Search

Logic, Logic, and Logic collects some thirty papers of the late George Boolos. The exoteric 'Gottlob Frege and the Foundations of Arithmetic' appears for the first time; the reprint of 'Must We Believe in Set Theory?' has beaten its first appearance. The plan for the book was conceived by Boolos shortly before his death, and his editor and sometime co-author, Richard Jeffrey, has stuck to it save for repositioning one paper. The book has three parts, each of them logic. But this is logic for philosophers, philosophical logic, if you like, and in three senses. First, it is logic with philosophical significance: almost every paper combines some logic with philosophical reflection upon it, including fundamental questions about the intension and extension of 'logic' and 'logical truth'. Second, the logic can be understood by philosophers, no surprise for those brought up on the pedagogically astute Computability and Logic (Boolos and Jeffrey [1980]). Third, a theme that runs throughout the collection, but only occasionally wells up, is the discovery of philosophy within logic itself. Of course, like physicists, logicians can get by without much philosophical examination of their practice. But Boolos's point is that logical investigations can, if appropriately directed, be a contribution to a kind of philosophical analysis. More on this, and the missing middle term, mathematics, in Section 4.

The advantages and disadvantages of formalization in philosophy are summarized. It is concluded that formalized philosophy is an endangered speciality that needs to be revitalized and to increase its interactions with non-formalized philosophy. The enigmatic style that is common in philosophical logic must give way to explicit discussions of the problematic relationship between formal models and the philosophical concepts and issues that motivated their development.

This paper explores allowing truth value assignments to be undetermined or "partial" (no truth values) and overdetermined or "inconsistent" (both truth values), thus returning to an investigation of the four-valued semantics that I initiated in the sixties. I examine some natural consequence relations and show how they are related to existing logics, including Łukasiewicz's three-valued logic, Kleene's three-valued logic, Anderson and Belnap's (first-degree) relevant entailments, Priest's "Logic of Paradox", and the first-degree fragment of the Dunn-McCall system "R-mingle". None of these systems have nested implications, and I investigate twelve natural extensions containing nested implications, all of which can be viewed as coming from natural variations on Kripke's semantics for intuitionistic logic. Many of these logics exist antecedently in the literature, in particular Nelson's "constructible falsity".

In this paper, I defend the thesis that alleffects of extra-linguistic context on the truth-conditions of an assertion are traceable to elements in the actual syntactic structure of the sentence uttered. In the first section, I develop the thesis in detail, and discuss its implications for the relation between semantics and pragmatics. The next two sections are devoted to apparent counterexamples. In the second section, I argue that there are no convincing examples of true non-sentential assertions. In the third section, I argue that there are no convincing examples of what John Perry has called ‘unarticulated constituents’. I conclude by drawing some consequences of my arguments for appeals to context-dependence in the resolution of problems in epistemology and philosophical logic.

In “Logical consequence: A defense of Tarski” (Journal of Philosophical Logic, vol. 25, 1996, pp. 617–677), Greg Ray defends Tarski"s account of logical consequence against the criticisms of John Etchemendy. While Ray"s defense of Tarski is largely successful, his attempt to give a general proof that Tarskian consequence preserves truth fails. Analysis of this failure shows that de facto truth preservation is a very weak criterion of adequacy for a theory of logical consequence and should be replaced by a stronger absence-of-counterexamples criterion. It is argued that the latter criterion reflects the modal character of our intuitive concept of logical consequence, and it is shown that Tarskian consequence can be proved to satisfy this criterion for certain choices of logical constants. Finally, an apparent inconsistency in Ray"s interpretation of Tarski"s position on the modal status of the consequence relation is noted.

Paraconsistent logic is an area of philosophical logic that has yet to find acceptance from a wider audience. The area remains, in a word, disreputable. In this essay, we try to reassure potential consumers that it is not necessary to become a radical in order to use paraconsistent logic. According to the radicals, the problem is the absurd classical account of contradiction: Classically inconsistent sets explode only because bourgeois classical semantics holds, in the face of overwhelming evidence to the contrary, that both A and ∼ A cannot simultaneously be true! We suggest (more modestly) that there is, at least sometimes, something else worth preserving, even in an inconsistent, unsatisfiable premise set. In this paper we present, in a new guise, a very general version of this “preservationist” approach to paraconsistency.

