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Switch to: Citations
References in:
Immanent Reasoning or Equality in Action: A Plaidoyer for the Play Level
Cham, Switzerland: Springer Verlag (2018)
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This book, written by one of philosophy's pre-eminent logicians, argues that many of the basic assumptions common to logic, philosophy of mathematics and metaphysics are in need of change. It is therefore a book of critical importance to logical theory. Jaakko Hintikka proposes a new basic first-order logic and uses it to explore the foundations of mathematics. This new logic enables logicians to express on the first-order level such concepts as equicardinality, infinity, and truth in the same language. The famous (...) |
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The extensive research in logic conducted by using concepts and methods of game theory as documented in this collection of papers, allows to see dialogue logic in a number of new perspectives. This situation may gain further clarity by looking back to the inception of dialogue logic in the late fifties and early sixties. |
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[Wilfrid Hodges] During the last forty or so years it has become popular to offer explanations of logical notions in terms of games. There is no doubt that many people find games helpful for understanding various logical phenomena. But we ask whether anything is really 'explained' by these accounts, and we analyse Paul Lorenzen's dialogue foundations for constructive logic as an example. The conclusion is that the value of games lies in their ability to provide helpful metaphors and representations, rather (...) |
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The two different layers of logical theory—epistemological and ontological—are considered and explained. Special attention is given to epistemic assumptions of the kind that a judgement is granted as known, and their role in validating rules of inference, namely to aid the inferential preservation of epistemic matters from premise judgements to conclusion judgement, while ordinary Natural Deduction assumptions serve to establish the holding of consequence from antecedent propositions to succedent proposition. |
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Drawing upon Martin-Löf’s semantic framework for his constructive type theory, semantic values are assigned also to natural-deduction derivations, while observing the crucial distinction between consequence among propositions and inference among judgements. Derivations in Gentzen’s format with derivable formulae dependent upon open assumptions, stand, it is suggested, for proof-objects, whereas derivations in Gentzen’s sequential format are proof-acts. |
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In the present paper I wish to regard constructivelogic as a self-contained system for the treatment ofepistemological issues; the explanations of theconstructivist logical notions are cast in anepistemological mold already from the outset. Thediscussion offered here intends to make explicit thisimplicit epistemic character of constructivism.Particular attention will be given to the intendedinterpretation laid down by Heyting. This interpretation, especially as refined in the type-theoretical work of Per Martin-Löf, puts thesystem on par with the early efforts of Frege andWhitehead-Russell. This quite (...) |
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This chapter tells how, within a century, the notions of judgment and inference were driven out of logical theory and replaced by propositions and consequence. Systematic considerations guide the treatment. The history is unashamedly Whiggish: the current position is shown as the outcome, or even culmination, of a historical development. |
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This completely self-contained study, widely considered the best book in the field, is intended to serve both as an introduction to quantification theory and as ... |
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I consider the proper interpretation of the process of ecthesis which Aristotle uses several times in the Prior analytics for completing a syllogistic mood, i.e., showing how to produce a deduction of a conclusion of a certain form from premisses of certain forms. I consider two interpretations of the process which have been advocated by recent scholars and show that one seems better suited to most passages while the other best fits a single remaining passage. I also argue that ecthesis (...) |
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A collection of some of Sellars' lectures and articles from 1951 to 1962. |
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The framework of natural deduction is extended by permitting rules as assumptions which may be discharged in the course of a derivation. this leads to the concept of rules of higher levels and to a general schema for introduction and elimination rules for arbitrary n-ary sentential operators. with respect to this schema, (functional) completeness "or", "if..then" and absurdity is proved. |
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Inferentialism claims that expressions are meaningful by virtue of rules governing their use. In particular, logical expressions are autonomous if given meaning by their introduction-rules, rules specifying the grounds for assertion of propositions containing them. If the elimination-rules do no more, and no less, than is justified by the introduction-rules, the rules satisfy what Prawitz, following Lorenzen, called an inversion principle. This connection between rules leads to a general form of elimination-rule, and when the rules have this form, they may (...) |
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Without violating the spirit of Game-Theoretical semantics, its results can be re-worked in Martin-Löf''s Constructive Type Theory by interpreting games as types of Myself''s winning strategies. The philosophical ideas behind Game-Theoretical Semantics in fact highly recommend restricting strategies to effective ones, which is the only controversial step in our interpretation. What is gained, then, is a direct connection between linguistic semantics and computer programming. |
