Geometrical Manual
This is a help-web to Spinoza Ethica [What it is about: Getting Started Reading Content] . Ethica, like every axiomatic deductive exposition, is a web. In logic and mathematics, every axiomatic deductive structure has a number of starting elements (definitions and axioms) and a number of end elements. Some end elements are chain-linked to all starting elements. Every element links back to some previous premiss-elements, and so on, until you are back at the starting elements. Generally, linking web pages, you can make reciprocal links and looped chains of links that bring you, through some pages, back to the original one. In a deductive structure, such things only happen when proofs are circular and hence the structure is flawed. The pure deductive structure of Ethica is modeled in the Pure Web packed for you to download in DeductiveStructure.zip. I found no loops in Ethica. This Pure Web is the origin of the on line notes Web you are now reading. But to make the notes Web, Ethica is merged again, linking to itself and to hundreds of external notes pages. So you are supposed to work with two webs: the downloaded Pure Web DeductiveStructure.zip and an on-line notes Web. Note that while handling these two webs you may be closer than any reader in the past to what Spinoza, almost beyond reasonable doubt, did himself: he had his propositions on separate sheets and thus could at any moment easily reshuffle, select, subselect and insert propositions while grinding his lenses.
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The Pure Web (to download)
If you download the DeductiveStructure.zip to your computer and import it in a web editor generating a clickable site map (like MS FrontPage and MS ExpressionWeb) you can click through screens as illustrated below, featuring the deductive elements als web pages. You can move an element-page to the centre, and click on an element-page to view it in the editing mode (then, if you want send it to your browser (type F12 in the web editors mentioned). The Pure Web exclusively models Spinoza’s own geometrical opinion concerning what follows from what, as transpires from what he refers to in his demonstrations.
A screen shot of the MS Expression Web links-view of the pure Web, proposition {1p11} set centre.
N.B. the direction of reference is Left to Right, so the direction of inference is Right to Left
The arrows point to the deductive elements used in the deductive element from where the arrow originates. Hence the argument of Ethica runs to the left. On the left side you will see only propositions (.p..), since definitions (.d..) and axioms (.a..) are always starting points, hence not referring to anything. On the right side you typically see a mix of all types, propositions, axioms, definitions, and philosophical primitives where propositions usually form only a very small minority.
The On line Web
In the on-line web, where you are now, you can also click to notes, and the notes link back to elements not formally used as premises, which should assist the reader in evaluating the meaning of concepts. Understanding all concepts and their logical interrelations is the main challenge when studying Ethica. There are 76 defined concepts. To define them, thousands of other concepts are used, 52 of which have no clear and distinct meaning to every intelligent native English or Latin speaker at once. These 52 are designated philosophical primitives. Each has a note-page where you can click to, showing the concept used in one or more poignant contexts in Ethica.
To the expert
The Spinoza expert will probably go to the on-line notes Web All Entries-view to a locus under consideration and click around, then when things get serious, check the deductive structure in the downloaded “pure”-version to generate maps like the one above. The expert analyzing the overall structure benefits probably most of the geometrical report and its links.
