What Do Mathematicians Want? Probabilistic Proofs and the Epistemic Goals of Mathematicians
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Logique Et Analyse 45 (2002)
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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Citations of this work BETA
Don Fallis (2005). The Epistemic Costs and Benefits of Collaboration. Southern Journal of Philosophy 44 (Supplement):197-208.
Don Fallis (2006). The Epistemic Costs and Benefits of Collaboration. Southern Journal of Philosophy 44 (S1):197-208.
Alexander Paseau (2015). Knowledge of Mathematics Without Proof. British Journal for the Philosophy of Science 66 (4):775-799.
Alexander Paseau (2011). Mathematical Instrumentalism, Gödel's Theorem, and Inductive Evidence. Studies in History and Philosophy of Science Part A 42 (1):140-149.
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