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)

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)

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)

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)

Hintikka’s game theoretical approach to semantics has been successfully applied also to some non-classical logics. A recent example is Başkent (A game theoretical semantics for logics of nonsense, 2020. arXiv:2009.10878), where a game theoretical semantics based on three players and the notion of dominant winning strategy is devised to fit both Bochvar and Halldén’s logics of nonsense, which represent two basic systems of the family of weak Kleene logics. In this paper, we present and discuss a new game theoretic (...) semantics for Bochvar and Halldén’s logics, GTS-2, and show how it generalizes to a broader family of logics of variable inclusions. (shrink)

Typical applications of Hintikka’s game-theoretical semantics give rise to semantic attributes—truth, falsity—expressible in the $\Sigma^{1}_{1}$-fragment of second-order logic. Actually a much more general notion of semantic attribute is motivated by strategic considerations. When identifying such a generalization, the notion of classical negation plays a crucial role. We study two languages, $L_{1}$ and $L_{2}$, in both of which two negation signs are available: $\rightharpoondown $ and $\sim$. The latter is the usual GTS negation which transposes the players’ roles, while the (...) former will be interpreted via the notion of mode. Logic $L_{1}$ extends independence-friendly logic; $\rightharpoondown $ behaves as classical negation in $L_{1}$. Logic $L_{2}$ extends $L_{1}$, and it is shown to capture the $\Sigma^{2}_{1}$-fragment of third-order logic. Consequently the classical negation remains inexpressible in $L_{2}$. (shrink)

We consider two versions of truth as grounded in verification procedures: Dummett's notion of proof as an effective way to establish the truth of a statement and Hintikka's GTS notion of truth as given by the existence of a winning strategy for the game associated with a statement. Hintikka has argued that the two notions should be effective and that one should thus restrict one's attention to recursive winning strategies. In the context of arithmetic, we show that the (...) two notions do not coincide: on the one hand, proofs in PA do not yield recursive winning strategies for the associated game; on the other hand, there is no sound and effective proof procedure that captures recursive GTS truths. We then consider a generalized version of Game Theoretical Semantics by introducing games with backward moves. In this setting, a connection is made between proofs and recursive winning strategies. We then apply this distinction between two kinds of verificationist procedures to a recent debate about how we recognize the truth of Gödelian sentences. (shrink)

Jaakko Hintikka was born on January 12th, 1929. He received his doctorate from the University of Helsinki under the supervision of Professor G. H. von Wright at the age of 24 in 1953. Hintikka was appointed Professor of philosophy at the University of Helsinki in 1959. Since the late 50s, he has shared his time between Finland and the U.S.A. He was appointed Professor of philosophy at Stanford University in 1964. As from 1970 Hintikka has been permanent (...) research professor of the Academy of Finland. He has published 13 books and about 200 articles, not to mention the various editorial and organizational activities he has played an active role in. The present collection of essays has been edited to honour Jaakko Hintikka on the occasion of his fiftieth birthday. By dedicating a Festschrift to Jaakko Hintikka, the contributors wish to pay homage to this remarkable man whom they see not only as a scholar of prodigious energy and insight, but as a friend, colleague and former teacher. The contributors hope the essays collected here will bring pleasure to the man they are intended to honour. All of the essays touch upon topics Hintikka has taken an direct or indirect interest in, ranging from technical problems of mathematical logic and applications of formal methods through philosophical logic, philosophy of language, epistemology and history of philosophy to philosophical aesthetics. (shrink)

