Games of chance are developed in their physical consumer-ready form on the basis of mathematical models, which stand as the premises of their existence and represent their physical processes. There is a prevalence of statistical and probabilistic models in the interest of all parties involved in the study of gambling – researchers, game producers and operators, and players – while functional models are of interest more to math-inclined players than problem-gambling researchers. In this paper I present a structural analysis of (...) the knowledge attached to mathematical models of games of chance and the act of modeling, arguing that such knowledge holds potential in the prevention and cognitive treatment of excessive gambling, and I propose further research in this direction. (shrink)

The first learning game to be developed to help students to develop and hone skills in constructing proofs in both the propositional and first-order predicate calculi. It comprises an autotelic (self-motivating) learning approach to assist students in developing skills and strategies of proof in the propositional and predicate calculus. The text of VALIDITY consists of a general introduction that describes earlier studies made of autotelic learning games, paying particular attention to work done at the Law School of Yale University, called (...) the ALL Project (Accelerated Learning of Logic). Following the introduction, the game of VALIDITY is described, first with reference to the propositional calculus, and then in connection with the first-order predicate calculus with identity. Sections in the text are devoted to discussions of the various rules of derivation employed in both calculi. Three appendices follow the main text; these provide a catalogue of sequents and theorems that have been proved for the propositional calculus and for the predicate calculus, and include suggestions for the classroom use of VALIDITY in university-level courses in mathematical logic. (shrink)

What is new here is the detailed discussion of several important results in the classical foundations of mathematics and of the relation of logic to mathematics. As regards logical questions, the central thesis of Wittgenstein's later philosophy is well known, both from the earlier posthumous volume and from the writings of his many disciples. In the Investigations the thesis is applied to the "logic of our expressions" in everyday contexts; here he discusses in the same spirit the more (...) specialized language used in talking about the foundations of mathematics. (shrink)

We address simple voting games as mathematical objects in their own right, and study structures made up of these objects, rather than focusing on SVGs primarily as co-operative games. To this end it is convenient to employ the conceptual framework and language of category theory. This enables us to uncover the underlying unity of the basic operations involving SVGs.

On the question of whether gambling behavior can be changed as result of teaching gamblers the mathematics of gambling, past studies have yielded contradictory results, and a clear conclusion has not yet been drawn. In this paper, I bring some criticisms to the empirical studies that tended to answer no to this hypothesis, regarding the sampling and laboratory testing, and I argue that an optimal mathematical scholastic intervention with the objective of preventing problem gambling is possible, by providing the (...) principles that would optimize the structure and content of the teaching module. Given the ethical aspects of the exposure of mathematical facts behind games of chance, and starting from the slots case – where the parametric design is missing, we have to draw a line between ethical and optional information with respect to the mathematical content provided by a scholastic intervention. Arguing for the role of mathematics in problem-gambling prevention and treatment, interdisciplinary research directions are drawn toward implementing an optimal mathematical module in cognitive therapies. (shrink)

L’objectif de cet article est de rendre compte de la création et de la transmission d’un savoir mathématique lié aux combinaisons par le biais d’un support matériel particulier : les pavés mi-partis. Ces derniers sont des carrés du plan divisés par une diagonale en deux parties de couleur différente. Tour à tour objet d’ornement, objet de réflexion mathématique à partir du xviiie siècle grâce au Mémoire sur les combinaisons du père Truchet à l’Académie royale des sciences, objet pédagogique dans les (...) Récréations mathématiques d’Édouard Lucas au xixe siècle ou objet ludique, le pavé mi-parti présente une patrimonialisation originale d’un savoir mathématique, porté par un objet souvent considéré comme un simple jouet. (shrink)

Why do people stay together in monogamous relationships? Love? Fear? Habit? Ethics? Integrity? Desperation? In this paper I will consider a rather surprising answer that comes from mathematics. It turns out that cooperative behaviour, such as mutually-faithful marriages, can be given a firm basis in a mathematical theory known as game theory. I will suggest that faithfulness in relationships is fully accounted for by narrow self interest in the appropriate game theory setting. This is a surprising answer because faithful (...) behaviour is usually thought to involve love, ethics, and caring about the well being of your partner. It seems that the game-theory account of faithfulness has no need for such romantic notions. I will consider the philosophical upshot of the game-theoretic answer and see if it really does deliver what is required. Does the game-theoretic answer miss what is important about faithful relationships or does it help us get to the heart of the matter? Before we start looking at lasting, faithful relationships, though, let’s get a feel for how mathematics might be employed to help in matters of the heart. Let’s first consider how mathematics might shed light on dating to find a suitable partner. (shrink)

