David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Philosophia Mathematica 17 (3):341-362 (2009)
In a series of papers, Don Fallis points out that although mathematicians are generally unwilling to accept merely probabilistic proofs, they do accept proofs that are incomplete, long and complicated, or partly carried out by computers. He argues that there are no epistemic grounds on which probabilistic proofs can be rejected while these other proofs are accepted. I defend the practice by presenting a property I call ‘transferability’, which probabilistic proofs lack and acceptable proofs have. I also consider what this says about the similarities between mathematics and, on the one hand natural sciences, and on the other hand philosophy
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References found in this work BETA
Paul Benacerraf (1973). Mathematical Truth. Journal of Philosophy 70 (19):661-679.
D. Fallis (2000). The Reliability of Randomized Algorithms. British Journal for the Philosophy of Science 51 (2):255-271.
Don Fallis (2003). Intentional Gaps in Mathematical Proofs. Synthese 134 (1-2):45 - 69.
Don Fallis (1997). The Epistemic Status of Probabilistic Proof. Journal of Philosophy 94 (4):165-186.
Haim Gaifman (2004). Reasoning with Limited Resources and Assigning Probabilities to Arithmetical Statements. Synthese 140 (1-2):97 - 119.
Citations of this work BETA
A. Paseau (forthcoming). Knowledge of Mathematics Without Proof. British Journal for the Philosophy of Science:axu012.
Jeffrey C. Jackson (2009). Randomized Arguments Are Transferable. Philosophia Mathematica 17 (3):363-368.
Cory Juhl (2015). Statistical Data and Mathematical Propositions. Pacific Philosophical Quarterly 96 (1):100-115.
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