Linking Game-Theoretical Approaches with Constructive Type Theory

Clerbout, Nicolas; Rahman, Shahid

doi:10.1007/978-3-319-19063-1

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“…Without expressions of this category, there can be no speech acts of any kind, and hence no specifically linguistic practice" (Brandom, 2000, p. 125). 10 These remarks have already been pointed out in Clerbout and Rahman (2015), who also notice that although Brandom's approach and the dialogical frame share some important tenets, they are different frames after all. More precisely, although the pragmatist approach to meaning of the dialogical framework shares with Brandom's pragmatist inferentialism the claim that the meaning of linguistic expressions is related to their role in games of questions and answers and also endorses Brandom's notion of justification of a judgment as involving the interaction of commitments and entitlements, dialogicians maintain that more fundamental lowerlevels should be distinguished (see Appendix I).…”

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“…13 This hinges on a general problem of the standard dialogical approach to meaning where the dialogical semantics affects only logical constants. In pursuance of filling that gap in the dialogical theory of meaning new researches have linked dialogical logic with Per Martin-Löfs (1984) Constructive Type Theory (CTT), where a fully-interpreted language is unfolded (see Clerbout, 2013, 2014;Clerbout and Rahman, 2015;Rahman et al, 2015).…”

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“…The basic idea behind the notion of core is to get rid of redundant information (for example, different orders of moves) which we find in extensive forms of strategies (see Clerbout and Rahman, 2015). to Free Logic…”

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Um quadro dialógico para ficções como objetos hipotéticos

Rahman¹,

Redmond²

2015

Filosofia Unisinos

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Recent work on the development of a dialogical approach to the logic of fi ction stresses the notion of existence as choice. Moreover, this approach to existence has been combined with the notion of ontological dependence as deployed by A. Thomasson's artifactual theory of fi ction. In order to implement such a combination within the dialogical frame several predicates of ontological dependence have been defi ned. However, the defi nition of such predicates seems to lean on a model-theoretic semantics for modal logic after all. The main aim of the present paper is to set a dialogical frame for the study of fi ctions in the context of the dialogical approach of CTT recently developed by S. Rahman and N. Clerbout where a fully-interpreted language is unfolded. We will herewith develop the idea that in such a setting fi ctional entities are understood as hypothetical objects, that is, objects (functions) the existence of which is dependent upon one or more hypotheses that restrict the scope of choices available. We will fi nish the paper by suggesting that this provides both a natural and genuinely dialogical way to understand R. Frigg's take on scientifi c models as fi ctions and a new perspective on Thomasson's notion of generic ontological dependence.Keywords: fi ction, dialogues, dialogical logic, hypothetical objects, scientifi c models. ResumoTrabalhos recentes sobre o desenvolvimento de uma abordagem dialógica para a lógica da fi cção enfatizam a noção de existência como escolha. Além disso, 1 The present work is a result of the project Fondecyt Regular No. 1141260 (Principal Investigator: Juan Redmond). We thank the CONICYT (Chile) for fostering the preparation of this article and Nicolas Clerbout (University of Valparaíso, Convenio de Desempeño CDHACS, Instituto de Filosofía), for fruitful discussions during and after the meetings that took place within the frame of the project. IntroductionA brief examination of 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 into 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 J. v. Benthem puts it, is taking place where the epistemic aspects of inference are linked with game theoretical approaches to meaning 4 . In regard to the birth of this turn, it could be placed around the 1960s, when P. Lorenzen and K. Lorenz developed dialogical logic -inspired by Wittgenstein's language games and mathematical game theory -and when some time later Hintikka (1962Hintikka ( , 1973 combined game-theoretical semantics with epistemic (modal) logic 5 . However, while Hintikka's approach is based on a model theoretic semantics, ...

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Um quadro dialógico para ficções como objetos hipotéticos

Rahman¹,

Redmond²

2015

Filosofia Unisinos

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“…SeeRahman (2015) andRahman/Iqbal (2018).30 Notice that if the role of the Opponent in adversial dialogues is reduced to checking the achievement of logical truth, one would wonder what the role of the Opponent might be in more cooperation-featured dialogues: A soft interlocutor ready to accept weak arguments?…”

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Dialogues, Reasons and Endorsement

Rahman

Iqbal

Soufi

2019

Inferences by Parallel Reasoning in Islamic Jurisprudence

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The main aim of the present paper is to show that, if we follow the dialogical insight that reasoning and meaning are constituted during interaction, and we develop this insight in a dialogical framework for Martin-Löf's Constructive Type Theory, a conception of knowledge emerges that has important links with Robert Brandom's (1994 inferential pragmatism. However, there are also some significant differences that are at center of the dialogical approach to meaning. The present paper does not discuss explicitly phenomenology, however, one might see our proposal as setting the basis for a further study linking phenomenology and the dialogical conception of meaningthe development of such a link is part of several ongoing researches. I Shahid Rahman 2 2 Local reasonsRecent developments in dialogical logic show that the Constructive Type Theory approach to meaning is very natural to the game-theoretical approaches in which (standard) metalogical features are explicitly displayed at the object language-level. 3 This vindicates, albeit in quite a 2 In fact, the present paper relies on the main technical and philosophical results of Rahman/McConaugey/ Klev/Clerbout (2018). 3 Such as developed in Rahman/McConaugey/Klev/Clerbout (2018) and also in Clerbout/Rahman (2015). different fashion, Hintikka's plea for the fruitfulness of game-theoretical semantics in the context of epistemic approaches to logic, semantics, and the foundations of mathematics. 4 From the dialogical point of view, the actions-such as choices-that the particle rules associate with the use of logical constants are crucial elements of their full-fledged (local) meaning: if meaning is conceived as constituted during interaction, then all of the actions involved in the constitution of the meaning of an expression should be made explicit; that is, they should all be part of the object-language.This perspective roots itself in Wittgenstein's remark according to which one cannot position oneself outside language in order to determine the meaning of something and how it is linked to syntax; in other words, language is unavoidable: this is his Unhintergehbarkeit der Sprache. According to this perspective of Wittgensteins, language-games are supposed to accomplish the task of studying language from a perspective that acknowledges its internalized feature. This is what underlies the approach to meaning and syntax of the dialogical framework in which all the speech-acts that are relevant for rendering the meaning and the "formation" of an expression are made explicit. In this respect, the metalogical perspective which is so crucial for model-theoretic conceptions of meaning does not provide a way out. It is in such a context that Lorenz writes:Also propositions of the metalanguage require the understanding of propositions, […] and thus cannot in a sensible way have this same understanding as their proper object. The thesis that a property of a propositional sentence must always be internal, therefore amounts to articulating the insight that in propositions about ...

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“…However, the (Clerbout & Rahman, 2015) book was written from the CTT perspective on dialogical logic, rather than the other way round. The present book, Immanent Reasoning or Equality in Action, should provide the other perspective in the dialogue between the dialogical framework and Constructive Type Theory.…”

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