Book Review Luck, logic, and white lies: the mathematics of games, second edition by Jörg Bewersdorff, New York, Taylor & Francis, CRC Press, 2021, 568 pp., GBP 42.99 (paperback), ISBN 9780367548414, Number of chapters 51.

The article is devoted to the applicability of Wittgenstein’s following the rule in the context of his philosophy of mathematics to real mathematical practice. It is noted that in «Philosophical Investigations» and «Remarks on the Foundations of Mathematics» Wittgenstein resorted to the analysis of rather elementary mathematical concepts, accompanied also by the inherent ambiguity and ambiguity of his presentation. In particular, against this background, his radical conventionalism, the substitution of logical necessity with the «form of life» of the (...) community, as well as the inadequacy of the representation of arithmetic rules by a language game are criticized. It is shown that the reconstruction of the Wittgenstein concept of understanding based on the Fregian division of meaning and referent goes beyond the conceptual framework of Wittgenstein language games. (shrink)

When von Neumann's and Morgenstern's Theory of Games and Economic Behavior appeared in 1944, one thought that a complete theory of strategic social behavior had appeared out of nowhere. However, game theory has, to this very day, remained a fast-growing assemblage of models which have gradually been united in a new social theory - a theory that is far from being completed even after recent advances in game theory, as evidenced by the work of the three Nobel Prize winners, John (...) F. Nash, John C. Harsanyi, and Reinhard Selten. Two of them, Harsanyi and Selten, have contributed important articles to the present volume. This book leaves no doubt that the game-theoretical models are on the right track to becoming a respectable new theory, just like the great theories of the twentieth century originated from formerly separate models which merged in the course of decades. For social scientists, the age of great discover ies is not over. The recent advances of today's game theory surpass by far the results of traditional game theory. For example, modem game theory has a new empirical and social foundation, namely, societal experiences; this has changed its methods, its "rationality. " Morgenstern (I worked together with him for four years) dreamed of an encompassing theory of social behavior. With the inclusion of the concept of evolution in mathematical form, this dream will become true. Perhaps the new foundation will even lead to a new name, "conflict theory" instead of "game theory. (shrink)

Upshot: Leng attacks the indispensability argument for the existence of mathematical objects. She offers an account that treats the role of mathematics in science as an indispensable and useful part of theories, but retains nonetheless a fictionalist position towards mathematics. The result is an account of mathematics that is interesting for constructivists. Her view towards the nominalistic part of science is, however, more in conflict with radical constructivism.

Unlike his other major typescripts, the Big Typescript is divided into titled chapters, themselves divided into titled sections. But within a section we still get a collection of remarks typically without connecting tissue and lacking any transparently significant ordering or helpful signposting. So we still encounter the usual difficulties in trying to think our way through into what Wittgenstein might be wanting to say. Some enthusiasts like to try to persuade us that the aphoristic style is really of the essence. (...) But I’ve always wondered how true that is. So I here propose an experiment. Let’s take §108 of the ‘Big Typescript’ (the first of the sections in the part of the book titled ‘The Foundations of Mathematics’). There are four and a bit pages of remarks. I’m going to try to render them into rather more conventional prose. In the section that follows, then, I have embedded almost every sentence Wittgenstein wrote in his §108 – or rather, of course, I’ve embedded almost every sentence from the well-regarded translation. I have, however, often changed the order in which remarks appear, omitted some ‘and’s and ‘but’s and the like, changed some punctuation, demoted some passages to footnotes, but not – I hope – in any way that radically changes the significance of any remark, or distorts what is going on. And I’ve added a lot of signposting. I’ll comment, necessarily very briefly, on the results of the exercise starting in §3 below. So here we go . . (shrink)

Mathematical game theory has been embraced by a variety of scholars: social scientists, biologists, linguists, and now, increasingly, logicians. This volume illustrates the recent advances of game theory in the field. Logicians benefit from things like game theory's ability to explain informational independence between connectives; meanwhile, game theorists have even begun to benefit from logical epistemic analyses of game states. In concert with such pioneering work, this volume also present surprising developments in classical fields, including first-order logic and set theory.