Contents: Preface Introduction On referring Particular and general Singular terms and predication Identifying reference and truth-values The asymmetry of subjects and predicates Propositions, concepts and logical truths Grammar and philosophy Intention and convention in speech acts Meaning and truth Truth A problem about truth Truth: a reconsideration of Austin's views Index.

The mathematical concept of pragmatic truth, first introduced in Mikenberg, da Costa and Chuaqui (1986), has received in the last few years several applications in logic and the philosophy of science. In this paper, we study the logic of pragmatic truth, and show that there are important connections between this logic, modal logic and, in particular, Jaskowski's discussive logic. In order to do so, two systems are put forward so that the notions of pragmatic validity and pragmatic truth can be accommodated. One of the main results of this paper is that the logic of pragmatic truth is paraconsistent. The philosophical import of this result, which justifies the application of pragmatic truth to inconsistent settings, is also discussed.

Syntactical treatments of propositional attitudes are attractive to artificial intelligence researchers. But results of Montague (1974) and Thomason (1980) seem to show that syntactical treatments are not viable. They show that if representation languages are sufficiently expressive, then axiom schemes characterizing knowledge and belief give rise to paradox. Des Rivieres and Levesque (1988) characterize a class of sentences within which these schemes can safely be instantiated. These sentences do not quantify over the propositional objects of knowledge and belief. We argue that their solution is incomplete, and extend it by characterizing a more inclusive class of sentences over which the axiom schemes can safely range. Our sentences do quantify over propositional objects.

Ruth Barcan Marcus was a logician and important philosopher whose pioneering contributions in the forties gave rise to the quantified modal logic. The so-called "Barcan formula" is a very controversial axiom of quantified modal logic. In this survey we retrace the important contributions of Barcan Marcus in debates in the philosophy of logic as to the essentialist implications of the use of quantifiers in modal logic, in philosophy of language (especially with his contributions on the reference and on proper names), and meta -Ethics (especially with respect to the arguments on the possibility of moral dilemma based sull'assiomatizzazione deontica and implications for the debate about the moral realism and the so-called "practical necessity"). Ruth Barcan Marcus è stata una importante logica e filosofa i cui contributi pionieristici negli anni quaranta hanno dato origine alla logica modale quantificata. La cosiddetta formula Barcan è un assioma assai controverso della logica modale quantificata. Barcan Marcus ha contribuito in modo significativo anche a dibattiti di filosofia della logica riguardo alle implicazioni essenzialiste dell'uso di quantificatori modali, di filosofia del linguaggio (specialmente con i suoi contributi sul riferimento e sui nomi propri), e di meta-etica (specialmente riguardo agli argomenti sulla possibilità del dilemma morale basati sull'assiomatizzazione deontica e sulle implicazioni per il dibattito intorno al realismo morale e la cosiddetta necessità pratica).

Chapter 1. Semantic Defectiveness: A Dissolution of Semantic Pathology Bradley Armour-Garb and James A. Woodbridge.- Chapter 2. Emptiness and discharge in sequent calculus and natural deduction Michael Arndt and Luca Tranchini.- Chapter 3. The Knowability Paradox in the light of a Logic for Pragmatics Massimiliano Carrara and Daniele Chi.- Chapter 4. A Dialetheic Interpretation of Classical Logic Massimiliano Carrara and Enrico Martino.- Chapter 5. Strongly semantic information as information about the truth Gustavo Cevolani.- Chapter 6. Priest's Motorbike and Tolerant Identity Pablo Cobreros, Paul Egre, David Ripley and Robert van Rooij.- Chapter 7. How to unify Russellian and Strawsonian definite descriptions Marie Duzi.- Chapter 8. Tableau Metatheorem for Modal Logics Tomasz Jarmuzek.- Chapter 9. On the Essential Flatness of Possible Worlds Neil Kennedy.- Chapter 10. Collective Alternatives Franz von Kutschera.- Chapter 11. da Costa meets Belnap and Nelson Hitoshi Omori and Katsuhiko Sano.- Chapter 12. Explicating the Notion of Truth within Transparent Intensional Logic Jiri Raclavsky.- Chapter 13. Leibnizian intensional semantics for syllogistic reasoning Robert van Rooij.- Chapter 14. Inter-Model Connectives and Substructural Logics Igor Sedlar.

