A sound and complete axiomatization of two philosophy tabloids is given, Leiter Logic (KB) and Deontic Leiter Logic (KDB), in single agent format, the latter of which can be extended to Shame Game Logic for multiple players. The (B) schema captures the mechanism of tabloid inference, illustrating the perils of interpreting a provability operator as an epistemic modal. To mark this hazard, and to preserve Brouwer's good name, the (B) schema interpreted to govern epistemic (...) modals should be called The Blog Schema. (shrink)

There is at this point no shortage of testimonials regarding the practice of philosophy for children. In addition, there have been a number of studies which give further support to the claim that philosophy for children is a valuable classroom practice. The idea that pre-college instruction in philosophy is beneficial is no longer in doubt, nor is there a significant lack of materials for use in philosophy for children programs. From Lewis Carroll to Matthew Lipman authors (...) constructed texts that go far in engaging children's philosophical inclinations. If there is any weakness in the practice of philosophy for children it is usually found in the individual classroom. (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.

I LOGIC IN PHILOSOPHY— PHILOSOPHY OF LOGIC i. On the relation of logic to philosophy I n this book, the consequences of certain logical insights for ...

This paper provides a Genzten style formulation of the game logic framework GLm (0 m ), and proves the cut-elimination theorem for GLm. As its application, we prove the term existence theorem for GL used in Part I.

We investigate the expressive power of Parikh's Game Logic interpreted in Kripke structures, and show that the syntactical alternation hierarchy of this logic is strict. This is done by encoding the winning condition for parity games of rank n. It follows that Game Logic is not captured by any finite level of the modal -calculus alternation hierarchy. Moreover, we can conclude that model checking for the -calculus is efficiently solvable iff this is possible for (...) class='Hi'>Game Logic. (shrink)

Contemporary Complex Cinema. Complex conditions: the resurgence of narrative complexity ; Complex cinema as brain-candy for the empowered viewer ; Narrative taxonomies: simple, complex, puzzle plots -- Cognitive Approach to Contemporary Complex Cinema. Why an (embodied-)cognitive approach? ; Various forms of complexity and their effects on sense making ; Problematizing narrative linearity ; Complicating narrative structures and ontologies ; Under-stimulation and cognitive overload ; Contradictions and unreliabilities ; A cognitive approach to classifying complexity ; Deceptive unreliability and the twist film (...) ; Disorienting but solvable puzzle films ; Impossible puzzle films -- Narrative Complexity and Dissonant Cognitions. The concept of cognitive dissonance ; Cognitions in dissonance: from social psychology to narrative engagement ; Types of dissonance in narrative comprehension ; Narrative incongruities ; Narrative impossibilities ; Cognitive access to impossible storyworlds: immersed and reflected operations ; 'Impossibilities' and embodied cognition ; Disrupting viewers' reliance on image schemas by perceptual impossibility ; Disrupting viewers' reliance on image schemas by formal impossibility -- Taming Dissonance: Cognitive Operations and Interpretive Strategies. Cognitive dissonance versus narrative coherence ; Reducing dissonance: interpretation and naturalization ; Foregrounding ; Narrating agency and authorship ; Artefact emotions and metareflexive appreciation ; Interpretation as dissonance reduction ; Coping with dissonance: frame-switches and poetic and aesthetic readings ; Frame-switching as hermeneutic play in impossible puzzle films ; Switching between narrative and symbolical readings: Enemy and Mulholland Drive ; Cognitive hesitation and the fantastic -- Impossible Puzzle Films: Between Art-Cinema and (Post-) Classical Narration. From art-cinema to puzzle films ; Art-cinema as a narrative mode ; Dissonance in modernist art-cinema ; Art-cinema as a cognitive reception frame ; Narrative complexity and meaning-making in art-cinema ; Impossible puzzle films and (post-)classical narration ; High degree of tellability ; Identification with goal-oriented characters ; Strong reliance on classical genre elements ; Adherence to classical narrative cohesion devices ; Inclusion of quasi-rational frames of naturalization -- Wallowing in Dissonance: The Attractiveness of Impossible Puzzles. Hermeneutic play and interpretive multiplicity ; Orientation, navigation, mapping ; Game logic and the fascination in failure ; Effort justification ; Diegetization of decoupling ; Fascination in infinity ; Destabilized ontological certainty ; Eudaimonic motivations and intrinsic needs. (shrink)

