Cornerstone epistemology: scepticism, mathematics, non-evidentialism, consequentualism, pluralism (original) (raw)

2021, To be included in *Non-Evidentialist Epistemology*, edited by L. Moretti and N. J. L. L. Pedersen (Brill).

This paper explores a certain kind of concessive, non-evidentialist response to scepticism. The discussion is framed both at a general level and with a specific focus on mathematics. The general aim of the paper is to introduce and articulate a pluralist consequentialist form of concessive, non-evidentialist anti-scepticism. The view to be articulated is concessive and non-evidentialist because it grants that the sceptical challenge points to a genuine constraint on warrant for accepting cornerstone propositions (such as or ): it has to be non-evidential in nature. In making this point the paper offers a detailed presentation of a scepticial argument in the context of mathematics. Satisfiability is an important mathematical property: if a given mathematical theory is satisfiable, there is a structure that satisfies its axioms. A satisfiable theory can thus be said to successfully delineate a subject-matter. An unsatisfiable theory, on the other hand, cannot. I argue that, just like and other well-known anti-sceptical hypotheses are cornerstones for our thinking about the empirical world, the satisfiability proposition of a mathematical theory T () is a cornerstone for T-theorizing. Against this background, a mathematical sceptical argument is developed, transposing a familiar argument from mainstream epistemology and fitting the details to the mathematical case by drawing on Gödel's second incompleteness theorem. Having presented the mathematical sceptical argument, the remainder of the paper has a mostly general focus. I introduce a two fundamental, related challenges for concessive, non-evidentialist anti-sceptics. First, they must characterize a non-evidential notion of warrant that applies to cornerstone propositions (such as and ). Second, they must answer the question: what is epistemically good about cornerstone acceptance? I address both of these questions by developing a pluralist consequentialist framework. The framework is explicitly axiological, making it apt for addressing the second question concerning value. However, it is likewise apt for addressing the first issue, due to the nature of positive epistemic standings such as warrant, rationality, and being underwritten by epistemic reasons. Such standings are positive standings with respect to epistemic goods. Thus, answering the question of value naturally provides answers to questions concerning warrant, rationality, and other positive epistemic standings.