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RésuméCette première étude permet notamment de dégager ce résultat épistémologique: les différentes formes d’“inférence co-relationnelle” connues dans la jurisprudence islamique sous le nom de qiyās représentent une forme innovante et sophistiquée de raisonnement qui permet non seulement d'avoir une conception épistémologique plus claire du raisonnement légal en général, mais aussi de produire une mécanique bien huilée pour le “raisonnement parallèle”; cette mécanique du “raisonnement parallèle” peut être déployée selon un large spectre dans différents cadres de résolution de problèmes et ne (...) |
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RésuméAristote n'a pas développé une théorie de la quantification du prédicat, mais une étude récente de Hasnawi a montré qu'Ibn Sīnā a consacré à celle-ci une étude rigoureuse. Assumant la structure aristotélicienne sujet-prédicat, Ibn Sīnā qualifie les propositions qui comportent un prédicat quantifié, de propositions déviantes. Une conséquence de cette approche avicennienne est que la seconde quantification est absorbée par le prédicat. La distinction claire ainsi opérée entre un sujet quantifié, qui pose le domaine de la quantification, et une partie (...) |
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This volume consists of the first of the John Dewey Lectures delivered under the auspices of Columbia University's Philosophy Department as well as other essays by the author. Intended to clarify the meaning of the philosophical doctrines propounded by Professor Quine in 'Word and Objects', the essays included herein both support and expand those doctrines. |
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This volume examines the notion of an analytic proof as a natural deduction, suggesting that the proof's value may be understood as its normal form--a concept with significant implications to proof-theoretic semantics. |
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In this study, several proofs of the compactness theorem for propositional logic with countably many atomic sentences are compared. Thereby some steps are taken towards a systematic philosophical study of the compactness theorem. In addition, some related data and morals for the theory of mathematical explanation are presented. |
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In Cratylus 385 b-c Plato argues that if statements () can be true or false, names (),2 as parts () of statements, are also capable of being true or false. From Aristotle onwards this view has often been challenged,3 and R. Robinson put the case against it trenchantly when he wrote:4 This argument is bad; for names have no truth-value, and the reason given for saying that they do is a fallacy of division. No one in the dialogue points out (...) |
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In Cratylus 385 b-c Plato argues that if statements () can be true or false, names (),2 as parts () of statements, are also capable of being true or false. From Aristotle onwards this view has often been challenged,3 and R. Robinson put the case against it trenchantly when he wrote:4This argument is bad; for names have no truth-value, and the reason given for saying that they do is a fallacy of division. No one in the dialogue points out that (...) |
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Three parts of philosophical papers concerned with works, matters and traditions, respectively, present ways of dealing methodically with problems that arise while having and articulating experience. The contents range from philosophy in Antiquity as well as Buddhist to existentialism and analytic philosophy, from relating science and art to the antagonism between freedom and justice. By reflecting on the particular steps of argument the papers become samples of dialogical philosophy with respect both to subject matter and means of procedure. |
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The extensive research in logic conducted by using concepts and methods of game theory as documented in this collection of papers, allows to see dialogue logic in a number of new perspectives. This situation may gain further clarity by looking back to the inception of dialogue logic in the late fifties and early sixties. |
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Section 1 contains a survey of options in constructing a formal system of dialogue rules. The distinction between material and formal systems is discussed (section 1.1). It is stressed that the material systems are, in several senses, formal as well. In section 1.2 variants as to language form (choices of logical constants and logical rules) are pointed out. Section 1.3 is concerned with options as to initial positions and the permissibility of attacks on elementary statements. The problem of ending a (...) |
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Section 1 contains a survey of options in constructing a formal system of dialogue rules. The distinction between material and formal systems is discussed (section 1.1). It is stressed that the material systems are, in several senses, formal as well. In section 1.2 variants as to language form (choices of logical constants and logical rules) are pointed out. Section 1.3 is concerned with options as to initial positions and the permissibility of attacks on elementary statements. The problem of ending a (...) |
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On the basis of Martin-Löf’s meaning explanations for his type theory a detailed justification is offered of the rule of identity elimination. Brief discussions are thereafter offered of how the univalence axiom fares with respect to these meaning explanations and of some recent work on identity in type theory by Ladyman and Presnell. |