_An in-depth look at the philosophical issues behind HBO's _Game of Thrones_ television series and the books that inspired it_ George R.R. Martin's _New York Times_ bestselling epic fantasy book series, A Song of Ice and Fire, and the HBO television show adapted from it, have earned critical acclaim and inspired fanatic devotion. This book delves into the many philosophical questions that arise in this complex, character-driven series, including: Is it right for a "good" king to usurp the throne of (...) a "bad" one and murder his family? How far should you go to protect your family and its secrets? In a fantasy universe with medieval mores and ethics, can female characters reflect modern feminist ideals? Timed for the premiere of the second season of the HBO _Game of Thrones_ series Gives new perspectives on the characters, storylines, and themes of _Game of Thrones_ Draws on great philosophers from ancient Greece to modern America to explore intriguing topics such as the strange creatures of Westeros, the incestuous relationship of Jaime and Cersei Lannister, and what the kings of Westeros can show us about virtue and honor as they play their game of thrones Essential reading for fans, _Game of Thrones and Philosophy_ will enrich your experience of your favorite medieval fantasy series. (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)

This volume presents mathematical game theory as an interface between logic and philosophy.

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)

This article examines Samantha Vice's essay ‘How Do I Live in This Strange Place?’, which sparked a storm of controversy in South Africa, as a starting point for interrogating understandings of whiteness and racism that are dominant in critical philosophy of race. I argue that a significant body of philosophical scholarship on whiteness in general and by white scholars in particular obfuscates the structural dimension of racism. The moralisation of racism that often permeates philosophical scholarship reproduces colourblind logics, which (...) provide individualistic explanations for structural problems, thereby sustaining white dominance. In the process, I show that notions of white guilt, white habits, white ignorance, white invisibility, white privilege, and white shame as they are theorised in much critical philosophy of race share a crucial limitation: they minimise white people's active interest in reproducing the racist status quo. Studies, such as Vice's, that frame racism as a moral dilemma while silencing its institutionalisation and the central cause for its existence and longevity – that is, white people's investment in maintaining economic, political, and symbolic power – further naturalise white supremacy. (shrink)

Not so long ago phenomenon of death was fundamental dimension of human being for continental philosophy. After Second World War postmodern culture deconstructed the “Subject” and the Age of Enlightenment’s values and the phenomenon of death also. It turned into the language game, metaphor, in other words, moved into the space of texts and linguistic. Now people in developed societies behave as if death does not exist. The main hidden barrier to the investigation of human mortal nature – (...) “shame of death” (F. Aries). People shame of aging and therefore death and avoid them. In the modern world there is a domination of technological immortality’s logic, i.e. aging/death is considered as a fatal mistake of Nature, which may be and must be corrected. Collapse of the Soviet communist system was the accomplished logic of immortality of limit-less man, who encountered inevitability of absolute historical and cultural limit. Unfortunately, phenomenon of death of the Soviet and post-Soviet person remained without serious attention of both Russian and West culture. However, from my point of view, logic of Soviet “mangod”, Soviet ideology and empire’s collapse hold answers on most cardinal issues of modern period of world history. The matter is not the returning to the religious values, but next step to the image of mortal being and, therefore, to the mortal human being, who is aware and demand human limits in practice. (shrink)

The information society is upon us. New technologies have given us back pocket libraries, online discussion forums, blogs, crowdbased opinion aggregators, social media and breaking news wherever, whenever. But are we more enlightened and rational because of it? With points of departure in philosophy, logic, social psychology, economics, and choice and game theory, Infostorms shows how information may be used to improve the quality of personal decisions and group thinking but also warns against the informatonal pitfalls which (...) modern information technology may amplify: From science to reality culture and what it really is, that makes you buy a book like this. "With this brilliant book, we have been warned. It is up to all of us in the world today to be stewards of the common resource that is trustworthy and relevant information". Adam Brandenburger, Stern School of Business, NYU "It is a highly recommended read for social scientists and concerned citizens alike". Christian List, London School of Economic. (shrink)

