Immanent Reasoning or Equality in Action: A Plaidoyer for the Play Level

Cham, Switzerland: Springer Verlag (2018)
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Abstract

This monograph proposes a new way of implementing interaction in logic. It also provides an elementary introduction to Constructive Type Theory. The authors equally emphasize basic ideas and finer technical details. In addition, many worked out exercises and examples will help readers to better understand the concepts under discussion. One of the chief ideas animating this study is that the dialogical understanding of definitional equality and its execution provide both a simple and a direct way of implementing the CTT approach within a game-theoretical conception of meaning. In addition, the importance of the play level over the strategy level is stressed, binding together the matter of execution with that of equality and the finitary perspective on games constituting meaning. According to this perspective the emergence of concepts are not only games of giving and asking for reasons, they are also games that include moves establishing how it is that the reasons brought forward accomplish their explicative task. Thus, immanent reasoning games are dialogical games of Why and How.

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Chapters

A Brief Introduction to Constructive Type Theory

Martin-Löf’s Constructive Type Theory is a formal language developed in order to reason constructively about mathematics. It is thus a formal language conceived primarily as a tool to reason with rather than a formal language conceived primarily as a mathematical system to reason about. Constructive... see more

Advanced Dialogues: Strategy Level

The strategy standpoint is but a generalisation of the procedure which is implemented at the play level; it is a systematic exposition of all the relevant variants of a game—the relevancy of the variants being determined from the viewpoint of one of the two players. For a more intuitive approach of ... see more

Concluding Remarks: A Plaidoyer for the Play Level

To some extent, the criticisms the dialogical approach to logic has been subject to have provided an opportunity for clarifying its basic tenets. Moreover, our responses to the objections have highlighted crucial distinctions constituting the originality and flexibility of this logical framework. We... see more

Advanced Dialogues: Play Level

This chapter will provide a more technical approach to the standard dialogical framework at the play level. The next chapter will do the same at the strategy level. It will then be possible to introduce local reasons in the dialogues and thus start making it explicit that dialogues are games of givi... see more

From Dialogical Strategies to CTT-Demonstrations and Back

In a nutshell, we take from the following two correspondences within a P-winning strategy, provided some exceptions to be discussed below:The result of applying a particle rule to a P-move corresponds to the application of an introduction rule of a CTT-demonstration rule .

Introduction: Some Brief Historical and Philosophical Remarks

The present volume develops a new way of linking Constructive Type Theory with dialogical logic by following these three complementary paths, as mentioned in the preface:The path observing that Sundholm’s notion of epistemic assumption is closely linked to the Copy-cat and Socraticrules and that it ... see more

Local Reasons and Dialogues for Immanent Reasoning

In this chapter we will provide the logical framework of dialogues for immanent reasoning, the dialogical framework incorporating features of Constructive Type Theory and making explicit the players’ reasons for asserting a proposition. We will therefore be using the material provided in Chaps. 10.1... see more

Material Dialogues

As pointed out by Krabbe , material dialogues—that is, dialogues in which propositions have content—receive in the writings of Paul Lorenzen and Kuno Lorenz priority over formal dialogues: material dialogues constitute the locus where the logical constants are introduced. However in the standard dia... see more

Basic Notions for Dialogical Logic

The dialogical approach to logic is not a specific logical system; it is rather a general framework having a rule-based approach to meaning which allows different logics to be developed, combined and compared within it. The main philosophical idea behind this framework is that meaning and rationalit... see more

The Remarkable Case of the Axiom of Choice

It is rightly said that the principle of set theory known as the Axiom of Choice is “probably the most interesting and in spite of its late appearance, the most discussed axiom of mathematics, second only to Euclid’s Axiom of Parallels which was introduced more than two thousand years ago” .

The Dialogical Roots of Equality: Dialogues for Immanent Reasoning

In this chapter we will spell out all the relevant rules of dialogues for immanent reasoning, that is, the dialogical framework incorporating features of Constructive Type Theory—a dialogical framework making the players’ reasons for asserting a proposition explicit. The rules can be divided, just a... see more

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Author Profiles

Ansten Klev
Czech Academy of Sciences
Shahid Rahman
Université Charles-de-Gaulle - Lille 3

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Empiricism and the philosophy of mind.Wilfrid Sellars - 1956 - Minnesota Studies in the Philosophy of Science 1:253-329.
Truth and other enigmas.Michael Dummett - 1978 - Cambridge: Harvard University Press.
Tractatus logico-philosophicus.Ludwig Wittgenstein - 1922 - Filosoficky Casopis 52:336-341.

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