Metaphors are natural language constructions that play an important role in the way human beings communicate knowledge and understand the world. Some formal philosophers such as Searle and Lakoff claim that the semantic analysis of expressions that involve fictional stories and metaphors are examples of the inadequacy of using predicate logic for the analysis of the meaning of language. D’Hanis proposes that using predicate logic in combination of non-monotonic reasoning is possible to interpret metaphorical expressions. In this paper, we introduce an approach for modelling metaphorical thinking using a particular form of logic programming called answer set programming (ASP). ASP essentially enhances the logical apparatus of predicate calculus by introducing mechanisms such as negation as a failure that enable the system to accomplish non-monotonic reasoning. We show that using ASP is possible to model the meaning of some expressions involving metaphorical constructions and the implementation of metaphorical reasoning mechanisms that could be a great addition to any knowledge-based application.

Modal notions play an important role in science. Many scientifically useful predicates are dispositional in nature, and the scientific practice of experiment presupposes the possibility of active intervention in the course of nature. It is therefore interesting to ask which kinds of modality are involved, and how we can best understand them. In this paper we focus on the representation of things in modal contexts occurring in science, and ask which formal methods of philosophical logic are adequate for reidentifying, or tracing, things from case to case. We illustrate the importance of tracing via a discussion of possible experiments in science and in everyday life. After pointing out shortcomings of standard systems of quantified modal logic, we introduce CIFOL, case-intensional first order logic, as a newly established formal framework that helps to elucidate the notion of tracing. We illustrate the framework by discussing the identity of biological individuals with lumps of matter.

T × W logic is a combination of tense and modal logic for worlds or histories with the same time order. It is the basis for logics of causation, agency and conditionals, and therefore an important tool for philosophical logic. Semantically it has been defined, among others, by R. H. Thomason. Using an operator expressing truth in all worlds, first discussed by C. M. Di Maio and A. Zanardo, an axiomatization is given and its completeness proved via D. Gabbay’s irreflexivity lemma. Given this lemma the proof is more or less straight forward. At the end an alternative axiomatization is sketched in which Di Maio’s and Zanardo’s operator is replaced by a version of “actually”.

QUINE'S CRITIQUE Quine and his critique Today there appears to be a widespread impression that W. V. Quine's notorious critique of modal logic, based on certain ideas about reference, has been successfully answered. As one writer put it some years ago: “His objections have been dead for a while, even though they have not yet been completely buried.” What is supposed to have killed off the critique? Some would cite the development of a new “possible-worlds” model theory for modal logics in the 1960s; others, the development of new “direct” theories of reference for names in the 1970s. These developments do suggest that Quine's unfriendliness towards any formal logics but the classical, and indifference towards theories of reference for any singular terms but variables, were unfortunate. But in this study I will argue, first, that Quine's more specific criticisms of modal logic have not been refuted by either of the developments cited, and further, that there was much that those who did not share Quine's unfortunate attitudes might have learned about modality and about reference by attention to that critique when it first appeared, so that it was a misfortune for philosophical logic and philosophy of language that early reactions to it were as defensive and uncomprehending as they generally were.

In an article in the Journal of Philosophical Logic in 1996, “Towards a Model Theory of Venn Diagrams,” (Vol. 25, No. 5, pp. 463–482), Hammer and Danner proved the full completeness of Shin’s formal system for reasoning with Venn Diagrams. Their proof is eight pages long. This note gives a brief five line proof of this same result, using connections between diagrammatic and sentential representations.

