The paper presents an application of game-theoretical ideas to the semantics of natural language, especially the analysis of quantifiers and anaphora. The paper also introduces the idea of games of imperfect information and connects to partial logics.

Since the first chapter of this book presents an intro duction to the present state of game-theoretical semantics (GTS), there is no point in giving a briefer survey here. Instead, it may be helpful to indicate what this volume attempts to do. The first chapter gives a short intro duction to GTS and a survey of what is has accomplished. Chapter 2 puts the enterprise of GTS into new philo sophical perspective by relating its basic ideas to Kant's phi losophy (...) of mathematics, space, and time. Chapters 3-6 are samples of GTS's accomplishments in understanding different kinds of semantical phenomena, mostly in natural languages. Beyond presenting results, some of these chapters also have other aims. Chapter 3 relates GTS to an interesting line of logical and foundational studies - the so-called functional interpretations - while chapter 4 leads to certain important methodological theses. Chapter 7 marks an application of GTS in a more philo sophical direction by criticizing the Frege-Russell thesis that words like "is" are multiply ambiguous. This leads in turn to a criticism of recent logical languages (logical notation), which since Frege have been based on the ambi guity thesis, and also to certain methodological sug gestions. In chapter 8, GTS is shown to have important implications for our understanding of Aristotle's doctrine of categories, while chapter 9 continues my earlier criticism of Chomsky's generative approach to linguistic theorizing. (shrink)

SummaryTruth‐definitions play a crucial role in the foundations of logic and semantics. Tarsik‐type truth‐definitions are not possible to formulate in a usual first‐order language for itself, and they have been criticized because they do not account for what makes them definitions of truth. It has been suggested that truth should instead be characterized by reference to the «language‐games» of verification and falsification. The author's game‐theoretical semantics here explained for formal first‐order languages, can be thought of as a realization of this (...) idea. More technically speaking, GTS can also be thought of as a systematization of the well‐known aepsilon‐delta, definitions in the foundations of analysis. In GTS, truth is not defined by reference to winning a play of a game, but as the existence of a winning strategy in the game for the verifier. In a first‐order language, the game‐theoretical truth‐condition of a sentence S can accordingly be expressed by an explicit second‐order sentence asserting the existence of the Skolem function of S.The semantical games of GTS must be distinguished not only from the «games» of formal proof but also from the «games» in volved in our ordinary activities of verification and falsification. The latter have been modelled as games of inquiry by the author, and they are essentially epistemic games where the meaning of truth is taken for granted and where the aim of the game is to come to know certain truths. To assimilate them to the semantical games constitutive of truth is a form of Meno's paradox. (shrink)

Les articles présentés et traduits dans le présent ouvrage, réunis sous un titre qu'approuva l’auteur lors de sa première publication, portent sur la période qui s’ouvre peu d’années après la publication de Knowledge and Belief et qui s’étend jusqu’aux prémices des découvertes qui ont relancé une recherche particulièrement féconde — la sémantique des jeux, parfois plus connue sous l’acronyme de GTS, et la Logique IF, ou Independance Friendly Logic, développée avec Gabriel Sandu. L’Intentionnalité et les mondes possibles montre jusqu’où la (...) sémantique des mondes possibles permet de rendre compte de l’intentionnalité et d’en explorer les multiples dimensions : les six articles dégagent les méthodes et les directions de recherche ainsi ouvertes. Une postface de la traductrice les met en perspective relativement aux aboutissements actuels des travaux de Hintikka, en explorant sommairement certaines des méthodes et des recherches des deux premières décennies du vingt et unième siècle — occasion de s’apercevoir que l’épistémologie générale et spéciale, l’informatique théorique contemporaine aussi bien que l’exploration de la nature de la métaphore trouvent à se nourrir de la relance permanente du questionnement assurée par l’enquête-Hintikka, et ce, parfois, de manière très surprenante. (shrink)

Inspired by Hintikka’s ideas on constructivism, we are going to ‘effectivize’ the game-theoretic semantics for independence-friendly first-order logic, but in a somewhat different way than he did in the monograph ‘The Principles of Mathematics Revisited’. First we show that Nelson’s realizability interpretation—which extends the famous Kleene’s realizability interpretation by adding ‘strong negation’—restricted to the implication-free first-order formulas can be viewed as an effective version of GTS for FOL. Then we propose a realizability interpretation for IF-FOL, inspired by the so-called (...) ‘trump semantics’ which was discovered by Hodges, and show that this trump realizability interpretation can be viewed as an effective version of GTS for IF-FOL. Finally we prove that the trump realizability interpretation for IF-FOL appropriately generalises Nelson’s restricted realizability interpretation for the implication-free first-order formulas. (shrink)

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 impossibility results by Gödel and Tarski that have dominated the field for the last sixty years turn out to be much less significant than has been thought. All of ordinary mathematics can in principle be done on this first-order level, thus dispensing with the existence of sets and other higher-order entities. (shrink)

Quel sens donner à l'intrusion quand celle-ci est inséparable d'une mise en danger potentiellement mortelle de ce qui se pense ' un ', mais qu'elle est en même temps nécessaire pour que quelque chose advienne? Quelles perspectives ontologiques, esthétiques et politiques la venue de l'autre ouvre-t-elle alors qu'il peut nous mettre ' hors de nous '? Comment, de fait, l'intrus ne vient-il pas toujours d'ailleurs? La lecture de L'Intrus de Jean-Luc Nancy et des liens qui se tissent entre le philosophe, (...) la réalisatrice Claire Denis et les réalisateurs Nicolas Klotz et Rabah Ameur-Zaïmeche, permet d'envisager comment la notion d'ex-criture donne lieu à des gestes cinématographiques: greffe, adoption, adaptation ou encore intégration. (shrink)

