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77. - Geometrical Method

from G

Published online by Cambridge University Press:  09 January 2025

By
Aaron Garrett
Edited by
Karolina Hübner  and
Justin Steinberg
Karolina Hübner
Affiliation:
Cornell University, New York
Justin Steinberg
Affiliation:
Cornell University, New York
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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).

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Chapter
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The Cambridge Spinoza Lexicon , pp. 201 - 206
Publisher: Cambridge University Press
Print publication year: 2024

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References

Recommended Reading

Adams, M. P. (2014). Hobbes, definitions, and simplest conceptions. Hobbes Studies, 27(1), 35–60.CrossRefGoogle Scholar
Allison, H. E. (2022). An Introduction to the Philosophy of Spinoza. Cambridge University Press.CrossRefGoogle Scholar
Curley, E. (1988). Behind the Geometrical Method: A Reading of Spinoza’s Ethics. Princeton University Press.CrossRefGoogle Scholar
Garrett, A. (2003). Meaning in Spinoza’s Method. Cambridge University Press.CrossRefGoogle Scholar
Garrett, A. (2017). Virtues of geometry. In Rocca, M. Della (ed.), The Oxford Handbook of Spinoza (pp. 18–44). Oxford University Press.Google Scholar
Gueroult, M. (1968). Spinoza, vol. i: Dieu (Éthique, 1). Aubier-Montaigne.Google Scholar
Hübner, K. (2015). Spinoza on essences, universals, and beings of reason. Pacific Philosophical Quarterly, 97(1), 58–88.CrossRefGoogle Scholar
Meshelski, K. (2011). Two kinds of definition in Spinoza’s Ethics. British Journal for the History of Philosophy, 19(2), 201–18.CrossRefGoogle Scholar
Ribe, N. M. (1997). Cartesian optics and the mastery of nature. Isis, 88(1), 42–61.CrossRefGoogle ScholarPubMed
Wolfson, H. A. (1934). The Philosophy of Spinoza: Unfolding the Latent Processes of His Reasoning. 2 vols. Harvard University Press.Google Scholar

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