Anti-Mathematicism and Formal Philosophy

MCMP – Philosophy of Mathematics

Eric Schliesser (Ghent) gives a talk at the MCMP Colloquium (25 June, 2014) titled "Anti-Mathematicism and Formal Philosophy". Abstract: Hannes Leitgeb rightly claims that "contemporary critics of mathematization of (parts of) philosophy do not so much put forward arguments as really express a feeling of uneasiness or insecurity vis-à-vis mathematical philosophy." (Leitgeb 2013: 271) This paper is designed to articulate arguments in the place of that feeling of uneasiness. The hope is that this will facilitate more informed discussion between partisans and critics of formal philosophy. In his (2013) paper Leitgeb articulates and refutes one argument from Kant against formal philosophy. This paper will show, first, that Kant's argument as part of a much wider 18th century debates of formal methods in philosophy (prompted by success of Newton and anxiety over Spinoza). Now, obviously 'philosophy' has a broader scope in the period, so I will confine my discussion of arguments about formal methods in aeas we still consider 'philosophical' (metaphysics, epistemology, moral philosophy, etc.) In order to facilitate discussion I offer the fllowing taxonomy of arguments: (i) the global strategy, by which we mean that that the epistemic authority and security of mathematical applications as such are challenged and de-privileged; (ii) the containment strategy, by which the successful application of mathematical technique is restricted only to some limited domain; (iii) non-epistemic theories, by which the apparent popularity of mathematics within some domain of application is explained away in virtue of some non-truth-tracking features. The non-epistemic theory is generally part of a debunking strategy. I will offer examples from Hume and Mandeville of all three strategies. The second main aim is to articulate arguments that call attention to potential limitations of formal philosophy. By 'limitation' I do not have in mind formal, intrinsic limits (e.g., Godel). I explore two: (A) firs, formal philosophers often assume a kind of topic neutrality or generality when justifying their methods (even if this idea has been challenged from within Dutilh Novaes 2011). But this means that formal methods are not self-justifying (outside logic and mathematics, perhaps) and unable to ground their own worth; it follows straightforwardly that for such grounding formal approaches require substantive (often normative) non-formal premises. (B) Second, Leitgeb (2013: 274-5) insightfully discusses the ways in which formal approaches like any other method, may be abused. But because abuses with esoteric techniques may be hard to detect by bystanders (philosophical and otherwise) absent other means of control and containment, there is a heavy responsibility on practitioners of formal philosophy to develop institutional and moral safeguards that are common in, say, engineering and medical sciences against such abuses. Absent safeguards, formal philosophers require a strong collective self-policing ethos; it is unlikely that current incentives promote such safeguards.