The discourse on labor engagement, underutilization, and unemployment has been a prominent focus in development literature, particularly in developing economies. These issues influence migration patterns and gross domestic output and, in some cases, contribute to youth restiveness. This study delves into the intricate relationship between investments in human capital, represented by spending on education and health, and its repercussions on youth employment outcomes in India. We gathered annual data spanning the years 1990 to 2021 from various Indian states. We employed (...) the bootstrap-based bias correction for panel fixed effects estimation techniques to enhance the analytical accuracy. The findings of our investigation reveal that investments in human capital, encompassing both private and government health expenditures as well as expenditures on primary, secondary, and tertiary education, exert significant but varying impacts on youth employment in India. These results carry important policy implications. To effectively address the persistent challenge of youth unemployment in India, it is imperative to prioritize consistent and disproportionate investments in education over health. This shift in focus could prove instrumental in reversing the trend of youth unemployment and fostering sustainable economic growth. (shrink)

Let us assume that you are entrusted by UNESCO with an important task. You are asked to devise a universal logical language, a Begriffsschrift in Frege's sense, which is to serve the purposes of science, business and everyday life. What requirements should such a “conceptual notation” satisfy? There are undoubtedly many relevant desiderata, but here I am focusing on one unmistakable one. In order to be a viable lingua universalis, your language must in any case be capable of representing any (...) possible configuration of dependence and independence between different variables. For if such a configuration is possible in principle, there is no guarantee that it might not one day show up among the natural, human or social phenomena we have to study.But how are dependencies and independencies between variables expressed in our familiar logical notation? Every logician worth his or her truth-table knows the answer. Dependencies between two variables are expressed by dependencies between the quantifiers to which they are bound. For instance, inthe variable y depends on x, while inz depends on x but not on y, while u depends on both x and y.But how is the dependence of a quantifier on another one expressed in familiar logical languages? Obviously by occurring in its scope, indicated by the pair of parentheses following it. But the nesting of scopes is a transitive and antisymmetrical relation which allows branching only in one direction. Hence other kinds of structures of dependence and independence between variables are not representable in the received logical notation. Such previously inexpressible structures form the subject matter of what has been referred to as independence-friendly logic. (shrink)

Against some very common views (e.g. Dummett), this paper argues that Frege did not have a standard interpretation of higher-order logic and for this reason his programme in the foundations of mathematics was a nonstarter.

Let us assume that you are entrusted by UNESCO with an important task. You are asked to devise a universal logical language, a Begriffsschrift in Frege's sense, which is to serve the purposes of science, business and everyday life. What requirements should such a “conceptual notation” satisfy? There are undoubtedly many relevant desiderata, but here I am focusing on one unmistakable one. In order to be a viable lingua universalis, your language must in any case be capable of representing any (...) possible configuration of dependence and independence between different variables. For if such a configuration is possible in principle, there is no guarantee that it might not one day show up among the natural, human or social phenomena we have to study.But how are dependencies and independencies between variables expressed in our familiar logical notation? Every logician worth his or her truth-table knows the answer. Dependencies between two variables are expressed by dependencies between the quantifiers to which they are bound. For instance, inthe variable y depends on x, while inz depends on x but not on y, while u depends on both x and y.But how is the dependence of a quantifier on another one expressed in familiar logical languages? Obviously by occurring in its scope, indicated by the pair of parentheses following it. But the nesting of scopes is a transitive and antisymmetrical relation which allows branching only in one direction. Hence other kinds of structures of dependence and independence between variables are not representable in the received logical notation. Such previously inexpressible structures form the subject matter of what has been referred to as independence-friendly logic. (shrink)

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.

Like Leibniz, C. S. Peirce drew much of the inspiration for his philosophical work from a close study of logical and mathematical reasoning. Now what insights did this study reveal to Peirce? His own answer is formulated as follows: “My first real discovery about mathematical procedure was that there are two kinds of necessary reasoning, which I call the Corollarial and the Theorematic.…” The import of this discovery was lost on philosophers for a long time. The purpose of the present (...) paper is to show what Peirce's insight amounts to, to point out some of its applications, relate it to certain recent developments in the philosophy of logic, and thereby vindicate Peirce's distinction. This undoubtedly will also help to show its present day relevance. (shrink)

The following analysis shows how developments in epistemic logic can play a nontrivial role in cognitive neuroscience. We argue that the striking correspondence between two modes of identification, as distinguished in the epistemic context, and two cognitive systems distinguished by neuroscientific investigation of the visual system (the "where" and "what" systems) is not coincidental, and that it can play a clarificatory role at the most fundamental levels of neuroscientific theory.

Like Leibniz, C. S. Peirce drew much of the inspiration for his philosophical work from a close study of logical and mathematical reasoning. Now what insights did this study reveal to Peirce? His own answer is formulated as follows: “My first real discovery about mathematical procedure was that there are two kinds of necessary reasoning, which I call the Corollarial and the Theorematic.…” The import of this discovery was lost on philosophers for a long time. The purpose of the present (...) paper is to show what Peirce's insight amounts to, to point out some of its applications, relate it to certain recent developments in the philosophy of logic, and thereby vindicate Peirce's distinction. This undoubtedly will also help to show its present day relevance. (shrink)