David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Philosophia Mathematica 14 (3):269-286 (2006)
From ancient times to the present, the discovery and presentation of new proofs of previously established theorems has been a salient feature of mathematical practice. Why? What purposes are served by such endeavors? And how do mathematicians judge whether two proofs of the same theorem are essentially different? Consideration of such questions illuminates the roles that proofs play in the validation and communication of mathematical knowledge and raises issues that have yet to be resolved by mathematical logicians. The Appendix, in which several proofs of the Fundamental Theorem of Arithmetic are compared, provides a miniature case study.
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Alexander Paseau (2011). Proofs of the Compactness Theorem. History and Philosophy of Logic 31 (1):73-98.
S. Pollard (2013). Mathematics and the Good Life. Philosophia Mathematica 21 (1):93-109.
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