, or performs a variety of actions depending solely on the mind's will or the exercise of thought. However, no one has hitherto laid down the limits to the powers of the body, that is, no one has as yet been taught by experience what the body can accomplish solely by the laws of nature, in so far as she is regarded as extension. No one hitherto has gained such an accurate knowledge of the bodily mechanism, that he can explain all its functions; nor need I call attention to the fact that many actions are observed in the lower animals, which far transcend human sagacity, and that somnambulists do many things in their sleep, which they would not venture to do when awake: these instances are enough to show, that the body can by the sole laws of its nature do many things which the mind wonders at.
SCHOLIUM: Haec clarius intelliguntur ex iis quae in scholio propositionis 7 partis II dicta sunt quod scilicet mens et corpus una eademque res sit quae jam sub cogitationis jam sub extensionis attributo concipitur. Unde fit ut ordo sive rerum concatenatio una sit sive natura sub hoc sive sub illo attributo concipiatur, consequenter ut ordo actionum et passionum corporis nostri simul sit natura cum ordine actionum et passionum mentis : quod etiam patet ex modo quo propositionem 12 partis II demonstravimus. At quamvis haec ita se habeant ut nulla dubitandi ratio supersit, vix tamen credo nisi rem experientia comprobavero, homines induci posse ad haec quo animo perpendendum adeo firmiter persuasi sunt corpus ex solo mentis nutu jam moveri jam quiescere plurimaque agere quae a sola mentis voluntate et excogitandi arte pendent. Etenim quid corpus possit, nemo hucusque determinavit hoc est neminem hucusque experientia docuit quid corpus ex solis legibus naturae quatenus corporea tantum consideratur, possit agere et quid non possit nisi a mente determinetur. Nam nemo hucusque corporis fabricam tam accurate novit ut omnes ejus functiones potuerit explicare ut jam taceam quod in brutis plura observentur quae humanam sagacitatem longe superant et quod somnambuli in somnis plurima agant quae vigilando non auderent; quod satis ostendit ipsum corpus ex solis suae naturae legibus multa posse quae ipsius mens admiratur.
Again, no one knows how or by what means the mind moves the body, nor how many various degrees of motion it can impart to the body, nor how quickly it can move it. Thus, when men say that this or that physical action has its origin in the mind, which latter has dominion over the body, they are using words without meaning, or are confessing in specious phraseology that they are ignorant of the cause of the said action, and do not wonder at it.
But, they will say, whether we know or do not know the means whereby the mind acts on the body, we have, at any rate, experience of the fact that unless the human mind is in a fit state to think, the body remains inert. Moreover, we have experience, that the mind alone can determine whether we speak or are silent, and a variety of similar states which, accordingly, we say depend on the mind's decree. But, as to the first point, I ask such objectors, whether experience does not also teach, that if the body be inactive the mind is simultaneously unfitted for thinking? For when the body is at rest in sleep, the mind simultaneously is in a state of torpor also, and has no power of thinking, such as it possesses when the body is awake. Again, I think everyone's experience will confirm the statement, that the mind is not at all times equally fit for thinking on a given subject, but according as the body is more or less fitted for being stimulated by the image of this or that object, so also is the mind more or less fitted for contemplating the said object.
Deinde nemo scit qua ratione quibusve mediis mens moveat corpus neque quot motus gradus possit corpori tribuere quantaque cum celeritate idem movere queat. Unde sequitur cum homines dicunt hanc vel illam actionem corporis oriri a mente quae imperium in corpus habet, eos nescire quid dicant nec aliud agere quam speciosis verbis fateri se veram illius actionis causam absque admiratione ignorare. At dicent sive sciant sive nesciant quibus mediis mens moveat corpus, se tamen experiri quod nisi mens humana apta esset ad excogitandum, corpus iners esset. Deinde se experiri in sola mentis potestate esse tam loqui quam tacere et alia multa quae proinde a mentis decreto pendere credunt. Sed quod ad primum attinet, ipsos rogo num experientia non etiam doceat quod si contra corpus iners sit, mens simul ad cogitandum sit inepta? Nam cum corpus somno quiescit, mens simul cum ipso sopita manet nec potestatem habet veluti cum vigilat, excogitandi. Deinde omnes expertos esse credo mentem non semper que aptam esse ad cogitandum de eodem objecto sed prout corpus aptius est ut in eo hujus vel illius objecti imago excitetur, ita mentem aptiorem esse ad hoc vel illud objectum contemplandum.
