77. - Geometrical Method

Summary

Many of Spinoza’s writings make use of demonstrative procedures which he identifies either narrowly or broadly with mathematical demonstration. The importance of mathematical demonstration is underscored by the subtitle of the Ethics: “Ordine Geometrico demonstrate” (demonstrated in a geometrical order). Spinoza’s DPP has a similar subtitle: “More Geometrico Demonstratae”: demonstrated in a geometrical manner. Both works derive propositions from definitions and axioms in a manner reminiscent of Euclid’s axiomatic deduction of basic propositions of plane geometry in the Elements. The KV also includes an argument for three propositions (1.114–16) derived from seven axioms. The TP is not explicitly presented in a Euclidean form. But Spinoza asserts (TP1.4) that the argument is demonstrative and pursued in the same “free” manner in which mathematicians investigate mathematical subjects. Furthermore, according to Spinoza the conclusions of the TP follow demonstratively from the “necessity of human nature” and the “universal striving all men have to preserve themselves” (3.18).