Philosophical Studies 173 (10):2605-2628 (2016)

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 are best understood as a dialogue between two 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.
Keywords Reductio ad absurdum  Mathematical proofs  Dialogues
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DOI 10.1007/s11098-016-0667-6
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References found in this work BETA

The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History.Reviel Netz - 1999 - Cambridge and New York: Cambridge University Press.
Proofs and Refutations (IV).I. Lakatos - 1963 - British Journal for the Philosophy of Science 14 (56):296-342.
Proofs and Refutations.Imre Lakatos - 1980 - Noûs 14 (3):474-478.

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Citations of this work BETA

Limits of Abductivism About Logic.Ulf Hlobil - 2021 - Philosophy and Phenomenological Research 103 (2):320-340.
Dialogical Logic.Laurent Keiff - 2010 - Stanford Encyclopedia of Philosophy.
God is Not a Person.Simon Hewitt - 2019 - International Journal for Philosophy of Religion 85 (3):281-296.

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