But, it will be urged, it is impossible that solely from the laws of nature considered as extended substance, we should be able to deduce the causes of buildings, pictures, and things of that kind, which are produced only by human art; nor would the human body, unless it were determined and led by the mind, be capable of building a single temple. However, I have just pointed out that the objectors cannot fix the limits of the body's power, or say what can be concluded from a consideration of its sole nature, whereas they have experience of many things being accomplished solely by the laws of nature, which they would never have believed possible except under the direction of mind: such are the actions performed by somnambulists while asleep, and wondered at by their performers when awake. I would further call attention to the mechanism of the human body, which far surpasses in complexity all that has been put together by human art, not to repeat what I have already shown, namely, that from nature, under whatever attribute she be considered, infinite results follow. As for the second objection, I submit that the world would be much happier, if men were as fully able to keep silence as they are to speak. Experience abundantly shows that men can govern anything more easily than their tongues, and restrain anything more easily than their appetites; when it comes about that many believe, that we are only free in respect to objects which we moderately desire, because our desire for such can easily be controlled by the thought of something else frequently remembered, but that we are by no means free in respect to what we seek with violent emotion, for our desire cannot then be allayed with the remembrance of anything else. At dicent ex solis legibus naturae quatenus corporea tantum consideratur, fieri non posse ut causae dificiorum, picturarum rerumque hujusmodi quae sola humana arte fiunt, possint deduci nec corpus humanum nisi a mente determinaretur ducereturque, pote esset ad templum aliquod dificandum. Verum ego jam ostendi ipsos nescire quid corpus possit quidve ex sola ipsius naturae contemplatione possit deduci ipsosque plurima experiri ex solis naturae legibus fieri quae nunquam credidissent posse fieri nisi ex mentis directione ut sunt ea quae somnambuli in somnis agunt quque ipsi, dum vigilant, admirantur. Addo hic ipsam corporis humani fabricam quae artificio longissime superat omnes quae humana arte fabricatae sunt, ut jam taceam, quod supra ostenderim, ex natura sub quovis attributo considerata, infinita sequi. Quod porro ad secundum attinet, sane longe felicius sese res humanae haberent si que in hominis potestate esset tam tacere quam loqui. At experientia satis superque docet homines nihil minus in potestate habere quam linguam nec minus posse quam appetitus moderari suos; unde factum ut plerique credant nos ea tantum libere agere quae leviter petimus quia earum rerum appetitus facile contrahi potest memoria alterius rei cujus frequenter recordamur sed illa minime quae magno cum affectu petimus et qui alterius rei memoria sedari nequit.
However, unless such persons had proved by experience that we do many things which we afterwards repent of, and again that we often, when assailed by contrary emotions, see the better and follow the worse, there would be nothing to prevent their believing that we are free in all things. Thus an infant believes that of its own free will it desires milk, an angry child believes that it freely desires vengeance, a timid child believes that it freely desires to run away; further, a drunken man believes that he utters from the free decision of his mind words which, when he is sober, he would willingly have withheld: thus, too, a delirious man, a garrulous woman, a child, and others of like complexion, believe that they speak from the free decision of their mind, when they are in reality unable to restrain their impulse to talk. Experience teaches us no less clearly than reason, that men believe themselves to be free, simply because they are conscious of their actions, and unconscious of the causes whereby those actions are determined; and, further, it is plain that the dictates of the mind are but another name for the appetites, and therefore vary according to the varying state of the body. Everyone shapes his actions according to his emotion, those who are assailed by conflicting emotions know not what they wish; those who are not attacked by any emotion are readily swayed this way or that. All these considerations clearly show that a mental decision and a bodily appetite, or determined state, are simultaneous, or rather are one and the same thing, which we call decision, when it is regarded under and explained through the attribute of thought, and a conditioned state, when it is regarded under the attribute of extension, and deduced from the laws of motion and rest. This will appear yet more plainly in the sequel.  Verumenimvero nisi experti essent nos plura agere quorum postea pnitet nosque spe, quando scilicet contrariis affectibus conflictamur, meliora videre et deteriora sequi, nihil impediret quominus crederent nos omnia libere agere. Sic infans se lac libere appetere credit, puer autem iratus vindictam velle et timidus fugam. Ebrius deinde credit se ex libero mentis decreto ea loqui quae postea sobrius vellet tacuisse : sic delirans, garrula, puer et hujus farin plurimi ex libero mentis decreto credunt loqui cum tamen loquendi impetum quem habent, continere nequeant, ita ut ipsa experientia non minus clare quam ratio doceat quod homines ea sola de causa liberos se esse credant quia suarum actionum sunt conscii et causarum a quibus determinantur, ignari et praeterea quod mentis decreta nihil sint praeter ipsos appetitus, quae propterea varia sunt pro varia corporis dispositione. Nam unusquisque ex suo affectu omnia moderatur et qui praeterea contrariis affectibus conflictantur, quid velint nesciunt; qui autem nullo, facili momento huc atque illuc pelluntur. quae omnia profecto clare ostendunt mentis tam decretum quam appetitum et corporis determinationem simul esse natura vel potius unam eandemque rem quam quando sub cogitationis attributo consideratur et per ipsum explicatur, decretum appellamus et quando sub extensionis attributo consideratur et ex legibus motus et quietis deducitur, determinationem vocamus; quod adhuc clarius ex jam dicendis patebit.
