Visual representations of Ethics

Spinoza’s Ethics 2.0

NB: this project was posted in a previous year and is being re-posted to adapt to the new website format.

Torin Doppelt is a PhD student at Queen’s University in Kingston, Canada, working on issues surrounding the geometrical method. He has constructed a series of tables – Spinoza’s Ethics 2.0 – which presents a visual representation of the geometrical structure of Spinoza’s Ethics. Torin says: “I hope to use the tables to both generate new puzzles about Spinoza’s use of the geometrical method (they have already done so, in fact), and perhaps even resolve old puzzles. At the very least I hope they can be used to help scholars (especially myself) avoid missing important details of Spinoza’s notoriously opaque text.”

There are colour-coded tables for each part of the Ethics, in which each column represents a proposition or other demonstrated element, and each row represents the elements that can be used in the proofs. There are three main ways the tables can be used: the explicit uses of an element can be determined by tracing across to cells which contain letters representing the type of use (e.g., in a main demonstration, or in a corollary, scholium, etc.), and then tracing upwards (or downwards) to determine the location. Alternatively, the explicit elements used in a given demonstration can be determined simply by noting all the filled-in cells in a column. The tables can also illuminate the way in which elements of the Ethics depend on other elements, in a way that is not apparent from the text: by tracing backwards from the elements used in a given demonstration to their columns, it is easy to determine on which further elements the first demonstration depends. There are also other ways to derive information, including tabulating usage statistics, and producing graphs of data from different sections. In this way, much information contained in the Ethics that had not been easy to see before is now accessible at a glance.

The tables are available here:

A Statistical Study of Spinoza’s Ethics

NB: this project was posted on the SRN website last year and is being re-posted to adapt to the new website format.

From Herb Roseman: Spinoza’s Euclidian logic can be represented by a mathematical object called a digraph (directed graph) which can be used to visualize and explore the Ethics.  Although others have published studies of the Ethics as a digraph on the Internet, I believe the approach can be pushed further by applying recently developed statistical tools for studying social networks and exploiting the latest graphical software. I am in the initial stages of this study, and would like to demonstrate some initial results to elicit feedback and suggestions.

Three of the files on the website are diagrams of the digraphs of Parts I, II and III of the Ethics. The color scheme distinguishes between definitions, axioms, propsitions, etc. A glance at these diagrams gives one an immediate impression of the complexity of Spinoza’s project. Statistical analysis of the digraph representing Spinoza’s Ethics may raise questions that enable us to better interpret this important and elusive text.

Some of the initial results of this project can be found on my website: