Spinoza's Epistemology through a Geometrical Lens by Matthew Homan

Abstract

Reviewed by: Spinoza's Epistemology through a Geometrical Lens by Matthew Homan Yitzhak Y. Melamed Matthew Homan. Spinoza's Epistemology through a Geometrical Lens. London: Palgrave Macmillan, 2021. Pp. xv + 256. Hardback, €114.39. Like most, if not all, of his contemporaries, Spinoza never developed a full-fledged philosophy of mathematics. Still, his numerous remarks about mathematics attest not only to his deep interest in the subject (a point that is also confirmed by the significant presence of mathematical books in his library), but also to his quite elaborate and perhaps unique understanding of the nature of mathematics. At the very center of his thought about mathematics stands a paradox (or, at least, an apparent paradox): Mathematics provides Spinoza with an epistemic model. Mathematical knowledge is certain (Spinoza, Opera, ed. Carl Gebhardt [Heidelberg: Carl Winters Universitätsbuchhandlung, 1925], referred to as G and cited by volume.page.line number; G II.138.9), clear (G IV.261.8), and free from teleological thinking (G II.79.33), but the objects of mathematical knowledge—namely, mathematical entities—are nothing but "auxilia imaginationis [aids of the imagination]" (G IV.57.16 and II.83.15; quotations are from The Collected Works of Spinoza, trans. Edwin Curley, 2 vols. [Princeton, NJ: Princeton University Press, 1985–2016]), entities that are not real and merely assist the imagination in carving up the world in a manner that is suitable to our limited and distortive cognitive capacities. Matthew Homan's new book is a study of Spinoza's epistemology "based on an interpretation of the epistemic and ontological status of mathematical entities in Spinoza" (4). The book has many virtues. It is well written, clear, and highly informed by the secondary literature. For the most part, Homan defends his claims through serious engagement and [End Page 329] consideration of objections and alternatives to his reading. The book is also quite ambitious in its scope as it describes Spinoza's response to skepticism, his view of the ontology of mathematics, his scientific methodology, his understanding of essence, and the notion of scientia intuitiva, the highest kind of cognition in Spinoza's epistemology. It is impossible to do justice to such a book in a brief review. For this reason, I will focus my discussion here on two critical points: one related to Spinoza's understanding of mathematics, the other to his understanding of the proper order of philosophizing. According to Homan, Spinoza is a (weak) realist about mathematics and mathematization. He defines this notion of realism as the thesis "that all finite bodies in nature are geometrical inasmuch as they have some figure—whether circular, triangular, or what have you—just by virtue of being spatially extended" (8). Thus, to count as a genuine realist it would suffice to assert that "bodies must have one kind of shape or another" (9). This radically relaxed definition of mathematical realism includes even views that assert that mathematical entities "exist [only] as properties of bodies" (8), as long as these entities (or properties) are mind-independent (views of this latter kind Homan calls "weak realism" [8]). According to Homan, the category of weak realism encompasses not only the views of Aristotle and his followers, but also those of Pierre Gassendi, Thomas Hobbes, and even Spinoza (9). One might question the analytical benefit of employing such a deflationary definition of mathematical realism (few philosophers will count as nonrealist under this definition), but for my part, I was still unsure whether Spinoza would count as a realist even under Homan's permissive definition. In one of his late letters, Spinoza notes that geometrical shapes are just "beings of reason, and not real beings" (G IV.335.4). Addressing this passage, Homan suggests that Spinoza might be referring in this passage only to shapes that are abstracted from concrete bodies, while shapes that are embedded determinations of concrete bodies are—so claims Homan—real (148; cf. 70). Unfortunately, Homan provides hardly any textual support for the suggestion that Spinoza draws such a distinction between different conceptions of shape. Moreover, one may wonder in what sense embedded shapes are the objects of mathematics (prima facie, geometrical proofs seem to be indifferent to the fact...