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Nous montrons dans cet article comment les approches dynamiques en logique contemporaine ont retrouvé, quoique sous d ’ autres attendus, une configuration théorique qu ’ on peut attribuer à Aristote au moment de la rédaction des Topiques. Dans cette configuration, la logique et la rhétorique – ou au moins la dialectique – se complètent dans le cadre conceptuel homogène offert par la dialectique, entendue comme une certaine forme relativement codifiée de débat critique. L ’ idée principale est qu ’ aujourd (...) |
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Nous présentons ici une version modale des dialogues de recherche de conditions (SSD) que nous avons introduits dans [Rahman & Keiff 2004]. La sémantique utilisée correspond à celle des systèmes modaux non normaux. |
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In the present paper we confront Martin- Löf’s analysis of the axiom of choice with J. Hintikka’s standing on this axiom. Hintikka claims that his game theoretical semantics for Independence Friendly Logic justifies Zermelo’s axiom of choice in a first-order way perfectly acceptable for the constructivists. In fact, Martin- Löf’s results lead to the following considerations:Hintikka preferred version of the axiom of choice is indeed acceptable for the constructivists and its meaning does not involve higher order logic.However, the version acceptable (...) |
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The basic ideas of game-theoretical semantics are implicit in logicians' and mathematicians' folklore but used only sporadically (e.g., game quantifiers, back-and-forth methods, partly ordered quantifiers). the general suggestions of this approach for natural languages are emphasized: the univocity of "is," the failure of compositionality, a reconstruction of aristotelian categories, limitations of generative grammars, unity of sentence and discourse semantics, a new treatment of tenses and other temporal notions, etc. |
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This book, written by one of philosophy's pre-eminent logicians, argues that many of the basic assumptions common to logic, philosophy of mathematics and metaphysics are in need of change. It is therefore a book of critical importance to logical theory. Jaakko Hintikka proposes a new basic first-order logic and uses it to explore the foundations of mathematics. This new logic enables logicians to express on the first-order level such concepts as equicardinality, infinity, and truth in the same language. The famous (...) |
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In the present day and age, it seems that every constructivist philosopher of mathematics and her brother wants to be known as an intuitionist. In this paper, It will be shown that such a self-identification is in most cases mistaken. For one thing, not any old (or new) constructivism is intuitionism because not any old relevant construction is carried out mentally in intuition, as Brouwer envisaged. (edited). |
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One may formulate the dependent product types of Martin-Löf type theory either in terms of abstraction and application operators like those for the lambda-calculus; or in terms of introduction and elimination rules like those for the other constructors of type theory. It is known that the latter rules are at least as strong as the former: we show that they are in fact strictly stronger. We also show, in the presence of the identity types, that the elimination rule for dependent (...) |
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This study aims to develop systems of belief revision in which acquisition of knowledge and interactive aspects of meaning are captured as a set of questions and answers with respect to an initial set of assumptions expressed in the object language. This process is performed by a progressive deployment of hypothetical insights contained in a context of interaction of information received by an agent. This study also gives the opportunity to express interactive aspects of meaning in semantics tableaux. And thus (...) |
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In this paper, we provide a detailed critical review of current approaches to ecthesis in Aristotle’s Prior Analytics, with a view to motivate a new approach, which builds upon previous work by Marion & Rückert (2016) on the dictum de omni. This approach sets Aristotle’s work within the context of dialectic and uses Lorenzen’s dialogical logic, hereby reframed with use of Martin-Löf's constructive type theory as ‘immanent reasoning’. We then provide rules of syllogistic for the latter, and provide proofs of (...) |
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We present a new proof of soundness/completeness of tableaux with respect to dialogical games in Classical First-Order Logic. As far as we know it is the first thorough result for dialogical games where finiteness of plays is guaranteed by means of what we call repetition ranks. |
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This book is the first in the field of paraconsistency to offer a comprehensive overview of the subject, including connections to other logics and applications in information processing, linguistics, reasoning and argumentation, and philosophy of science. It is recommended reading for anyone interested in the question of reasoning and argumentation in the presence of contradictions, in semantics, in the paradoxes of set theory and in the puzzling properties of negation in logic programming. Paraconsistent logic comprises a major logical theory and (...) |
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Ordinary dialogical logic offers processing memory as a history of dialogues. Find a reference in this history is an ambiguous process, which can transform in complex or impossible issues the questions that compose a dialogue. Thus, two researches of justifications overlap in a dual problem of justification. In addition, this consideration of the memory uses a lot of technical resources.We propose a dialogical formalism that solves these problems: double justification, composition, memory saving. To do this, we will develop "special" rules (...) |
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