An evening discussion between professors Jaakko Hintikka and Simo Knuuttila on September 2, 2007, at the Helsinki conference: Knuuttila: Ladies and gentlemen. Thank you for inviting us to this event and for this opportunity to discuss the latest volume of the Library of Living Philosophers, which was published last spring. The title of the volume is “The Philosophy of Jaakko Hintikka”. Probably most people here know this series, which was founded in 1939 by P. A. Schilpp. The idea (...) of the volumes is to invite some prominent philosophers to describe their lives and ideas and then ask other philosophers to write and comment on topics which the first author has written about. Then the philosopher to whom the book is dedicated answers and discusses these other people’s papers about his or her philosophy. These volumes gradually became a very popular series which most philosophical libraries wanted to have. It was considered such a good idea, giving rise to one of the most prestigious series in philosophy. It is also considered as a kind of philosophical honor for the philosopher to be chosen to be among these living philosophers. The books always have the same structure; first, an intellectual autobiography, pretty extensive, then the papers on the basic author’s philosophy and, last, the papers are answered separately. So there is a kind of discussion going on. The book on Jaakko Hintikka’s philosophy consists of almost 1000 pages. It is also available as a paperback. Now, I have prepared some questions. (shrink)

Jaakko Hintikka’s work in logic and epistemology has won him the Rolf Schock Prize for Logic and Philosophy, widely viewed as the Nobel of its field. He is also one of only four philosophers this century to be the subject of a volume of the Library of Living Philosophers. Hintikka is professor of philosophy at Boston University.

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)

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)

The purpose of this study is to scrutinize the economic challenges encountered by the Indian economy over the preceding 13 years and the implemented strategies to surmount them, particularly in the context of the prevailing crisis and recession. A qualitative research design was employed, integrating secondary data sources, including government reports, academic journals, and expert interviews. This facilitates a comprehensive understanding of the Indian economy’s trajectory during the specified period. Utilizing statistical indicators such as the Consumer Price Index, GDP, Gross (...) Savings and Investment Rates, Trade Ratio of GDP, Share of Manufacturing and Industry in GDP, and Bank NPA, the study aimed to elucidate the causes of the economic deceleration. Findings indicate that the Indian economy has grappled with formidable challenges in recent years, notably exacerbated by the COVID-19 pandemic, resulting in a downturn in economic growth, consumer spending, investment, and exports. Nonetheless, the study unearthed resilience within the Indian economy, evidenced by a resurgence in 2022 attributable to governmental and monetary policy interventions. Limitations of the study encompass reliance on secondary data sources and a paucity of comprehensive data concerning the pandemic’s impact on the Indian economy. Further research is imperative to garner a more nuanced understanding of the economic challenges confronted by the Indian economy and the efficacy of the implemented management strategies. The practical implications of the study underscore its relevance for policymakers and business leaders, accentuating the imperative of effective management strategies to navigate the challenges confronting the Indian economy. These challenges bear significant social ramifications, impinging on the livelihoods of millions and precipitating ripple effects across the broader economy. Consequently, the study’s findings offer critical insights into the social repercussions of the recent crisis and recession on the Indian economy. This study furnishes distinctive insights into the economic challenges encountered by the Indian economy over the years and the strategies employed to surmount them, thereby enriching the existing corpus of knowledge with a comprehensive analysis of the recent crisis and recession’s impact on the Indian economy. (shrink)

I n order to appreciate properly what we are doing in this book it is necessary to realize that our approach to linguistic theorizing differs from the prevailing views. Our approach can be described by indicating what distinguishes it from the methodological ideas current in theoretical linguistics, which I consider seriously misguided. Linguists typically construe their task in these days as that of making exceptionless generalizations from particular examples. This explanatory strategy is wrong in several different ways. It presupposes that (...) we can have "intuitions" about particular examples, usually examples invented by the linguist himself or herself, reliable and sharp enough to serve as a basis of sharp generalizations. It also presupposes that we cannot have equally reliable direct access to general linguistic regularities. Both assumptions appear to me extremely dubious, and the first of them has in effect been challenged by linguists like Dwight Bol inger. There is also some evidence that the degree of unanimity among linguists is fairly low when it comes to less clear cases, even in connection with such relatively simple questions as grammaticality (acceptability). For this reason we have tried to rely more on quotations from contemporary fiction, newspapers and magazines than on linguists' and philosophers' ad hoc examples. I also find it strange that some of the same linguists as believe that we all possess innate ideas about general characteristics of humanly possible grammars assume that we can have access to them only via their particular consequences. (shrink)