For the present I wish to call attention to another point, namely, that we cannot act by the decision of the mind, unless we have a remembrance of having done so. For instance, we cannot say a word without remembering that we have done so. Again, it is not within the free power of the mind to remember or forget a thing at will. Therefore the freedom of the mind must in any case be limited to the power of uttering or not uttering something which it remembers. But when we dream that we speak, we believe that we speak from a free decision of the mind, yet we do not speak, or, if we do, it is by a spontaneous motion of the body. Again, we dream that we are concealing something, and we seem to act from the same decision of the mind as that, whereby we keep silence when awake concerning something we know. Lastly, we dream that from the free decision of our mind we do something, which we should not dare to do when awake.
Now I should like to know whether there be in the mind two sorts of decisions, one sort illusive, and the other sort free? If our folly does not carry us so far as this, we must necessarily admit, that the decision of the mind, which is believed to be free, is not distinguishable from the imagination or memory, and is nothing more than the affirmation, which an idea, by virtue of being an idea, necessarily involves (II. xlix.). Wherefore these decisions of the mind arise in the mind by the same necessity, as the ideas of things actually existing. Therefore those who believe, that they speak or keep silence or act in any way from the free decision of their mind, do but dream with their eyes open.
Nam aliud est quod hic apprime notari vellem nempe quod nos nihil ex mentis decreto agere possumus nisi ejus recordemur. Exempli gratia non possumus verbum loqui nisi ejusdem recordemur. Deinde in libera mentis potestate non est rei alicujus recordari vel ejusdem oblivisci. Quare hoc tantum in mentis potestate esse creditur quod rem cujus recordamur vel tacere vel loqui ex solo mentis decreto possumus. Verum cum nos loqui somniamus, credimus nos ex libero mentis decreto loqui nec tamen loquimur vel si loquimur, id ex corporis spontaneo motu fit. Somniamus deinde nos quaedam homines celare idque eodem mentis decreto quo dum vigilamus ea quae scimus, tacemus. Somniamus denique nos ex mentis decreto quaedam agere quae dum vigilamus non audemus atque adeo pervelim scire an in mente duo decretorum genera dentur, phantasticorum unum et liberorum alterum? Quod si eo usque insanire non libet, necessario concedendum est hoc mentis decretum quod liberum esse creditur, ab ipsa imaginatione sive memoria non distingui nec aliud esse praeter illam affirmationem quam idea quatenus idea est, necessario involvit (vide propositionem 49 partis II). Atque adeo haec mentis decreta eadem necessitate in mente oriuntur ac ideae rerum actu existentium. Qui igitur credunt se ex libero mentis decreto loqui vel tacere vel quicquam agere, oculis apertis somniant. 
3p03 actiones adaequatis passiones inadaequatis 3p03 actiones adaequatis passiones inadaequatis [geomap]
PROP. III. The activities of the mind arise solely from adequate ideas; the passive states of the mind depend solely on inadequate ideas. PROPOSITIO III: Mentis actiones ex solis ideis adaequatis oriuntur, passiones autem a solis inadaequatis pendent. 
Proof.-The first element, which constitutes the essence of the mind, is nothing else but the idea of the actually existent body (II. xi. and xiii.), which (II. xv.) is compounded of many other ideas, whereof some are adequate and some inadequate (II. xxix. Coroll., II. xxxviii. Coroll.). Whatsoever therefore follows from the nature of mind, and has mind for its proximate cause, through which it must be understood, must necessarily follow either from an adequate or from an inadequate idea. But in so far as the mind (III. i.) has inadequate ideas, it is necessarily passive: wherefore the activities of the mind follow solely from adequate ideas, and accordingly the mind is only passive in so far as it has inadequate ideas. Q.E.D. DEMONSTRATIO: Primum quod mentis essentiam constituit, nihil aliud est quam idea corporis actu existentis (per propositiones 11 {2p11} et 13 partis II {2p13}) quae (per propositionem 15 partis II) ex multis aliis componitur quarum quaedam (per corollarium propositionis 38 partis II {2p38c}) sunt adaequatae, quaedam autem inadaequatae (per corollarium propositionis 29 partis II {2p29c}). Quicquid ergo ex mentis natura sequitur et cujus mens causa est proxima per quam id debet intelligi, necessario ex idea adaequata vel [excl exh] inadaequata sequi debet. At quatenus mens (per propositionem 1 hujus {3p01}) ideas habet inadaequatas eatenus necessario patitur; ergo mentis actiones ex solis ideis adaequatis sequuntur et mens propterea tantum patitur quia ideas habet inadaequatas. Q.E.D. 
3p03s passiones ad mentem non referri nisi 3p03s passiones ad mentem non referri nisi
Note.-Thus we see, that passive states are not attributed to the mind, except in so far as it contains something involving negation, or in so far as it is regarded as a part of nature, which cannot be clearly and distinctly perceived through itself without other parts: I could thus show, that passive states are attributed to individual things in the same way that they are attributed to the mind, and that they cannot otherwise be perceived, but my purpose is solely to treat of the human mind. SCHOLIUM: Videmus itaque passiones ad mentem non referri nisi quatenus aliquid habet quod negationem involvit sive quatenus consideratur ut naturae pars quae per se absque aliis non potest clare et distincte percipi et hac ratione ostendere possem passiones eodem modo ad res singulares ac ad mentem referri nec alia ratione posse percipi sed meum institutum est de sola mente humana agere. 
