Title

Logic and Interaction: The Dialogical Turn

Abstract

A brief examination on the most recent literature in logic will make it apparent that a host of research in this area is devoted to the study of the interface between games, logic and epistemology. These studies provide the basis of ongoing enquiries in the history and philosophy of logic, going from the Indian, the Greek, the Arabic, the Obligationes of the Middle Ages to the most contemporary developments in the fields of theoretical computer science, computational linguistics, artificial intelligence, social sciences and legal reasoning. In fact, a dynamic turn, as Johan van Benthem puts it, is taking place where the epistemic aspects of inference are linked with game theoretical approaches to meaning. In regard to the birth of this turn, it could be placed around the 1960's when Paul Lorenzen and Kuno Lorenz developed dialogical logic, inspired by Wittgenstein's language games and mathematical game theory, and when some time later on Jaakko Hintikka combined game-theoretical semantics with epistemic (modal) logic. If we were to pinpoint a precise date, the very beginnings of the dynamic turn could be situated in 1958, with Lorenzen's talk “Logik und Agon”. However, the dynamic take on the epistemic conception of logic in both of its brands, the dialogical one and the one based on Hintikka’s GTS, disregarded a major advance in precisely the epistemic approach to logic, namely, the development by Per Martin-Löf of Constructive Type Theory (CTT) - with the sole exception of the pioneering paper of Aarne Ranta (1988). This frame, that provides a type theoretical development of the Curry-Howard-isomorphism and introduces dependent-types, leads to the formulation of a fully-interpreted language ­- a language with content that challenges the standard metalogical approach to meaning of model theoretic semantics in general and of the modal-interpretation of epistemic logic in particular. Furthermore, an inferential and contentual language based on CTT has now been successfully applied not only to the semantics of natural languages but also to the foundations of logic, computer sciences and constructive mathematics.

Indeed, from the dialogical point of view, in order to grasp the meaning of an expression, the individual does not need to know the moves ensuring his victory (he must not have a winning strategy) and does not even need to win at all. What is required is that he knows what are the relevant moves he is entitled and committed to (local meaning) in order to develop a play, in a similar way to knowing how to play chess does not necessarily mean to actually be in possession of a winning strategy. Knowing how to play allows to know what can count as a winning strategy, when there is one: strategic legitimacy (Geltung) is not to be found at the level of meaning-explanation. Thus, one way to see the motivations that animate the proposal to link CTT and games is to furnish the technical elements that bind the pragmatist approach to the grasp of concepts in Brandom’s style with the proof-theoretical CTT take on meaning.

    At this point of the discussion, we hope that the grounds - or at least a glimpse of them - for working out systematically the links between game theoretical approaches and CTT should be clear enough. A pending task, that we will not undertake here, is to discuss how the rigorous elaboration of a fully-interpreted language in the terms of CTT fits with Brandom’s pragmatic inferentialism.

References

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Contact

shahid.rahman@univ-lille3.fr