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date: 22 July 2018

Abstract and Keywords

Spinoza consistently used geometrical demonstrations to present his philosophical ideas. This is evident in the Ethics, Short Treatise, and Descartes’ Principles of Philosophy Demonstrated in the Geometric Manner. In Tractatus de Intellectu Emendatione, Spinoza talks about “a way of healing the intellect, and purifying it” that might precede geometrical demonstration but gives no definition of the intellect or any general procedure for acquiring true definitions. This chapter examines how one acquires these definitions, discussing first what Spinoza might have considered to be the advantages or virtues of geometrical demonstration: transparency, force, security, scale, compactness, flexibility, generality, and sense-independence. It then analyzes Spinoza’s relation to Descartes, highlighting the distinction between the analytic and the synthetic method, their different sense of geometrical order, and another virtue of geometry: ease. Finally, it invokes the idea of method Spinoza outlined in Emendatione as a solution to the puzzle mentioned earlier.

Keywords: Spinoza, geometry, Tractatus de Intellectu Emendatione, intellect, virtues, transparency, Descartes, geometrical order, ease, emendative method

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