Spinoza: Empirical and Mathematical Science

I examine the (mediated) correspondence between Spinoza and Robert Boyle concerning the latter’s account of fluidity and his experiments on reconstitution of niter in the light of the epistemology and doctrine of method contained in the Treatise on the Emendation of the Intellect. I argue that both the Treatise and the correspondence reveal that for Spinoza, the proper method of science is not experimental, and that he accepted a powerful under-determination thesis. I argue that, in contrast to modern versions, Spinoza’s (...) form of naturalism was a highly rationalist and anti-empirical one. I conclude with a brief account of the value of experience and experimentation for Spinoza’s scientific method. (shrink)

In 1665, in a response to a question posed by Robert Boyle, Spinoza gave a definition of the coherence between bodies in the universe that seems to be inconsistent both with what he had written in a previous letter to Boyle (1661) and with what he would later write in his main work, the Ethics (1677). Specifically, Spinoza’s 1665 letter to Boyle asserts that bodies can adapt themselves to another body in a non-mechanistic way and absent the agency of an (...) external cause. This letter – Letter 32 – seems, therefore, to be in clear contradiction with the metaphysical determinism that is an important and characteristic element of his philosophy. This article suggests that the viewpoint expressed by Spinoza in Letter 32 may have been inspired by a spectacular discovery made by Christiaan Huygens a few months prior, namely, the self-synchronization of pendulum clocks. As I argue in this article, this new, hypothesized link to Huygens’ pendulum experiments may account for Spinoza’s otherwise paradoxical answer to Boyle in Letter 32. (shrink)

Spinoza scholars have claimed that we are faced with a dilemma: either Spinoza's definitions in his Ethics are real, in spite of indications to the contrary, or the definitions are nominal and the propositions derived from them are false. I argue that Spinoza did not recognize the distinction between real and nominal definitions. Rather, Spinoza classified definitions according to whether they require a priori or a posteriori justification, which is a classification distinct from either the real/nominal or the intensional/extensional classification. (...) I argue that Spinoza uses both a priori and a posteriori definitions in the Ethics and that recognizing both types of definitions allows us to understand Spinoza's geometric method in a new way. We can now understand the geometric method as two methods, one resulting in propositions that Spinoza considers to be absolutely certain and another resulting in propositions that Spinoza does not consider certain. The latter method makes use of a posteriori definitions and postulates, whereas the former method uses only a priori definitions and axioms. (shrink)

In this paper, I comment, in the last letters exchanged between Tschirnhaus and Spinoza, the criticism of the latter to Descartes ́s notion of extension, and the correlation of this criticism with the spinozistic theory of genetic definition. I propose that such a correlation express, in the physical and logical contexts, the spinozistic solution for the classical problem known as “problem of the One and the Many”, in the ontological context.

Gravity was a major theme in the seventeenth century scientific discussion. Trendsetters in the renewal of natural science were Galilei and Descartes. The first required a unified theory of all phenomena of gravity ; the second provided one with his vortex-hypothesis, which explained gravity by the mechanical push of subtile bodies of the vortex. This conception was tested and generally followed by Christiaan Huygens, whereas Newton presented the laws of the so called 'attraction' by which he did not at all (...) indicate the causes of those laws of motion. Spinoza comes on the scene of polemics as a critical Cartesian. Motion (of which downward motion of heavy bodies is only one instance) was explained by Descartes, but not so the rest of bodies or the equilibrium in the power relation between opposite forces, neither the reason why in some cases the particles form a hard body. Full fledged mechanism and consistent determinism lead Spinoza to account for rest and solidity in the same way, namely by means of the pressure of small and mostly unvisible bodies in the whirling environment. This paradoxical law was acknowledged as a real and important contribution to physical science by the Dutch spinozistic Cartesians Cuffeler and Overkamp, by the mathematician De Volder, by Spinoza's younger friend Tschirnhaus and in France by Malebranche. By the end of the century it was quite normal to speak about „the gravity of the air” and to consider the gravity of gross bodies as an illusion. (shrink)