3p04 nisi a causa externa destrui 3p04 nisi a causa externa destrui [geomap]
PROP. IV. Nothing can be destroyed, except by a cause external to itself. PROPOSITIO IV: Nulla res nisi a causa externa potest destrui. 
Proof.-This proposition is self-evident, for the definition of anything affirms the essence of that thing, but does not negative it; in other words, it postulates the essence of the thing, but does not take it away. So long therefore as we regard only the thing itself, without taking into account external causes, we shall not be able to find in it anything which could destroy it. Q.E.D. DEMONSTRATIO: Haec propositio per se patet; definitio enim cujuscunque rei ipsius rei essentiam affirmat sed non negat  sive [mng eqv] rei essentiam ponit sed non tollit. Dum itaque ad rem ipsam tantum, non autem ad causas externas attendimus, nihil in eadem poterimus invenire quod ipsam possit destruere. Q.E.D. 
3p05 Res contrariae sunt naturae 3p05 Res contrariae sunt naturae [geomap]
PROP. V. Things are naturally contrary, that is, cannot exist in the same object, in so far as one is capable of destroying the other. PROPOSITIO V: Res eatenus contrariae sunt naturae hoc est eatenus in eodem subjecto esse nequeunt quatenus una alteram potest destruere. 
Proof.-If they could agree together or co-exist in the same object, tmaps/3p07 Conatus essentiam.html here would then be in the said object something which could destroy it; but this, by the foregoing proposition, is absurd, therefore things, &c. Q.E.D. DEMONSTRATIO: Si enim inter se convenire vel [mng eqv] in eodem subjecto simul esse possent, posset ergo in eodem subjecto aliquid dari quod ipsum posset destruere, quod (per propositionem praecedentem {3p04}) est absurdum. Ergo res etc. Q.E.D. 
3p06 Unaquaeque in suo perseverare conatur 3p06 Unaquaeque in suo perseverare conatur [geomap]
PROP. VI. Everything, in so far as it is in itself, endeavours to persist in its own being. PROPOSITIO VI: Unaquaeque res quantum in se est, in suo esse perseverare conatur
Proof.-Individual things are modes whereby the attributes of God are expressed in a given determinate manner (I. xxv. Coroll.); that is, (I. xxxiv.), they are things which express in a given determinate manner the power of God, whereby God is and acts; now no thing contains in itself anything whereby it can be destroyed, or which can take away its existence (III. iv.); but contrariwise it is opposed to all that could take away its existence (III. v.). Therefore, in so far as it can, and in so far as it is in itself, it endeavours to persist in its own being. Q.E.D. DEMONSTRATIO: Res enim singulares modi sunt quibus Dei attributa certo et determinato modo exprimuntur (per corollarium propositionis 25 partis I {1p25}) hoc est (per propositionem 34 partis I {1p34}) res quae Dei potentiam qua Deus est et agit, certo et determinato modo exprimunt neque ulla res aliquid in se habet a quo possit destrui sive [mng eqv]  quod ejus existentiam tollat (per propositionem 4 hujus {3p04}) sed contra ei omni quod ejusdem existentiam potest tollere, opponitur (per propositionem praecedentem {3p05}) adeoque quantum potest et in se est, in suo esse perseverare conatur. Q.E.D. 
3p07 Conatus essentiam.  3p07 Conatus essentiam [geomap]
PROP. VII. The endeavour, wherewith everything endeavours to persist in its own being, is nothing else but the actual essence of the thing in question. PROPOSITIO VII: Conatus quo unaquque res in suo  esse perseverare conatur, nihil est praeter [prf eqv] ipsius rei actualem essentiam
Proof.-From the given essence of any thing certain consequences necessarily follow (I. xxxvi.), nor have things any power save such as necessarily follows from their nature as determined (I. xxix.); wherefore the power of any given thing, or the endeavour whereby, either alone or with other things, it acts, or endeavours to act, that is (III. vi.), the power or endeavour, wherewith it endeavours to persist in its own being, is nothing else but the given or actual essence of the thing in question. Q.E.D. DEMONSTRATIO: Ex data cujuscunque rei essentia quaedam necessario sequuntur (per propositionem 36 partis I {1p36}) nec res aliud possunt quam id quod ex determinata earum natura necessario sequitur (per propositionem 29 partis I {1p29}); quare cujuscunque rei potentia sive [mng eqv]  conatus quo ipsa vel [excl exh]  sola vel [excl exh] cum aliis quidquam agit vel [non-excl non-exh] agere conatur hoc est [prf eqv] (per propositionem 6 hujus {3p06}) potentia sive [mng eqv]  conatus quo in suo esse perseverare conatur, nihil est praeter ipsius rei datam sive [mng eqv]  actualem essentiam. Q.E.D. 