Slot machines gained a high popularity despite a specific element that could limit their appeal: non-transparency with respect to mathematical parameters. The PAR sheets, exposing the parameters of the design of slot machines and probabilities associated with the winning combinations are kept secret by game producers, and the lack of data regarding the configuration of a machine prevents people from computing probabilities and other mathematical indicators. In this article, I argue that there is no rational justification for this secrecy by (...) giving two reasons, one psychological and the other mathematical. For the latter, I show that mathematics provides us with some statistical methods of retrieving the missing data, which are essential for the numerical probability computations in slots. The slots case raises the problem of the exposure of the parametric configuration and mathematical facts of any game of chance as an ethical obligation. (shrink)

Journal of Mathematical Logic, Volume 22, Issue 03, December 2022. Hirschfeldt and Jockusch (2016) introduced a two-player game in which winning strategies for one or the other player precisely correspond to implications and non-implications between [math] principles over [math]-models of [math]. They also introduced a version of this game that similarly captures provability over [math]. We generalize and extend this game-theoretic framework to other formal systems, and establish a certain compactness result that shows that if an implication [math] between two (...) principles holds, then there exists a winning strategy that achieves victory in a number of moves bounded by a number independent of the specific run of the game. This compactness result generalizes an old proof-theoretic fact noted by H. Wang (1981), and has applications to the reverse mathematics of combinatorial principles. We also demonstrate how this framework leads to a new kind of analysis of the logical strength of mathematical problems that refines both that of reverse mathematics and that of computability-theoretic notions such as Weihrauch reducibility, allowing for a kind of fine-structural comparison between [math] principles that has both computability-theoretic and proof-theoretic aspects, and can help us distinguish between these, for example by showing that a certain use of a principle in a proof is “purely proof-theoretic”, as opposed to relying on its computability-theoretic strength. We give examples of this analysis to a number of principles at the level of [math], uncovering new differences between their logical strengths. (shrink)

Contents. Introduction. 1. Preliminaries. 2. Normal Form Games. 3. Extensive Games. 4. Applications of Game Theory. 5. The Methodology of Game Theory. Conclusion. Appendix. Bibliography. Index. Does game theory—the mathematical theory of strategic interaction—provide genuine explanations of human behaviour? Can game theory be used in economic consultancy or other normative contexts? Explaining Games: The Epistemic Programme in Game Theory—the first monograph on the philosophy of game theory—is an attempt to combine insights from epistemic logic and the philosophy of science to (...) investigate the applicability of game theory in such fields as economics, philosophy and strategic consultancy. I prove new mathematical theorems about the beliefs, desires and rationality principles of individual human beings, and explore in detail the logical form of game theory as it is used in explanatory and normative contexts. I argue that game theory reduces to rational choice theory if used as an explanatory device, and that game theory is nonsensical if used as a normative device. A provocative account of the history of game theory reveals that this is not bad news for all of game theory, though. Two central research programmes in game theory tried to find the ultimate characterisation of strategic interaction between rational agents. Yet, while the Nash Equilibrium Refinement Programme has done badly thanks to such research habits as overmathematisation, model-tinkering and introversion, the Epistemic Programme, I argue, has been rather successful in achieving this aim. "The 'epistemic' approach to game theory has emerged over the past twenty-five years. What is this approach? How does it differ from the conventional equilibrium-based approach to game theory? What have been its strengths and weaknesses to date? To find out, read this comprehensive and excellently written account". Adam Brandenburger, J. P. Valles Professor of Business Economics and Strategy, Stern School of Business, New York University "Reading Boudewijn de Bruin's book should be rewarding both for game theorists interested in the conceptual foundations of their discipline and for philosophers who want to learn more about formal analysis of strategic interaction. It provides an in-depth logical study of the currently dominant epistemic approaches to non-cooperative games, with an eye both to the attractions and to the serious challenges facing the Epistemic Programme". Wlodek Rabinowicz, Professor of Practical Philosophy, Department of Philosophy, Lund University . (shrink)

Games are played everywhere: from economics and online auctions to social interactions, and game theory is about how to play such games in a rational way, and how to maximize their outcomes. This VSI reveals, without mathematical equations, the insights the theory can bring to everything from how to play poker optimally to the sex ratio among bees.

