Default reasonableness and the mathoids

Synthese 190 (17):3695-3713 (2013)
Abstract
In this paper I will argue that (principled) attempts to ground a priori knowledge in default reasonable beliefs cannot capture certain common intuitions about what is required for a priori knowledge. I will describe hypothetical creatures who derive complex mathematical truths like Fermat’s last theorem via short and intuitively unconvincing arguments. Many philosophers with foundationalist inclinations will feel that these creatures must lack knowledge because they are unable to justify their mathematical assumptions in terms of the kind of basic facts which can be known without further argument. Yet, I will argue that nothing in the current literature lets us draw a principled distinction between what these creatures are doing and paradigmatic cases of good a priori reasoning (assuming that the latter are to be grounded in default reasonable beliefs). I will consider, in turn, appeals to reliability, coherence, conceptual truth and indispensability and argue that none of these can do the job
Keywords Epistemology  A priori  Basic knowledge
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References found in this work BETA
Paul Benacerraf (1973). Mathematical Truth. Journal of Philosophy 70 (19):661-679.
Paul Boghossian (2003). Blind Reasoning. Aristotelian Society Supplementary Volume 77 (1):225–248.
Elijah Chudnoff (2013). Intuitive Knowledge. Philosophical Studies 162 (2):359-378.
Sinan Dogramaci (2012). Reverse Engineering Epistemic Evaluations. Philosophy and Phenomenological Research 84 (3):513-530.

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