Hume on the Social Construction of Mathematical Knowledge Tamás Demeter Abstract Mathematics for Hume is the exemplary field of demonstrative knowledge. Ideally, this knowledge is a priori as it arises only from the comparison of ideas without any further empirical input; it is certain because demonstration consist of steps that are intuitively evident and infallible; and it is also necessary because the possibility of its falsity is inconceivable as it would imply a contradiction. But this is only the ideal, because demonstrative sciences are human enterprises and as such they are just as fallible as their human practitioners. According to the reading suggested here, Hume develops a radical sceptical challenge for mathematics, and thereby he undermines the knowledge claims associated with demonstrative reasoning. But Hume does not stop there: he also offers resources for a sceptical solution to this challenge, one that appeals crucially to social practices, and sketches the social genealogy of a community-wide mathematical certainty. While explaining this process, he relies on the conceptual resources of his faculty psychology that helps him to distinguish between the metaphysics and practices of mathematical knowledge. His account explains why we have reasons to be dubious about our reasoning capacities, and also how human nature and sociability offers some remedy from these epistemic adversities. Keywords: certainty, demonstrative reasoning, mathematical practice, metaphysics of knowledge, faculties, scepticism, sceptical solution, sympathy I. Introduction One classification of knowledge Hume introduces is based on the “degrees of evidence” (T 1.3.11.2) that can be assigned to propositions and arguments. In the Treatise these degrees are called “knowledge”, “proof” and “probability”, a classification Hume retains in the first Enquiry (Section 6) except for replacing the label “knowledge” by “demonstration”. This first
Acknowledgements I am indebted to Krisztián Pete for useful discussions leading to this paper. Its first version was presented at the Oxford Hume Forum in April 2017. I am grateful to Dan O’Brien and Lorenzo Greco for the invitation, and to the audience, especially Don Garrett, Peter Millican and Eric Schliesser for helpful comments and discussion. My work has been supported by the MTA BTK “Morals and Science” Lendület Project. Hume’s T – A Treatise of Human Nature, ed. by David Fate Norton, Marthe Norton, Oxford: Clarendon, 2007. Enquiry – An Enquiry concerning Human Understanding, ed. by Tom Beauchamp, Oxford: Clarendon, 2000. Secondary literature Allison, Henry, 2008, Custom and Reason in Hume: A Kantian Reading of the First Book of the Treatise, Oxford: OUP. Badici, Emil, 2011, “Standards of Equality and Hume’s View of Geometry”, Pacific Philosophical Quarterly 92, 448-467. Beebee, Helen, 2011, “Hume’s Two Definitions: The Procedural Interpretation”, Hume Studies 37, 243-274. Bloor, David, 1997, Wittgenstein, Rules and Institutions, London: Routledge. Boehm, Miren, 2016, “Hume’s Foundational Project in the Treatise”, European Journal of Philosophy 24, 55-77. Buckle, Stephen, 2002, Hume’s Enlightenment Oxford: OUP. Rachel, 2008, Hume’s Morality: Feeling and Fabrication, Oxford: OUP. Coleman, Dorothy, 1979, “Is Mathematics for Hume Synthetic a Priori?”, The Southwestern Journal of Philosophy 10, 113–126. Demeter, Tamás & Láng, Benedek & Schmal, Dániel, 2015, “Scientia” in Marco Sgarbi (ed.), Encyclopedia of Renaissance Philosophy, Cham: Springer, DOI Demeter, Tamás, 2016, David Hume and the Culture of Scottish Newtonianism: Methodology and Ideology in Enlightenment Inquiry, Leiden: Brill.