Default Reasonableness and the Mathoids

Synthese 190 (17):3695-3713 (2013)
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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.

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Sharon Berry
Indiana University, Bloomington

Citations of this work

(Probably) Not companions in guilt.Sharon Berry - 2018 - Philosophical Studies 175 (9):2285-2308.
Hybrid Virtue Epistemology and the A Priori.Jonathan Jenkins Ichikawa - forthcoming - In Dylan Dodd & Elia Zardini (eds.), The A Priori: Its Significance, Sources, and Extent. Oxford University Press.
Small Steps and Great Leaps in Thought: The Epistemology of Basic Deductive Rules.Joshua Schechter - 2019 - In Magdalena Balcerak Jackson & Brendan Balcerak Jackson (eds.), Reasoning: New Essays on Theoretical and Practical Thinking. Oxford: Oxford University Press.
Aiming at Aptness.Joshua Schechter - 2019 - Episteme 16 (4):438-452.

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References found in this work

Mathematical truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.
A Study of Concepts.Christopher Peacocke - 1992 - Studia Logica 54 (1):132-133.

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