Knowledge of Mathematics without Proof

British Journal for the Philosophy of Science 66 (4):775-799 (2015)
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Abstract

Mathematicians do not claim to know a proposition unless they think they possess a proof of it. For all their confidence in the truth of a proposition with weighty non-deductive support, they maintain that, strictly speaking, the proposition remains unknown until such time as someone has proved it. This article challenges this conception of knowledge, which is quasi-universal within mathematics. We present four arguments to the effect that non-deductive evidence can yield knowledge of a mathematical proposition. We also show that some of what mathematicians take to be deductive knowledge is in fact non-deductive. 1 Introduction2 Why It Might Matter3 Two Further Examples and Preliminaries4 An Exclusive Epistemic Virtue of Proof?5 Analyses of Knowledge6 The Inductive Basis of Deduction7 Physical to Mathematical Linkages8 Conclusion.

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A. C. Paseau
University of Oxford

References found in this work

Epistemology and cognition.Alvin I. Goldman - 1986 - Cambridge: Harvard University Press.
Knowledge and Its Limits.Timothy Williamson - 2000 - Philosophy 76 (297):460-464.
Knowledge and Its Limits.Timothy Williamson - 2003 - Philosophical Quarterly 53 (210):105-116.

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