Reductio ad absurdum from a dialogical perspective

Catarina Dutilh Novaes*

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

It is well known that reductio ad absurdum arguments raise a number of interesting philosophical questions. What does it mean to assert something with the precise goal of then showing it to be false, i.e. because it leads to absurd conclusions? What kind of absurdity do we obtain? Moreover, in the mathematics education literature number of studies have shown that students find it difficult to truly comprehend the idea of reductio proofs, which indicates the cognitive complexity of these constructions. In this paper, I start by discussing four philosophical issues pertaining to reductio arguments. I then briefly present a dialogical conceptualization of deductive arguments, according to which such arguments (especially mathematical proofs) are best understood as a dialogue between two (fictitious) participants—Prover and Skeptic. Finally, I argue that many of the philosophical and cognitive difficulties surrounding reductio arguments are dispelled or at least further clarified once one adopts a dialogical perspective.

Original languageEnglish
Pages (from-to)2605-2628
Number of pages24
JournalPhilosophical Studies
Volume173
Issue number10
DOIs
Publication statusPublished - 1 Oct 2016
Externally publishedYes

Keywords

  • Dialogues
  • Mathematical proofs
  • Reductio ad absurdum

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