3p08 Conatus tempus indefinitum involvit 3p08 Conatus tempus indefinitum involvit [geomap]
PROP. VIII. The endeavour, whereby a thing endeavours to persist in its own being, involves no finite time, but an indefinite time. PROPOSITIO VIII: Conatus quo unaquque res in suo esse perseverare conatur, nullum tempus finitum sed indefinitum involvit
Proof.-If it involved a limited time, which should determine the duration of the thing, it would then follow solely from that power whereby the thing exists, that the thing could not exist beyond the limits of that time, but that it must be destroyed; but this (III. iv.) is absurd. Wherefore the endeavour wherewith a thing exists involves no definite time; but, contrariwise, since (III. iv.) it will by the same power whereby it already exists always continue to exist, unless it be destroyed by some external cause, this endeavour involves an indefinite time. DEMONSTRATIO: Si enim tempus limitatum involveret quod rei durationem determinaret, tum ex sola ipsa potentia qua res existit, sequeretur quod res post limitatum illud tempus non posset existere sed quod deberet destrui; atqui hoc (per propositionem 4 hujus {3p04}) est absurdum : ergo conatus quo res existit, nullum tempus definitum involvit sed contra quoniam (per eandem propositionem 4 hujus) si a nulla externa causa destruatur, eadem potentia qua jam existit, existere perget semper, ergo hic conatus tempus indefinitum involvit. Q.E.D. 
3p09 conatus est conscia  3p09 conatus est conscia [geomap]
PROP. IX. The mind, both in so far as it has clear and distinct ideas, and also in so far as it has confused ideas, endeavours to persist in its being for an indefinite period, and of this endeavour it is conscious. PROPOSITIO IX: Mens tam quatenus claras et distinctas quam quatenus confusas habet ideas, conatur in suo esse perseverare indefinita quadam duratione et hujus sui conatus est conscia
Proof.-The essence of the mind is constituted by adequate and inadequate ideas (III. iii.), therefore (III. vii.), both in so far as it possesses the former, and in so far as it possesses the latter, it endeavours to persist in its own being, and that for an indefinite time (III. viii.). Now as the mind (II. xxiii.) is necessarily conscious of itself through the ideas of the modifications [Lat: affectiones] of the body, the mind is therefore (III. vii.) conscious of its own endeavour. DEMONSTRATIO: Mentis essentia ex ideis adaequatis et inadaequatis constituitur (ut in propositione 3 hujus ostendimus {3p03}) adeoque (per propositionem 7 hujus {3p07}) tam quatenus has quam quatenus illas habet, in suo esse perseverare conatur idque (per propositionem 8 hujus) indefinita quadam duratione. Cum autem mens (per propositionem 23 partis II {2p23}) per ideas affectionum corporis necessario sui sit conscia, est ergo (per propositionem 7 hujus {3p07}) mens sui conatus conscia. Q.E.D. 
3p09s conatus voluntas appetitus essentia cupiditas 3p09s conatus voluntas appetitus essentia cupiditas
Note.-This endeavour, when referred solely to the mind, is called will, when referred to the mind and body in conjunction it is called appetite; it is, in fact, nothing else but man's essence, from the nature of which necessarily follow all those results which tend to its preservation; and which man has thus been determined to perform.
Further, between appetite and desire there is no difference, except that the term desire is generally applied to men, in so far as they are conscious of their appetite, and may accordingly be thus defined: Desire is appetite with consciousness thereof. It is thus plain from what has been said, that in no case do we strive for, wish for, long for, or desire anything, because we deem it to be good, but on the contrary we deem a thing to be good, because we strive for it, wish for it, long for it, or desire it.
SCHOLIUM: Hic conatus cum ad mentem solam refertur, voluntas appellatur sed cum ad mentem et corpus simul refertur, vocatur appetitus, qui proinde nihil aliud est quam ipsa hominis essentia ex cujus natura ea quae ipsius conservationi inserviunt, necessario sequuntur atque adeo homo ad eadem agendum determinatus est. Deinde inter appetitum et cupiditatem nulla est differentia nisi quod cupiditas ad homines plerumque referatur quatenus sui appetitus sunt conscii et propterea sic definiri potest nempe cupiditas est appetitus cum ejusdem conscientia. Constat itaque ex his omnibus nihil nos conari, velle, appetere neque cupere quia id bonum esse judicamus sed contra nos propterea aliquid bonum esse judicare quia id conamur, volumus, appetimus atque cupimus. 