How does language represent the world it can be used to talk about? Or does it? A negative answer is maintained by one of the main traditions in language theory that includes Frege, Wittgenstein, Heidegger, Quine and Rorty. A test case is offered by the question whether the critical ''mirroring'' relations, especially the notion of truth, are themselves expressible in language. Tarski's negative thesis seemed to close the issue, but dramatic recent developments have decided the issue in favour of the (...) expressibility of truth. At the same time, the "mirroring" relations are not natural ones, but constituted by rule-governed human activities a la Wittgenstein's language games. These relations are nevertheless objective, because they depend only on the rules of these "games", not on the idiosyncrasies of the players. It also turns out that the "truth games" for a language are the same as the language games that give it its meaning in the first place. Thus truth and meaning are intrinsically intertwined. (shrink)

R. G. Collingwood saw one of the main tasks of philosophers and of historians of human thought in uncovering what he called the ultimate presuppositions of different thinkers, of different philosophical movements and of entire eras of intellectual history. He also noted that such ultimate presuppositions usually remain tacit at first, and are discovered only by subsequent reflection. Collingwood would have been delighted by the contrast that constitutes the overall theme of the essays collected in this volume. Not only has (...) this dichotomy ofviews been one ofthe mostcrucial watersheds in the entire twentieth-century philosophical thought. Not only has it remained largely implicit in the writings of the philosophers for whom it mattered most. It is a truly Collingwoodian presupposition also in that it is not apremise assumed by different thinkers in their argumentation. It is the presupposition of a question, an assumption to the effect that a certain general question can be raised and answered. Its role is not belied by the fact that several philosophers who answered it one way or the other seem to be largely unaware that the other answer also makes sense - if it does. This Collingwoodian question can be formulated in a first rough approximation by asking whether language - our actual working language, Tarski's "colloquiallanguage" - is universal in the sense of being inescapable. This formulation needs all sorts of explanations, however. (shrink)

The papers collected in this volume were written over a period of some eight or nine years, with some still earlier material incorporated in one of them. Publishing them under the same cover does not make a con tinuous book of them. The papers are thematically connected with each other, however, in a way which has led me to think that they can naturally be grouped together. In any list of philosophically important concepts, those falling within the range of application (...) of modal logic will rank high in interest. They include necessity, possibility, obligation, permission, knowledge, belief, perception, memory, hoping, and striving, to mention just a few of the more obvious ones. When a satisfactory semantics (in the sense of Tarski and Carnap) was first developed for modal logic, a fascinating new set of methods and ideas was thus made available for philosophical studies. The pioneers of this model theory of modality include prominently Stig Kanger and Saul Kripke. Several others were working in the same area independently and more or less concurrently. Some of the older papers in this collection, especially 'Quantification and Modality' and 'Modes of Modality', serve to clarify some of the main possibilities in the semantics of modal logics in general. (shrink)

Equally surprisingly, Descartes’s paranoid belief was shared by several contemporary mathematicians, among them Isaac Barrow, John Wallis and Edmund Halley. (Huxley 1959, pp. 354-355.) In the light of our fuller knowledge of history it is easy to smile at Descartes. It has even been argued by Netz that analysis was in fact for ancient Greek geometers a method of presenting their results (see Netz 2000). But in a deeper sense Descartes perceived something interesting in the historical record. We are looking (...) in vain in the writings of Greek mathematicians for a full explanation of what this famous method was. And I will argue for an answer to the question why this lacuna is there: Not because Greek geometers wanted to hide this method, but because they did not fully understand it. It is instructive to note the ambivalent attitude of the most rigorous mathematician of the period, Isaac Newton, to the method of analysis. He used it himself in his own mathematical work and in the expositions of that work. Yet when the mathematical push came to physical and cosmological shove, he formulated his Principia entirely in.. (shrink)