The current study evaluates qualitatively how the mathematical dimension of gambling is reflected in the content of gambling websites. A number of gambling websites have been reviewed for their content in that respect. A statistical analysis recorded the presence of the mathematical dimension of gambling and its forms in the content of the participating websites, and a qualitative research study analyzed and assessed the quality of the content with respect to that dimension. The technical reports associated with this study describe (...) the methods used in the processes of review and content analysis, details of the processes, and the specific challenges and difficulties that they posed. (shrink)

Inquisitive first-order logic, InqBQ, is a system which extends classical first-order logic with formulas expressing questions. From a mathematical point of view, formulas in this logic express properties of sets of relational structures. This paper makes two contributions to the study of this logic. First, we describe an Ehrenfeucht–Fraïssé game for InqBQ and show that it characterizes the distinguishing power of the logic. Second, we use the game to study cardinality quantifiers in the inquisitive setting. That is, we study what (...) statements and questions can be expressed in InqBQ about the number of individuals satisfying a given predicate. As special cases, we show that several variants of the question how many individuals satisfy α(x) are not expressible in InqBQ, both in the general case and in restriction to finite models. (shrink)

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)

The paper has a twofold aim. On the one hand, it provides what appears to be the first game-theoretic modeling of Napoleon’s last campaign, which ended dramatically on 18 June 1815 at Waterloo. It is specifically concerned with the decision Napoleon made on 17 June 1815 to detach part of his army against the Prussians he had defeated, though not destroyed, on 16 June at Ligny. Military historians agree that this decision was crucial but disagree about whether it was rational. (...) Hypothesizing a zero-sum game between Napoleon and Blücher, and computing its solution, we show that it could have been a cautious strategy on the former's part to divide his army, a conclusion which runs counter to the charges of misjudgement commonly heard since Clausewitz. On the other hand, the paper addresses methodological issues. We defend its case study against the objections of irrelevance that have been raised elsewhere against “analytic narratives”, and conclude that military campaigns provide an opportunity for successful application of the formal theories of rational choice. Generalizing the argument, we finally investigate the conflict between narrative accounts – the historians' standard mode of expression – and mathematical modeling. (shrink)

Game theory is a branch of mathematics that studies strategic interactions, i.e., interactions which involve more than one agent and in which each agent makes her/his decision while striving to predict the decisions of other agents. Game theory has been successfully applied in many areas of both the natural and social sciences, and it is the belief of this book's author that it can also be gainfully invoked in the area of legal philosophy. In this book, Wojciech Zaluski analyzes (...) legal-philosophical concepts - such as legal interpretation, justice, legal rights, contract law, tort law, and property law - through the lens of game theory. The book appeals mainly to game theory's conceptual rather than the technical side, and intertwines game-theoretical analysis with the philosophical. It will be accessible to a wider circle of readers interested in legal and moral philosophy. (shrink)

We define a new type of two player game occurring on a tree. The tree may have no root and may have arbitrary degrees of nodes. These games extend the class of games considered by Gurevich-Harrington in [5]. We prove that in the game one of the players has a winning strategy which depends on finite bounded information about the past part of a play and on future of each play that is isomorphism types of tree nodes. This result extends (...) further the Gurevich-Harrington determinacy theorem from [5]. (shrink)

Computational models such as E-Z Reader and SWIFT are ideal theoretical tools to test quantitatively our current understanding of eye-movement control in reading. Here we present a mathematical analysis of word skipping in the E-Z Reader model by semianalytic methods, to highlight the differences in current modeling approaches. In E-Z Reader, the word identification system must outperform the oculomotor system to induce word skipping. In SWIFT, there is competition among words to be selected as a saccade target. We conclude that (...) it is the question of competitors in the “game” of word skipping that must be solved in eye movement research. (shrink)

