Synthese 198 (8):7377-7399 (2020)

Authors
Jeremy Avigad
Carnegie Mellon University
Abstract
Of all the demands that mathematics imposes on its practitioners, one of the most fundamental is that proofs ought to be correct. It has been common since the turn of the twentieth century to take correctness to be underwritten by the existence of formal derivations in a suitable axiomatic foundation, but then it is hard to see how this normative standard can be met, given the differences between informal proofs and formal derivations, and given the inherent fragility and complexity of the latter. This essay describes some of the ways that mathematical practice makes it possible to reliably and robustly meet the formal standard, preserving the standard normative account while doing justice to epistemically important features of informal mathematical justification.
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DOI 10.1007/s11229-019-02524-y
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References found in this work BETA

Intention, Plans, and Practical Reason.Michael Bratman - 1987 - Cambridge: Cambridge, MA: Harvard University Press.
Rigor and Structure.John P. Burgess - 2015 - Oxford, England: Oxford University Press UK.

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Citations of this work BETA

Reconciling Rigor and Intuition.Silvia De Toffoli - 2021 - Erkenntnis 86 (6):1783-1802.
What Are Mathematical Diagrams?Silvia De Toffoli - 2022 - Synthese 200 (2):1-29.
Philosophy of Mathematics.Leon Horsten - 2008 - Stanford Encyclopedia of Philosophy.

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