3p10 mente secludit contraria 3p10 mente secludit contraria [geomap]
PROP. X. An idea, which excludes the existence of our body, cannot be postulated in our mind, but is contrary thereto. PROPOSITIO X: Idea quae corporis nostri existentiam secludit in nostra mente dari nequit sed eidem est contraria
Proof.-Whatsoever can destroy our body, cannot be postulated therein (III. v.). Therefore neither can the idea of such a thing occur in God, in so far as he has the idea of our body (II. ix. Coroll.); that is (II. xi., xiii.), the idea of that thing cannot be postulated as in our mind, but contrariwise, since (II. xi., xiii.) the first element, that constitutes the essence of the mind, is the idea of the human body as actually existing, it follows that the first and chief endeavour of our mind is the endeavour to affirm the existence of our body: thus, an idea, which negatives the existence of our body, is contrary to our mind, &c. Q.E.D. DEMONSTRATIO: Quicquid corpus nostrum potest destruere, in eodem dari nequit (per propositionem 5 hujus {3p05}) adeoque neque ejus rei idea potest in Deo dari quatenus nostri corporis ideam habet (per corollarium propositionis 9 partis II {2p09}) hoc est (per propositiones 11 {2p11} et 13 {2p13} partis II) ejus rei idea in nostra mente dari nequit sed contra quoniam (per propositiones 11 {2p11} et 13 essentiam constituit, est idea corporis actu existentis, primum et praecipuum nostrae mentis conatus est (per propositionem 7 hujus {3p07}) corporis nostri existentiam affirmare atque adeo idea quae corporis nostri existentiam negat, nostrae menti est contraria etc. Q.E.D. 
3p11 agendi potentiam mentis cogitandi 3p11 agendi potentiam mentis cogitandi [geomap]
PROP. XI. Whatsoever increases or diminishes, helps or hinders the power of activity in our body, the idea thereof increases or diminishes, helps or hinders the power of thought in our mind. PROPOSITIO XI: Quicquid corporis nostri agendi potentiam auget vel [excl non-exh] minuit, juvat vel [non-excl non-exh] coercet, ejusdem rei idea mentis nostrae cogitandi potentiam auget vel [excl non-exh] minuit, juvat vel [excl non-exh] coercet. 
Proof.-This proposition is evident from II. vii. or from II. xiv. DEMONSTRATIO: Haec propositio patet ex propositione 7 partis II {2p07} vel [non-excl non-exh] etiam {aliter reference} ex propositione 14 partis II. 
3p11s pati mutationes majorem minorem perfectionem 3p11s pati mutationes majorem minorem perfectionem
Note.-Thus we see, that the mind can undergo many changes, and can pass sometimes to a state of greater perfection, sometimes to a state of lesser perfection. These passive transitions explain to us the emotions of pleasure and pain. By pleasure therefore in the following propositions I shall signify a passive transition wherein the mind passes to a greater perfection. By pain I shall signify a passive transition wherein the mind passes to a lesser perfection. Further, the emotion of pleasure in reference to the body and mind together I shall call stimulation (titillatio) or merriment (hilaritas), the emotion of pain in the same relation I shall call suffering or melancholy. But we must bear in mind, that stimulation and suffering are attributed to man, when one part of his nature is more affected than the rest, merriment and melancholy, when all parts are alike affected. What I mean by desire I have explained in the note to Prop. ix. of this part; beyond these three I recognize no other primary emotion; I will show as I proceed, that all other emotions arise from these three. SCHOLIUM: Videmus itaque mentem magnas posse pati mutationes et jam ad majorem jam autem ad minorem perfectionem transire, quae quidem passiones nobis explicant affectus laetitiae et tristitiae. Per laetitiam itaque in sequentibus intelligam passionem qua mens ad majorem perfectionem transit. Per tristitiam autem passionem qua ipsa ad minorem transit perfectionem. Porro affectum laetitiae ad mentem et corpus simul relatum titillationem vel hilaritatem voco, tristitiae autem dolorem vel melancholiam. Sed notandum titillationem et dolorem ad hominem referri quando una ejus pars prae reliquis est affecta; hilaritatem autem et melancholiam quando omnes pariter sunt affect. Quid deinde cupiditas sit in scholio propositionis 9 hujus partis explicui et praeter hos tres nullum alium agnosco affectum primarium nam reliquos ex his tribus oriri in sequentibus ostendam.
But, before I go further, I should like here to explain at greater length Prop. x of this part, in order that we may clearly understand how one idea is contrary to another. In the note to II. xvii. we showed that the idea, which constitutes the essence of mind, involves the existence of body, so long as the body itself exists. Again, it follows from what we pointed out in the Corollary to II. viii., that the present existence of our mind depends solely on the fact, that the mind involves the actual existence of the body. Lastly, we showed (II. xvii., xviii. and note) that the power of the mind, whereby it imagines and remembers things, also depends on the fact, that it involves the actual existence of the body. Whence it follows, that the present existence of the mind and its power of imagining are removed, as soon as the mind ceases to affirm the present existence of the body. Now the cause, why the mind ceases to affirm this existence of the body, cannot be the mind itself (III. iv.), nor again the fact that the body ceases to exist. For (by II. vi.) the cause, why the mind affirms the existence of the body, is not that the body began to exist; therefore, for the same reason, it does not cease to affirm the existence of the body, because the body ceases to exist; but (II. xvii.) this result follows from another idea, which excludes the present existence of our body and, consequently, of our mind, and which is therefore contrary to the idea constituting the essence of our mind. Sed antequam ulterius pergam, lubet hic fusius propositionem 10 hujus partis explicare ut clarius intelligatur qua ratione idea ideae sit contraria. In scholio propositionis 17 partis II ostendimus ideam quae mentis essentiam constituit, corporis existentiam tamdiu involvere quamdiu ipsum corpus existit. Deinde ex iis quae in corollario propositionis 8 partis II et in ejusdem scholio ostendimus, sequitur praesentem nostrae mentis existentiam ab hoc solo pendere quod scilicet mens actualem corporis existentiam involvit. Denique mentis potentiam qua ipsa res imaginatur earumque recordatur, ab hoc etiam pendere ostendimus (vide propositiones 17 et 18 partis II cum ejus scholio) quod ipsa actualem corporis existentiam involvit. Ex quibus sequitur mentis praesentem existentiam ejusque imaginandi potentiam tolli simulatque mens praesentem corporis existentiam affirmare desinit. At causa cur mens hanc corporis existentiam affirmare desinit, non potest esse ipsa mens (per propositionem 4 hujus) nec etiam quod corpus esse desinit. Nam (per propositionem 6 partis II) causa cur mens corporis existentiam affirmat, non est quia corpus existere incepit : quare per eandem rationem nec ipsius corporis existentiam affirmare desinit quia corpus esse desinit sed (per propositionem 8 partis II) hoc ab alia idea oritur quae nostri corporis et consequenter nostrae mentis praesentem existentiam secludit quque adeo ideae quae nostrae mentis essentiam constituit, est contraria.  