Game theory is the mathematical study of strategy and conflict. It has wide applications in economics, political science, sociology, and, to some extent, in philosophy. Where rational choice theory or decision theory is concerned with individual agents facing games against nature, game theory deals with games in which all players have preference orderings over the possible outcomes of the game. This paper gives an informal introduction to the theory and a survey of applications in diverse branches of philosophy. No criticism (...) is reviewed. Game theory is shown at work in discussions about epistemological dependence, liberalism and efficiency, Hume’s concept of convention, morality and rationality, and distributive justice and egalitarianism. A guide to the literature provides hints at applications in collective intentionality, epistemology, ethics, history of philosophy, logic, philosophy of language, and political philosophy. (shrink)

Game theory is a mathematical theory of strategic interactions between rational agents. With much success, it has been widely applied in various areas of the social sciences, especially economics and sociology. However, it has been relatively and rarely used in the analyses pursued in legal theory and legal dogmatics. The present collection fills this gap and discusses game theory as a useful tool for legal scholars in solving the various problems of legal philosophy or legal dogmatics. It also includes two (...) skeptical voices regarding the applicability of game theory in legal analysis. The book will be useful for scholars in the field of legal theory, as well as for philosophers and economists. (shrink)

This paper addresses the theoretical notion of a game as it arisesacross scientific inquiries, exploring its uses as a technical andformal asset in logic and science versus an explanatory mechanism. Whilegames comprise a widely used method in a broad intellectual realm(including, but not limited to, philosophy, logic, mathematics,cognitive science, artificial intelligence, computation, linguistics,physics, economics), each discipline advocates its own methodology and aunified understanding is lacking. In the first part of this paper, anumber of game theories in formal studies are (...) critically surveyed. Inthe second part, the doctrine of games as explanations for logic isassessed, and the relevance of a conceptual analysis of games tocognition discussed. It is suggested that the notion of evolution playsa part in the game-theoretic concept of meaning. (shrink)

We give a new proof of a theorem of Shelah which states that for every family of labeled trees, if the cardinality κ of the family is much larger (in the sense of large cardinals) than the cardinality λ of the set of labels, more precisely if the partition relation holds, then there is a homomorphism from one labeled tree in the family to another. Our proof uses a characterization of such homomorphisms in terms of games.

The ancient puzzle of the Liar was shown by Tarski to be a genuine paradox or antinomy. I show, analogously, that certain puzzles of contemporary game theory are genuinely paradoxical, i.e., certain very plausible principles of rationality, which are in fact presupposed by game theorists, are inconsistent as naively formulated. ;I use Godel theory to construct three versions of this new paradox, in which the role of 'true' in the Liar paradox is played, respectively, by 'provable', 'self-evident', and 'justifiable'. I (...) also construct in modal operator logic a paradox involving reflexive empirical reasoning. Unlike the paradox of the Liar, the paradox of reflexive reasoning does not depend on self-reference. ;I consider various solutions to the Liar paradox and evaluate how well these solutions cope with the paradox of reflexive reasoning. I then formalize the solution to the paradoxes which I favor: the indexical-hierarchical approach, first sketched out by Charles Parsons and Tyler Burge. In this solution, occurrences of the predicate 'true' in sentence-tokens are contextually relativized to levels of a hierarchy. Drawing also on some brief remarks of Bertrand Russell and Charles Parsons, I develop an account of the kind of schematic generality needed for this theory to be statable. ;Finally, I demonstrate that the principles shown to be paradoxical are in fact presupposed by contemporary game theorists in their reliance on the notion of common knowledge or, more precisely, mutual belief. I create novel analyses of and corresponding solutions to several recalcitrant puzzles within game theory, including the "chain-store paradox". (shrink)

Game Logic is a modal logic which extends Propositional Dynamic Logic by generalising its semantics and adding a new operator to the language. The logic can be used to reason about determined 2-player games. We present an overview of meta-theoretic results regarding this logic, also covering the algebraic version of the logic known as Game Algebra.

