## Spinoza and ‘Anti-Mathematics’

Abstract:

In this paper I define the concept ‘anti-mathematics’ and show how it illuminates a range of philosophical debates through the eighteenth century. By ‘anti-mathematics’ I mean to capture the expressed reservations about the authority and utility of the application of mathematics in the sciences. Such reservations can be found in major eighteenth-century thinkers, including: Berkeley, Hume, Buffon, Diderot, Toland, and Mandeville. My paper recognizes three kinds of strategies of anti-mathematics. I also argue that these reservations have shared, Spinozistic roots. So, part of the significance of my argument is to point to a feature of Spinoza’s philosophy that is now commonly ignored, but was reasonably well understood in the eighteenth century. Admittedly, none of the authors I discuss say ‘I owe this to Spinoza’; but in all the authors I discuss Spinozistic themes are lurking. So this aim of the paper is also more speculative. To be clear, the arguments that I describe under the heading of ‘anti-mathematics’ draw on earlier, especially seventeenth-century, criticisms of the application of mathematics.[1] However, the context has shifted decisively: Newton’s Principia offers a successful and authoritative exemplar of how to do mathematical natural philosophy, especially after 1740.[2] In what follows I identify three anti-mathematical strategies:
(i) “The global strategy.” This refers to arguments that challenge and de-privilege the epistemic authority and security of mathematical applications as such.
(ii) “The containment strategy.” This refers to arguments that restricts the successful application of mathematical technique to a limited number of domains or sciences (e.g., astronomy, optics).
(iii) “The error theory.” This involves a debunking strategy that explains the apparent popularity of mathematics within some domain of application in virtue of some non-truth-tracking features.
In practice, there is blending of the three strategies, but in order to keep discussion simple, I keep them distinct. Often proponents of the three strategies will appeal to lack of utility of (some) application of mathematics, but the notion of ‘utility’ at play is context-sensitive. In the following three sections I discuss each strategy in more detail. In addition, I distinguish between and give exemplars of two versions of the first two strategies. Almost all the material I discuss is known specialist literatures, but I have found little evidence that these are connected to wider historical trends or themes common to a broader eighteenth century discussion. So, my paper is intended to instantiate a virtue that I associate with conceptual articulation: making visible what is latent in philosophical history.[3] I offer examples that are relatively straightforward exegetically. But I also chose my examples in order to make two subsidiary points: (i) the global strategy becomes less plausible after the main claims of Newton’s Principia appear fully vindicated (ca. 1740-50). That despite the fact that anti-mathematics has a Spinozistic provenance, (ii) these strategies cut across familiar existing classifications along, say, empiricist-rationalist lines or a moderate-radical Enlightenments. In the fifth section, I sketch the Spinozistic origins of anti-mathematics, and I explain in brief why (i) occurred.
[1] For example, Nelson, A. (1995). Micro-chaos and idealization in cartesian physics. Philosophical studies, 77(2), 377-391; Floridi, L. (2000). Mathematical Skepticism: The Cartesian Approach. In Proceedings of the twentieth world congress of philosophy (pp. 217-265) and . Floridi, L. (2004). Mathematical skepticism: The debate between Hobbes and Wallis. Skepticism in renaissance and post-renaissance thought: New interpretations, 143-183; Jesseph, D. M. (1993). Berkeley's Philosophy of Mathematics. University of Chicago Press; Schliesser, E (forthcoming) “Spinoza and the Philosophy of Science” Oxford Handbook of Spinoza, edited by Michael Della Rocca, Oxford: Oxford University Press.
[2] I have tried to analyze this feature by way of Newton’s Challenge. See Schliesser, E. (2011). Newton’s challenge to philosophy: A programmatic essay. HOPOS: The Journal of the International Society for the History of Philosophy of Science, 1(1), 101-128.
[3] Schliesser, E. (2013). Philosophic prophecy. Philosophy and its history aims and methods in the study of early modern philosophy, 209-235.