Informal logic is a new sub-discipline of philosophy, roughly definable as the philosophy of argument. Contributors have challenged the traditional concept of an argument as a premiss-conclusion complex, in favour of speech-act, functional and dialogical conceptions; they have identified as additional components warrants, modal qualifiers, rebuttals, and a dialectical tier. They have objected that "soundness" is neither necessary nor sufficient for a good argument. Alternative proposals include acceptability, relevance and sufficiency of the premisses; conformity to a valid (...) argument schema; conformity to rules for discussion aimed at rational resolution of a dispute. Informal logic is a significant part of philosophy. (shrink)

A threat to humanity portending the end of our species lurks in the cold recesses of space. Our only hope is an eleven-year-old boy. Celebrating the long-awaited release of the movie adaptation of Orson Scott Card’s novel about highly trained child geniuses fighting a race of invading aliens, this collection of original essays probes key philosophical questions raised in the narrative, including the ethics of child soldiers, politics on the internet, and the morality of war and genocide. Original essays dissect (...) the diverse philosophical questions raised in Card’s best-selling sci-fi classic, winner of the Nebula and Hugo Awards and which has been translated in 29 languages Publication coincides with planned release of major motion picture adaptation of _Ender’s Game_ starring Asa Butterfield and Harrison Ford Treats a wealth of core contemporary issues in morality and ethics, including child soldiers, the best kind of education and the use and misuse of global communications for political purposes A stand-out addition to the Blackwell Philosophy and Pop Culture series. (shrink)

This essay discusses Wittgenstein's conception of logic, early and late, and some of the types of logical system that he constructed. The essay shows that the common view according to which Wittgenstein had stopped engaging in logic as a philosophical discipline by the time of writing Philosophical Investigations is mistaken. It is argued that, on the contrary, logic continued to figure at the very heart of later Wittgenstein's philosophy; and that Wittgenstein's mature philosophy of (...) class='Hi'>logic contains many interesting thoughts that have gone widely unnoticed. (shrink)

In order to think of philosophy after automation, we have to ask if there is more in philosophy than the process of learning what philosophy is by inducing, from actual inferential practices, the future possible moves that are believed to produce philosophical truths. In the same way as the production of scientific hypothesis has been automated like a self-updating process which entails schemas of decisions and actions, philosophy itself, once conceived as a game where the (...) truth of the statements is measured with respect to the social reproduction of inferential moves, could be automated as well. (shrink)

We present a logically detailed case-study of Darwinian evolutionary explanation. Special features of Darwin’s explanatory schema made it an unusual theoretical breakthrough, from the point of view of the philosophy of science. The schema employs no theoretical terms, and puts forward no theoretical hypotheses. Instead, it uses three observational generalizations—Variability, Heritability and Differential Reproduction—along with an innocuous assumption of Causal Efficacy, to derive Adaptive Evolution as a necessary consequence. Adaptive Evolution in turn, with one assumption of scale (‘Deep Time’), (...) implies the observational generalization of Adaptation. It is a fascinating methodological task to regiment the premises and make the reasoning both rigorous and clear. Doing so reveals how surprisingly small an amount of mathematics is needed in order to carry out the argument. The investigation also reveals the crucial role played by heritability, and how heritability itself admits of Darwinian explanation. (shrink)

The point of view expressed in the present research is directed towards the ideational “torsion” from rationalism to the “language-games” drawing up an analysis according to which one can notice the rationalist and post-rationalist aspects in the philosophy of communication, and the consequences of these perspectives, which could be of great interest as regards the philosophical concepts related to communication, to man or to the human community. As a matter of fact, “the torsion” is only apparent; it cannot hold (...) a dramatic change of the thinking range, from “rationalism” to “neo-positivism”, as regards the comment on Habermas’ theory of communication, as compared to Wittgenstein’s ideas about “the language-games” as central elements of human communication. Jürgen Habermas manifest a specific turn in his way of thinking, aiming at the contemporary modulation of the rationalist approach by means of inter-subjectivism orhumanism, and stressing the modulation of the logical approach, by means of “language-games” and “life-forms.”. (shrink)