Journal of Philosophical Logic Volume 42 Number 6 December 2013 Special Issue on LOFT Sevilla Guest Editors: Giacomo Bonanno, Hans van Ditmarsch and Wiebe van der Hoek Editorial Introduction to the Special Issue LOFT Sevilla G. Bonanno I H. van Ditmarsch I W. van der Hoek 795 Computing Strong and Weak Permissions in Defeasible Logic G. Governatori I F. Olivieri I A. Rotolo I S. Scannapieco 799 Foundations of Everyday Practical Reasoning H. Lin 831 On the Epistemic Foundation for Iterated Weak Dominance: An Analysis in a Logic of Individual and Collective attitudes E. Lorini 863 Action Emulation between Canonical Models F. Sietsma I J. van Eijck 905

A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. This book presents a comprehensive overview on paraconsistent logical systems to change this situation. The book includes almost every major author currently working in the field. The papers are on the cutting edge of the literature some of which discuss current debates and others present important new ideas. The editors have avoided papers about technical details of paraconsistent logic, but instead concentrated upon works that discuss more "big picture" ideas. Different treatments of paradoxes takes centre stage in many of the papers, but also there are several papers on how to interpret paraconistent logic and some on how it can be applied to philosophy of mathematics, the philosophy of language, and metaphysics.

Although Frege spent his entire working life at the University of Jena teaching mathematics, he once remarked, “Every good mathematician is at least half a philosopher.”1 If he had done nothing else besides inventing modern predicate logic with the introduction of quantifiers and variables into his function-and-argument approach to analyzing sentences, Frege’s elevated place in the history of both logic and the philosophy of logic would be assured and his genius stamped and sealed for all time. His contributions, however, are not confined to philosophical logic and mathematical logic; on the contrary, they are of immense importance to the philosophy of language. Frege wrote his first published paper, ‘Funktion und Begriff, 122 years ago, and his last, ‘Nebengedanke’, 90 years ago.2 Despite the passage of time and the many developments that have shaped the course of semantics since, Frege’s ideas loom large today. Dummett not long ago observed, “There is scarcely a live question in contemporary philosophy of language for whose examination Frege’s views do not form at least the best starting point.” So it is with the topic of tone and the issues that it involves.

International audience; This special issue of the journal Synthese contains a selection of papers presented at the Third International Workshop on Logic, Rationality, and Interaction (LORI-III). Over the last decades, logic has developed as a discipline interfacing between mathematics, philosophy, computer science, and linguistics. In the last few years, a new research field emerged at the crossing point of all these domains: the focus on the study of rational agency and what is sometimes called 'intelligent interaction', which has led to new theories of information flow, communication, and goal-directed strategic interaction between many agents. This new perspective has led to further contacts between philosophical logic, computational logic, theories of agency in computer science, but also new partners such as game theory and social choice theory, linking logic to the social sciences. Examples of such merges are dynamic epistemic studies of rational behavior in games, 'social software' using computational techniques for analyzing patterns of social behavior, or applications of evolutionary games to linguistic semantics and pragmatics. Moreover, in this mix, increasing contacts can be noted betweenlogic and research in the experimental cognitive sciences. All this also affects older contacts, and in fact, social interactive information-based themes are also affecting modern philosophy.

The Vienna Circle and the Berlin Group were schools of scientific philosophy that fought a common enemy—philosophical idealism and philosophical traditionalism in general. Their historically decisive influence makes it all the more disappointing that their intertwined story has not come down to us with due regard to its complexity. For the received account—that the Vienna Circle directed the scientific philosophy of the 1920s and 1930s—perpetuates an oversimplified picture of a seminal development of twentieth-century Western intellectual history. The fact is that the Berlin Group was an equal partner with the Vienna Circle, albeit one that pursued an itinerary of its own. But while the latter presented its defining projects in readily discernible terms and became immediately popular, the Berlin Group, whose project was at least as significant as that of its Austrian counterpart, remained largely unrecognized. The task of this chapter is to distinguish the Berliners’ work from that of the Vienna Circle and to bring to light its impact in the history of scientific philosophy.