3p12 conatur agendi potentiam augent  3p12 conatur agendi potentiam augent [geomap]
PROP. XII. The mind, as far as it can, endeavours to conceive those things, which increase or help the power of activity in the body. PROPOSITIO XII: Mens quantum potest ea imaginari conatur quae corporis agendi potentiam augent vel [non-excl non-exh] juvant. 
Proof.-So long as the human body is affected in a mode, which involves the nature of any external body, the human mind will regard that external body as present (II. xvii.), and consequently (II. vii.), so long as the human mind regards an external body as present, that is (II. xvii. note), conceives it, the human body is affected in a mode, which involves the nature of the said external body; thus so long as the mind conceives things, which increase or help the power of activity in our body, the body is affected in modes which increase or help its power of activity (III. Post. i.); consequently (III. xi.) the mind's power of thinking is for that period increased or helped. Thus (III. vi., ix.) the mind, as far as it can, endeavours to imagine such things. Q.E.D. DEMONSTRATIO: Quamdiu humanum corpus affectum est modo qui naturam corporis alicujus externi involvit tamdiu mens humana idem corpus ut praesens contemplabitur (per propositionem 17 partis II {2p17}) et consequenter (per propositionem 7 partis II {2p07}) quamdiu mens aliquod externum corpus ut praesens contemplatur hoc est (per ejusdem propositionis 17 scholium {non-deductive reference}) imaginatur tamdiu humanum corpus affectum est modo qui naturam ejusdem corporis externi involvit atque adeo quamdiu mens ea imaginatur quae corporis nostri agendi potentiam augent vel [non-excl non-exh] juvant tamdiu corpus affectum est modis qui ejusdem agendi potentiam augent vel [non-excl non-exh] juvant (vide postulatum 1 hujus {3post1}) et consequenter (per propositionem 11 hujus {3p11}) tamdiu mentis cogitandi potentia augetur vel [non-excl non-exh] juvatur ac proinde (per propositionem 6 {3p06} vel [non-excl non-exh] {aliter reference} 9 hujus) mens quantum potest eadem imaginari conatur. Q.E.D. 
3p13 agendi potentiam minuunt recordari 3p13 agendi potentiam minuunt recordari [geomap]
PROP. XIII. When the mind conceives things which diminish or hinder the body's power of activity, it endeavours, as far as possible, to remember things which exclude the existence of the first-named things. PROPOSITIO XIII: Cum mens ea imaginatur quae corporis agendi potentiam minuunt vel [excl non-exh] coercent, conatur quantum potest rerum recordari quae horum existentiam secludunt. 
Proof.-So long as the mind conceives anything of the kind alluded to, the power of the mind and body is diminished or constrained (cf. III. xii. Proof); nevertheless it will continue to conceive it, until the mind conceives something else, which excludes the present existence thereof (II. xvii.); that is (as I have just shown), the power of the mind and of the body is diminished, or constrained, until the mind conceives something else, which excludes the existence of the former thing conceived: therefore the mind (III. ix.), as far as it can, will endeavour to conceive or remember the latter. Q.E.D. DEMONSTRATIO: Quamdiu mens quicquam tale imaginatur tamdiu mentis et corporis potentia minuitur vel [excl non-exh] coercetur (ut in praecedenti propositione demonstravimus {3p12}) et nihilominus id tamdiu imaginabitur donec mens aliud imaginetur quod hujus praesentem existentiam secludat (per propositionem 17 partis II {2p17}) hoc est (ut modo ostendimus) mentis et corporis potentia tamdiu minuitur vel [non-excl non-exh] coercetur donec mens aliud imaginetur quod hujus existentiam secludit quodque adeo mens (per propositionem 9 hujus {3p09}) quantum potest imaginari vel [non-excl non-exh] recordari conabitur. Q.E.D. 
