The Epistemic Status of Consistency Claims, By Dan Waxman
Department of Philosophy
New York University
Abstract: Our best mathematical theories (e.g. arithmetic, analysis, and set theory) are consistent — or, at least, so we typically think. But, on reflection, it is not at all obvious how we are justified in taking them to be so. My aim in this talk is to explore the epistemic status of consistency claims. To that end I will critically consider two routes to justification in consistency: one which involves deriving the fact that a theory is consistent from the fact that it is true, and another which infers that consistency is the best explanation of the lack of discovered inconsistencies in our theories and their applicability outside of mathematics. I will then go on to propose a conceivability-based account, according to which we obtain justification in a theory’s consistency by possessing a conception of a structure which satisfies it.