El artículo es un intento de determinar la naturaleza de la filosofía del lenguaje a través de las relaciones de esa disciplina con otras, tanto desde el punto de vista histórico como desde el sistemático. Se examina la forma en que la filosofía del lenguaje ha venido relacionándose de hecho con la lingüística, la lógica, la psicología y la propia filosofía, al tiempo que se hacen propuestas de clarificación de esas relaciones, en el sentido prescriptivo del término. De paso, se critican ciertas nociones que han venido oscureciendo el problema, como las de “lógica filosófica”, “filosofía lingüística” y otras, para terminar apoyando el papel fundamental de la filosofía del lenguaje dentro de la filosofía analítica, en un sentido amplio.

This is a selective summary of work done by philosophers on the concept of vagueness (or fuzziness) accompanied by a selective annotated bibliography organized topically. The main topics covered are: the sorites paradox, the semantic technique of supervaluations, the definition of first-order and higher-order borderline cases by means of a determinacy operator, arguments that the existence of vagueness precludes the coherence of observational predicates, such as color terms, and arguments (“The Problem of the Many”) that the existence of vagueness precludes the existence of ordinary things. Attempts to meet these last two arguments often encounter the problem of inappropriate precision, the problem of importing inappropriately high degrees of exactness into theoretical treatments of inexactness.

For a large class of cases-though not for all-in which we employ the word “meaning” it can be defined thus: the meaning of a word is its use in the language . Wittgenstein (1953, §43) The purpose of this paper is to defend Wittgenstein's idea – his so-called “usetheory” of meaning – against what is perhaps the most influential of the many arguments that have been levelled against it. I'm thinking of Kripke's critique of “dispositionalism”, which is a central component of his celebrated essay, Wittgenstein on Rules and Private Language. Kripke argues that meaning a certain thing by a word is not a matter of being disposed to use it in a certain way. And his argument has been well-received. Most commentators, whatever they say about Kripke's overall line of thought (leading up to his “sceptical conclusion” about meaning), tend to agree at least that the use-theory has been elegantly demolished. My main objective is to combat this impression. Just what Wittgenstein himself had in mind is not entirely clear; but that's not my topic. Rather, what I want to do here is to explore and support a certain version of the use-conception of meaning – one which seems to me to have some attractive features (and which I believe can be pinned on Wittgenstein).

Book Information Algebraic Methods in Philosophical Logic. By J. Michael Dunn and Gary Hardegree. Clarendon Press. Oxford. 2001. Pp. xv + 470. £60.50.

The spring of 1980 I spent as visiting lecturer at Utrecht. The volume of Heyting’s Collected Papers had not yet been put together, and his philosophical papers could not be found at Oxford. Accordingly, I availed myself of the opportunities offered by Dutch libraries and read the relevant papers. A couple of years earlier, I had learned about Constructive Type Theory from Per Martin-Lof, and Michael Beeson, who had just written a paper on a theory of constructions, was an eager sparring partner in almost daily discussions at Utrecht. The outcome of these ponderings was this chapter on which you are reading now as an afterword. It was ready toward the end of the summer 1981, and my Oxford Professor Dana Scott suggested to me that I should submit it to Richmond Thomason, the editor of the Journal of Philosophical Logic, at a meeting of authors for the Handbook of Philosophical Logic at Bad Homburg. I did so and the paper was readily accepted; however, a special issue on intuitionism was being prepared, and Thomason suggested that I might want to wait in order to have it appear in that issue. Thus, the paper appeared only in 1983 but had circulated rather widely in the intervening time.

In the Metaphysics, Aristotle called it βeβαιοτάτη πασὣυᾀpxή , “The firmest of all principles”1 - firmissimum omnium principiorum, the medieval theologians said. They referred to the principle that was to be known as the Law of Non-Contradiction (LNC). They called it firmissimum, for in the Western philosophical tradition the LNC was regarded as the most fundamental principle of knowledge and science. According to Thomas Reid the Law, in the form: “No proposition is both true and false”, was also a cornerstone of common sense, together with other basic truths that shape our experience (“Every complete sentence must have a verb”, for instance, or “Those things really happened which I distinctly remember”).

