The Method of Socratic Proofs: From the Logic of Questions to Proof Theory

In Moritz Cordes (ed.), Asking and Answering: Rivalling Approaches to Interrogative Methods. Tübingen: Narr Francke Attempto. pp. 183–198 (2021)
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Abstract

I consider two cognitive phenomena: inquiring and justifying, as complementary processes running in opposite directions. I explain on an example that the former process is driven by questions and the latter is a codification of the results of the first one. Traditionally, proof theory focuses on the latter process, and thus describes the former, at best, as an example of a backward proof search. I argue that this is not the best way to analyze cognitive processes driven by questions, and that proof-theoretical analysis of questions can bring mutual benefits for both proof theory and erotetic logic. In the second part of my paper (sect. 6.3) I introduce the structural rules of weakening and contraction. Results concerning their admissibility are discussed. I also sketch an erotetic interpretation of the rule of weakening as reducing information noise, and that of contraction as securing information.

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References found in this work

Basic proof theory.A. S. Troelstra - 1996 - New York: Cambridge University Press. Edited by Helmut Schwichtenberg.
Structural Proof Theory.Sara Negri, Jan von Plato & Aarne Ranta - 2001 - New York: Cambridge University Press. Edited by Jan Von Plato.
The Posing of Questions: Logical Foundations of Erotetic Inferences.Andrzej Wiśniewski - 1995 - Dordrecht and Boston: Kluwer Academic Publishers.
A Defeasible Calculus for Zetetic Agents.Jared A. Millson - 2021 - Logic and Logical Philosophy 30 (1):3-37.
Proof Analysis: A Contribution to Hilbert's Last Problem.Sara Negri & Jan von Plato - 2011 - Cambridge and New York: Cambridge University Press. Edited by Jan Von Plato.

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