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How to think about informal proofs

How to think about informal proofs It is argued in this study that (i) progress in the philosophy of mathematical practice requires a general positive account of informal proof; (ii) the best candidate is to think of informal proofs as arguments that depend on their matter as well as their logical form; (iii) articulating the dependency of informal inferences on their content requires a redefinition of logic as the general study of inferential actions; (iv) it is a decisive advantage of this conception of logic that it accommodates the many mathematical proofs that include actions on objects other than propositions; (v) this conception of logic permits the articulation of project-sized tasks for the philosophy of mathematical practice, thereby supplying a partial characterisation of normal research in the field. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Synthese Springer Journals

How to think about informal proofs

Synthese , Volume 187 (2) – Sep 9, 2011

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References (43)

Publisher
Springer Journals
Copyright
Copyright © 2011 by Springer Science+Business Media B.V.
Subject
Philosophy; Epistemology; Logic; Philosophy of Science; Metaphysics; Philosophy of Language
ISSN
0039-7857
eISSN
1573-0964
DOI
10.1007/s11229-011-0007-5
Publisher site
See Article on Publisher Site

Abstract

It is argued in this study that (i) progress in the philosophy of mathematical practice requires a general positive account of informal proof; (ii) the best candidate is to think of informal proofs as arguments that depend on their matter as well as their logical form; (iii) articulating the dependency of informal inferences on their content requires a redefinition of logic as the general study of inferential actions; (iv) it is a decisive advantage of this conception of logic that it accommodates the many mathematical proofs that include actions on objects other than propositions; (v) this conception of logic permits the articulation of project-sized tasks for the philosophy of mathematical practice, thereby supplying a partial characterisation of normal research in the field.

Journal

SyntheseSpringer Journals

Published: Sep 9, 2011

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