International audience; The target of this paper is twofold. The first part develops firstly a very general and abstract topic, by describing what philosophy of logic is, when it is embedded in a genuine philosophical system, and it secondly provides an explanation of the reason why intuitionism, assumed as genuine philosophical system, is in total harmony with the contemporary intuitionistic formal logic. This part ends on the definition of what is a stable philosophical system, and explains why Platonism and Intuitionism are stable. The second part deals with the contemporary critics against Intuitionism made by a logico-philosophical tentative to give a new rise of Stric Finitism in philosophy of logic. I give arguments to show that, at the moment, the Radical Semantic Anti-realism does not provide a philosophical system as stable as Intuitionism.

This paper develops a formal system, consisting of a language and semantics, called serial logic (SL). In rough outline, SL permits quantification over, and reference to, some finite number of things in an order, in an ordinary everyday sense of the word “order,” and superplural quantification over things thus ordered. Before we discuss SL itself, some mention should be made of an issue in philosophical logic which provides the background to the development of SL, and with respect to which I wish to contend that the system permits progress.

International audience; The origins of bisimulation and bisimilarity are examined, in the three fields where they have been independently discovered: Computer Science, Philosophical Logic (precisely, Modal Logic), Set Theory. Bisimulation and bisimilarity are coinductive notions, and as such are intimately related to fixed points, in particular greatest fixed points. Therefore also the appearance of coinduction and fixed points is discussed, though in this case only within Computer Science. The paper ends with some historical remarks on the main fixed-point theorems (such as Knaster-Tarski) that underpin the fixed-point theory presented.

Marek Sergot's technical contributions range over different subjects. He has developed a series of novel ideas and formal methods bridging different research domains, such as artificial intelligence, computational logic, philosophical logic, legal theory, artificial intelligence and law, multi-agent systems and bioinformatics. By combining his background in logic and computing with his interest in the law, deontic logic, action, and related areas, and applying to all his capacity to understand the subtleties of social interactions and normative reasoning, Marek has been able to open new directions of research, and has been a reference, an inspiration, and a model for many researchers in the many fields in which he has worked.

ispartof: pages:73-78 ispartof: Logic, Philosophy and History of Science in Belgium II. Proceedings of the Young Researchers Days 2010 pages:73-78 ispartof: Young Researchers Days location:Brussels date:6 Sep - 7 Sep 2010 status: published

A reader coming anew to the recent work on languages which contain their own truth predicates may be perplexed by the simple question of where to begin. A first approach to the literature suggests a field which is alive and busy with investigations heading in many different directions, but there is much less indication of how various pieces fit together. There are at least two sources of this confusion. First, the literature is large and diffuse (as befits a subject which goes back over 2000 years); Visser's survey [33] aptly describes the literature as “vast but scattered, repetitive, and disconnected.” Moreover, recent interest in the field has led to a proliferation of research and publication; it seems that almost any issue of any philosophical logic journal from the mid-1980s contains some article on the topic. The second reason, in part a consequence of the first, is that while a typical article in print usually presents a good internal motivation, with clear reference to its immediate intellectual antecedents, its place in the broader picture may not be so easily discerned. The problem can be especially acute in presentations of axiomatic approaches, because decisions on certain basic questions can lie hidden in the formal and notational details which abound in any axiomatization.In fact, though, the recent research on methods for handling self-referential truth can be seen as a body of work which is very well structured, one in which a few fundamental decisions suffice to locate any particular approach in its appropriate place on the landscape. My goal is to describe this structure and in particular to stress a few critical forks in the road, which will be the recurring metaphor throughout this paper. I will also pay particular attention to pointing out where the interesting technical and mathematical questions lie.

