Poincaré and Prawitz on mathematical induction

Yacin Hamami

Research output: Chapter in Book/Report/Conference proceedingConference paperResearch

Abstract

Poincaré and Prawitz have both developed an account of how one can acquire knowledge through reasoning by mathematical induction. Surprisingly, their two accounts are very close to each other: both consider that what underlies reasoning by mathematical induction is a certain chain of inferences by modus ponens ‘moving along’, so to speak, the well-ordered structure of the natural numbers. Yet, Poincaré’s central point is that such a chain of inferences is not sufficient to account for the knowledge acquisition of the universal propositions that constitute the conclusions of inferences by mathematical induction, as this process would require to draw an infinite number of inferences. In this paper, we propose to examine Poincaré’s point – that we will call the closure issue – in the context of Prawitz’s framework where inferences are represented as operations on grounds. We shall see that the closure issue is a challenge that also faces Prawitz’s own account of mathematical induction and which points out to an epistemic gap that the chain of modus ponens cannot bridge. One way to address the challenge is to introduce suitable additional inferential operations that would allow to fill the gap. We will end the paper by sketching such a possible solution.
Original languageEnglish
Title of host publicationThe Logica Yearbook 2014
PublisherCollege Publications
Pages149-164
Number of pages16
ISBN (Print)978-1-84890-177-3
Publication statusPublished - 2015
EventLogica 2014 - Hejnice, Hejnice, Czech Republic
Duration: 16 Jun 201420 Jun 2014

Conference

ConferenceLogica 2014
CountryCzech Republic
CityHejnice
Period16/06/1420/06/14

Keywords

  • Poincaré
  • Prawitz
  • mathematical induction

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