3p13c mens aversatur quae potentiam minuunt 3p13c mens aversatur quae potentiam minuunt [geomap]
Corollary.-Hence it follows that the mind shrinks from conceiving those things, which diminish or constrain the power of itself and of the body. COROLLARIUM {3p13}: Hinc sequitur quod mens ea imaginari aversatur quae ipsius et corporis potentiam minuunt vel [non-excl non-exh] coercent. 
3p13s amor odium  3p13s amor odium 
Note.-From what has been said we may clearly understand the nature of Love and Hate. Love is nothing else but pleasure accompanied by the idea of an external cause: Hate is nothing else but pain accompanied by the idea of an external cause. We further see, that he who loves necessarily endeavours to have, and to keep present to him, the object of his love; while he who hates endeavours to remove and destroy the object of his hatred. But I will treat of these matters at more length hereafter. SCHOLIUM: Ex his clare intelligimus quid amor quidque odium sit. Nempe amor nihil aliud est quam laetitia concomitante idea  causae externae et odium nihil aliud quam tristitia concomitante idea  causae externae. Videmus deinde quod ille qui amatae necessario conatur rem quam amatae praesentem habere et conservare et contra qui odit, rem quam odio habet, amovere et destruere conatur. Sed de his omnibus in sequentibus prolixius. 
3p14 duobus affectibus simul 3p14 duobus affectibus simul [geomap]
PROP. XIV. If the mind has once been affected by two emotions at the same time, it will, whenever it is afterwards affected by one of these two, be also affected by the other. PROPOSITIO XIV: Si mens duobus affectibus simul affecta semel fuit, ubi postea eorum alterutro afficietur, afficietur etiam alterius
Proof.-If the human body has once been affected by two bodies at once, whenever afterwards the mind conceives one of them, it will straightway remember the other also (II. xviii.). But the mind's conceptions indicate rather the emotions of our body than the nature of external bodies (II. xvi. Coroll. ii.); therefore, if the body, and consequently the mind (III. Def. iii.) has been once affected by two emotions at the same time, it will, whenever it is afterwards affected by one of the two, be also affected by the other. DEMONSTRATIO: Si corpus humanum a duobus corporibus simul affectum semel fuit, ubi mens postea eorum alterutrum imaginatur, statim et alterius recordabitur (per propositionem 18 partis II {2p18}). At mentis imaginationes magis nostri corporis affectus quam corporum externorum naturam indicant (per corollarium II propositionis 16 partis II {2p16}) : ergo si corpus et consequenter mens (vide definitionem 3 hujus {3d03}) duobus affectibus semel affecta fuit, ubi postea eorum alterutro afficietur, afficietur etiam altero. Q.E.D. 
3p15 quaecunque potest esse causa 3p15 quaecunque potest esse causa [geomap]
PROP. XV. Anything can, accidentally, be the cause of pleasure, pain, or desire. PROPOSITIO XV: Res quaecunque potest esse per accidens causa laetitiae, tristitiae vel [excl non-exh] cupiditatis
Proof.-Let it be granted that the mind is simultaneously affected by two emotions, of which one neither increases nor diminishes its power of activity, and the other does either increase or diminish the said power (III. Post. i.). From the foregoing proposition it is evident that, whenever the mind is afterwards affected by the former, through its true cause, which (by hypothesis) neither increases nor diminishes its power of action, it will be at the same time affected by the latter, which does increase or diminish its power of activity, that is (III. xi. note) it will be affected with pleasure or pain. Thus the former of the two emotions will, not through itself, but accidentally, be the cause of pleasure or pain. In the same way also it can be easily shown, that a thing may be accidentally the cause of desire. Q.E.D. DEMONSTRATIO: Ponatur mens duobus affectibus simul affici, uno scilicet qui ejus agendi potentiam neque auget neque minuit et altero qui eandem vel [excl non-exh] auget vel minuit (vide postulatum 1 hujus {3post01}). Ex praecedenti propositione patet quod ubi mens postea illo a sua vera causa quae (per hypothesin) per se ejus cogitandi potentiam nec auget nec minuit, afficietur, statim et hoc altero qui ipsius cognitandi potentiam auget vel [excl non-exh] minuit hoc est (per scholium propositionis 11 hujus {non-deductive reference}) laetitia vel [excl non-exh] tristitia afficietur atque adeo illa res non per se sed per accidens causa erit laetitiae vel [excl non-exh] tristitiae. Atque hac eadem via facile ostendi potest rem illam posse per accidens causam esse cupiditatis. Q.E.D. 
3p15c solo affectu contemplati 3p15c solo affectu contemplati [geomap]
Corollary. Simply from the fact that we have regarded a thing with the emotion of pleasure or pain, though that thing be not the efficient cause of the emotion, we can either love or hate it. COROLLARIUM: Ex eo solo quod rem aliquam affectu laetitiae vel [excl non-exh] tristitiae cujus ipsa non est causa efficiens, contemplati sumus, eandem amare vel [excl non-exh] odio habere possumus