The purpose of this paper is to work toward an explicit logic and semantics for a game theoretically inspired theory of action. The purpose of the logic is to explicate the conceptual machinery implicit in the dialogue-game model of rational discourse developed in Carlson (1983). A variety of ideas and techniques of modal and philosophical logic are used to define a model structure that generalizes the game theoretical notion of a game in extensive form (von Neumann and Morgenstern, 1944). Relative to this model structure, semantic characterizations are given to the action-theoretic notions oftime, possibility, belief, preference, ability, intention, action, andrationality. The unification of these characterizations under the game-theoretical paradigm leads to insights about the logical interdependences between these concepts. The resulting theory of rational interaction is applied to the explication of rational dialogue. The main benefit of the enterprise for a theory of rational dialogue is that concepts and results of game theory become accessible to the explication of dialogue. In particular, the task of proving the logical coherence of a discourse is reduced to the task of showing the rationality of strategy choices made in an associated dialogue game.

There is a long-standing distinction between characterizing an object and classifying it. To characterize an object is to compare it with others and find it similar in some way. It is to say, for example, that it is square, asymmetric, endothermic, crystalline at 500?K. To classify an object is to place it in a scheme of classes which embodies more than just a single fleeting comparison, but pur ports to encode the most important or salient features about it. It is to say, for example, that it is a golden eagle, a 1959 Cadillac De Ville, an automobile, some hydrogen sulfate, a gamma ray photon. This distinction has been recognized since antiquity. Aristotle distinguished predications in the category of substance, which tell us what something is?clas sifying it?from predications telling us how something is?characterizing it. (So, for example, predications in the categories of quantity, quality, place, rela tion etc., tell us what magnitude something is, what it is like, where it is, how it compares to another, etc.) The traditional distinction between characterizing and classifying an object has been rejected in modern philosophical logic, a fact reflected in the syntax and semantics of standard predicate logic. The predicates is a man and is white are dealt with equally as one-place predicates taking one nominal argument to form a sentence, and they are equally assigned a set of objects?those satisfying or falling under the predicate?as extension on a given interpretation. As Quine says, "Predication is illustrated indifferently by 'Mama is a woman', 'Mama is big', and 'Mama sings'. . . . The copula 'is' or 'is an' can accordingly be explained simply as a prefix serving to convert a general term from adjectival or

Jaspers demands from philosophy to become world philosophy. The author follows the question, what is the difference between world philosophy and past forms of philosophizing, if it contains more than the not so new demand that future philosophy must care about world peace and unity of the world? The author comes to the conclusion that the Jaspersian project of world philosophy—to which Jaspers dedicated the last years of his life—can only be made understandable by taking into account the specific prerequisites of Jaspers’ thinking. The crucial premise is that there cannot be world peace, unless it is preceded by making peace between the different philosophies and also between philosophy and religion—under the auspices of the truth, which connects all. This thought sheds a new light on the far reaching, partially gigantic projects and concepts of Jaspers philosophy: Periechontology, philosophical logic, the idea of a world history of philosophy, and foremost the concept of philosophical faith and the doctrine of ciphers.

We have now developed separate logics for knowledge update, inference, belief revision, and preference change. But concrete agency has all these entangled. A concrete intuitive setting where this happens is in games , and this chapter will explore such interactive scenarios. Our second reason for studying games here is as a concrete model of mid-term and long-term interaction over time (think of conversation or other forms of interactive agency), beyond the single steps that were the main focus in our logical systems so far. This chapter is a ‘mini-treatise’ on logic and games introducing the reader to a lively new area that draws on two traditions: computational and philosophical logic. We discuss both statics , viewing games as encoding all possible runs of some process, and the dynamics when events change games. We start with examples. Then we introduce logics for static game structure, from moves and strategies to preferences and uncertainty. About halfway, we make a turn and start exploring what our dynamic logics add in terms of update and revision steps that change game models as new information arrives. Our technical treatment is not exhaustive (we refer to further literature in many places, and van Benthem (to appearA) will go into more depth), but we do hope to convey the main picture.