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The Philosophy of Mathematical Practice$
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Paolo Mancosu

Print publication date: 2008

Print ISBN-13: 9780199296453

Published to Oxford Scholarship Online: February 2010

DOI: 10.1093/acprof:oso/9780199296453.001.0001

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Understanding Proofs

Understanding Proofs

(p.317) 12 Understanding Proofs
The Philosophy of Mathematical Practice

Jeremy Avigad

Oxford University Press

In informal speech, ascriptions of mathematical understanding are typically clarified by spelling out the kinds of abilities an agent is assumed to possess. This chapter argues that such an approach is fruitful in scientific domains as well. The practice of formal verification, which involves the use of computers to check mathematical proofs, is one example. In particular, understanding ordinary mathematical proofs involves being able to recognize interesting classes of high-level inferences.

Keywords:   mathematical understanding, formal verification, informal speech, mathematical proofs, high-level inferences

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