Crítica, Revista Hispanoamericana de Filosofía, Volume 49, number 145, abril 2017
Interacción e igualdad. La interpretación dialógica de la teoría constructiva de tipos
[Interaction and Equality Dialogical Interpretation of Constructive Type Theory]
Shahid Rahman
Département de Philosophie
CNRs, UMR 8163: STL
Université de Lille
Nicolas Clerbout
CDHACS/Instituto de Filosofía
Universidad de Valparaíso
Juan Redmond
Instituto de Filosofía
Universidad de Valparaíso

Abstract: The main aim of the present paper is to show, by means of a dialogical study, that the notion of judgemental equality of Constructive Type Theory (CTT), which in this theory furnishes the criterion of identity of a type, can be understood from the game-theoretical point of view as the result of a specific form of dialogical interaction governed by the development rule known as formal rule or (more recently) Socratic rule, which prescribes the use of copy-cat moves. It will be shown, as an example, how to develop the core of a winning strategy for Per Martin-Löf’s demonstration of the Axiom of Choice, who based his proof in the judgemental equality between the function in the antecedent and the function occurring in the consequent of the axiom.
Keywords: identity, game theory, Socratic rule, copy-cat moves, implicit interlocutor

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