Spinoza's Ethics as a Mathematical Object

Spinoza’s geometrical approach to his masterwork, the Ethics, can be represented by a digraph, a mathematical object whose properties have been extensively studied. The paper describes a project that developed a series of computer programs to analyze the Ethics as a digraph. The paper presents a statistical analysis of the distribution of the elements of the Ethics. It applies a network statistic, betweenness, to analyze the relative importance to Spinoza’s argument of the individual propositions. The paper finds that a small percentage of the propositions greatly exceed the majority in this importance. The paper then describes two logical structures that appear respectively in the Ethics and argues that they result in redundancy in the sense that about ten percent of the propositions could have been eliminated. The appendices list these structures and describes how the resources of the study can be made available to readers.