What Do Mathematicians Want? Probabilistic Proofs and the Epistemic Goals of Mathematicians

Logique Et Analyse 45 (2002)
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Abstract

Several philosophers have used the framework of means/ends reasoning to explain the methodological choices made by scientists and mathematicians (see, e.g., Goldman 1999, Levi 1962, Maddy 1997). In particular, they have tried to identify the epistemic objectives of scientists and mathematicians that will explain these choices. In this paper, the framework of means/ends reasoning is used to study an important methodological choice made by mathematicians. Namely, mathematicians will only use deductive proofs to establish the truth of mathematical claims. In this paper, I argue that none of the epistemic objectives of mathematicians that are currently on the table provide a satisfactory explanation of this rejection of probabilistic proofs.

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Don Fallis
Northeastern University

Citations of this work

Probabilistic proofs and transferability.Kenny Easwaran - 2009 - Philosophia Mathematica 17 (3):341-362.
Why Is Proof the Only Way to Acquire Mathematical Knowledge?Marc Lange - forthcoming - Australasian Journal of Philosophy.
Knowledge of Mathematics without Proof.Alexander Paseau - 2015 - British Journal for the Philosophy of Science 66 (4):775-799.
Non-deductive methods in mathematics.Alan Baker - 2010 - Stanford Encyclopedia of Philosophy.
The Epistemic Costs and Benefits of Collaboration.Don Fallis - 2006 - Southern Journal of Philosophy 44 (S1):197-208.

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