Journal of Mathematical Logic, Volume 24, Issue 03, December 2024. This paper has two parts. The first is concerned with a variant of a family of games introduced by Holy and Schlicht, that we call Welch games. Player II having a winning strategy in the Welch game of length [math] on [math] is equivalent to weak compactness. Winning the game of length [math] is equivalent to [math] being measurable. We show that for games of intermediate length [math], II winning implies (...) the existence of precipitous ideals with [math]-closed, [math]-dense trees. The second part shows the first is not vacuous. For each [math] between [math] and [math], it gives a model where II wins the games of length [math], but not [math]. The technique also gives models where for all [math] there are [math]-complete, normal, [math]-distributive ideals having dense sets that are [math]-closed, but not [math]-closed. (shrink)

We introduce possibilistic beliefs into strategic games, describing a player’s belief about his opponents’ strategies as the set of their strategies he regards as possible. We formulate possibilistic strategic games where each player has preferences over his own strategies conditional on his possibilistic belief about his opponents’ strategies. We define several solution concepts for possibilistic strategic games such as (strict) equilibria, rationalizable sets, iterated elimination of never-best responses, and iterated elimination of strictly dominated strategies, and we study their properties and (...) relationships. We develop a class of possibilistic strategic games called possibilistic supermodular games to relate supermodular games to possibilistic strategic games. Lastly, we discuss a direction of extending our possibilistic framework to games with incomplete information. (shrink)

The answer in a nutshell is: Yes, five years ago, but nobody has noticed. Nobody noticed because the majority of social scientists subscribe to one of the following views: (1) the ‘anomalous’ behaviour observed in standard prisoner’s dilemma or ultimatum game experiments has refuted standard game theory a long time ago; (2) game theory is flexible enough to accommodate any observed choices by ‘refining’ players’ preferences; or (3) it is just a piece of pure mathematics (a tautology). None of (...) these views is correct. This paper defends the view that GT as commonly understood is not a tautology, that it suffers from important (albeit very recently discovered) empirical anomalies, and that it is not flexible enough to accommodate all the anomalies in its theoretical framework. It also discusses the experiments that finally refuted game theory, and concludes trying to explain why it took so long for experimental game theorists to design experiments that could adequately test the theory. (shrink)

A feature of David Lewis's account of conventions in his book "Convention" which has received admiring notices from philosophers is his use of the mathematical theory of games. In this paper I point out a number of serious flaws in Lewis's use of game theory. Lewis's basic claim is that conventions cover 'coordination problems'. I show that game-Theoretical analysis tends to establish that coordination problems in Lewis's sense need not underlie conventions.

A dialogue arguing that morality has an objective basis in the mathematical object describing the "tit for tat" game theory. To play the game, a contractual obligation is freely made to cooperate and to fairly distribute the gains. Failure to meet these obligations results in social punishment.

We associate with any game G another game, which is a variant of it, and which we call . Winning strategies for have a lower recursive degree than winning strategies for G: if a player has a winning strategy of recursive degree 1 over G, then it has a recursive winning strategy over , and vice versa. Through we can express in algorithmic form, as a recursive winning strategy, many common proofs of non-constructive Mathematics, namely exactly the theorems of (...) the sub-classical logic Limit Computable Mathematics [6], Hayashi and Nakata [7]). (shrink)

This is a two-volume set that provides an introduction to non-cooperative Game Theory. Volume 1 covers the basic concepts, while Volume 2 is devoted to advanced topics. The book is richly illustrated with approximately 400 figures. It is suitable for both self-study and as the basis for an undergraduate course in game theory as well as a first-year graduate-level class. It is written to be accessible to anybody with high-school level knowledge of mathematics. At the end of each chapter (...) there is a collection of exercises accompanied by detailed answers. The book contains approximately 180 exercises. (shrink)

This chapter contains sections titled: Meaning as Use Language Games Mind and Matter Mathematics and Other Sciences Science, Myth, and Religion Seeing Aspects World Pictures The Inner and the Outer A Field of Diversity Further reading.

Game logics describe general games through powers of players for forcing outcomes. In particular, they encode an algebra of sequential game operations such as choice, dual and composition. Logic games are special games for specific purposes such as proof or semantical evaluation for first-order or modal languages. We show that the general algebra of game operations coincides with that over just logical evaluation games, whence the latter are quite general after all. The main tool in proving this is a representation (...) of arbitrary games as modal or first-order evaluation games. We probe how far our analysis extends to product operations on games. We also discuss some more general consequences of this new perspective for standard logic. (shrink)