How to think about informal proofs

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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
Original languageEnglish
Pages (from-to)715-730
Number of pages16
JournalSynthese
Volume187
Issue number2
Early online date9 Sept 2011
DOIs
Publication statusPublished - 1 Jul 2012

Keywords

  • informal proof
  • mathematical practice
  • inferential action
  • argumentation theory
  • speech-act

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