Socratic proofs

Journal of Philosophical Logic 33 (3):299-326 (2004)
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Abstract

Our aim is to express in exact terms the old idea of solving problems by pure questioning. We consider the problem of derivability: "Is A derivable from Δ by classical propositional logic?". We develop a calculus of questions E*; a proof (called a Socratic proof) is a sequence of questions ending with a question whose affirmative answer is, in a sense, evident. The calculus is sound and complete with respect to classical propositional logic. A Socratic proof in E* can be transformed into a Gentzen-style proof in some sequent calculi. Next we develop a calculus of questions E**; Socratic proofs in E** can be transformed into analytic tableaux. We show that Socratic proofs can be grounded in Inferential Erotetic Logic. After a slight modification, the analyzed systems can also be viewed as hypersequent calculi.

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Andrzej Wiśniewski
Adam Mickiewicz University

Citations of this work

Inquiring Attitudes and Erotetic Logic: Norms of Restriction and Expansion.Dennis Whitcomb & Jared Millson - forthcoming - Journal of the American Philosophical Association:1-23.
A Defeasible Calculus for Zetetic Agents.Jared A. Millson - 2021 - Logic and Logical Philosophy 30 (1):3-37.
Socratic Proofs for Quantifiers★.Andrzej Wiśniewski & Vasilyi Shangin - 2006 - Journal of Philosophical Logic 35 (2):147-178.

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References found in this work

First-order logic.Raymond Merrill Smullyan - 1968 - New York [etc.]: Springer Verlag.
Structural Proof Theory.Sara Negri, Jan von Plato & Aarne Ranta - 2001 - New York: Cambridge University Press. Edited by Jan Von Plato.
Multiple Conclusion Logic.D. J. Shoesmith & Timothy Smiley - 1978 - Cambridge, England / New York London Melbourne: Cambridge University Press. Edited by T. J. Smiley.
The Posing of Questions: Logical Foundations of Erotetic Inferences.Andrzej Wiśniewski - 1995 - Dordrecht and Boston: Kluwer Academic Publishers.
The method of hypersequents in the proof theory of propositional non-classical logics.Arnon Avron - 1977 - In Wilfrid Hodges (ed.), Logic. New York: Penguin Books. pp. 1-32.

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