This paper determines the state of mind, logic and language in medieval philosophy. It also exhibits the journey from medieval to early modern philosophy. In medieval philosophy, concept of mind was intimately connected soul or spirit with its harmony with religious tradition. Logic and language as well were corresponding with religion and faith. However in early modern philosophy the schema of mind, logic and language were different. These concepts were bailed from the clutches (...) of religious dogmatism and faith towards the mechanical correspondence. Mind was treated as non-modular. Logical truth which includes mostly inductive and deductive in medieval and modern period has been explained clearly. This paper shows the evolution of these concepts in the tradition of Rationalists, Empiricists and Critical Philosophers. In this paper I would as well show the interrelation between mind along with language and logic. This write up further shows the development of language in medieval period to early modern philosophy. it also demonstrates the footprints for the analytical study and international study in contemporary philosophy. (shrink)

This new volume on logic follows a recognizable format that deals in turn with the topics of mathematical logic, moving from concepts, via definitions and inferences, to theories and axioms. However, this fresh work offers a key innovation in its ‘pyramidal’ graph system for the logical formalization of all these items. The author has developed this new methodology on the basis of original research, traditional logical instruments such as Porphyrian trees, and modern concepts of classification, in which pyramids (...) are the central organizing concept. The pyramidal schema enables both the content of concepts and the relations between the concept positions in the pyramid to be read off from the graph. Logical connectors are analyzed in terms of the direction in which they connect within the pyramid. Additionally, the author shows that logical connectors are of fundamentally different types: only one sort generates propositions with truth values, while the other yields conceptual expressions or complex concepts. On this basis, strong arguments are developed against adopting the non-discriminating connector definitions implicit in Wittgensteinian truth-value tables. Special consideration is given to mathematical connectors so as to illuminate the formation of concepts in the natural sciences. To show what the pyramidal method can contribute to science, a pyramid of the number concepts prevalent in mathematics is constructed. The book also counters the logical dogma of ‘false’ contradictory propositions and sheds new light on the logical characteristics of probable propositions, as well as on syllogistic and other inferences. (shrink)

The philosophy of science is the branch of philosophy that examines the profound philosophical questions that arise from scientific research and theories. A sub-discipline of philosophy that emerged in the twentieth century, the philosophy of science is largely a product of the British and Austrian schools of thought and traditions. The first in-depth reference in the field that combines scientific knowledge with philosophical inquiry, The Philosophy of Science: An Encyclopedia is a two-volume set that brings (...) together an international team of leading scholars to provide over 130 entries on the essential concepts in the philosophy of science. The areas covered include biology, chemistry, epistemology and metaphysics, physics, psychology and mind, the social sciences, and key figures in the combined studies of science and philosophy. Essays range in length from 3,000 to 7,500 words and represent the most up-to-date philosophical thinking on timeless scientific topics such as determinism, explanation, laws of nature, perception, individuality, time, and economics as well as timely topics like adaptation, conservation biology, quantum logic, consciousness, evolutionary psychology, and game theory. Offering thorough explorations and destined to become the most authoritative presentation of the field available, this Encyclopedia is a unique and groundbreaking guide to this fascinating field. (shrink)

The syllogistic figures and moods can be taken to be argument schemata as can the rules of the Stoic propositional logic. Sentence schemata have been used in axiomatizations of logic only since the landmark 1927 von Neumann paper [31]. Modern philosophers know the role of schemata in explications of the semantic conception of truth through Tarski’s 1933 Convention T [42]. Mathematical logicians recognize the role of schemata in first-order number theory where Peano’s second-order Induction Axiom is approximated by (...) Herbrand’s Induction-Axiom Schema [23]. Similarly, in first-order set theory, Zermelo’s second-order Separation Axiom is approximated by Fraenkel’s first-order Separation Schema [17]. In some of several closely related senses, a schema is a complex system having multiple components one of which is a template-text or scheme-template, a syntactic string composed of one or more “blanks” and also possibly significant words and/or symbols. In accordance with a side condition the template-text of a schema is used as a “template” to specify a multitude, often infinite, of linguistic expressions such as phrases, sentences, or argument-texts, called instances of the schema. The side condition is a second component. The collection of instances may but need not be regarded as a third component. The instances are almost always considered to come from a previously identified language (whether formal or natural), which is often considered to be another component. This article reviews the often-conflicting uses of the expressions ‘schema’ and ‘scheme’ in the literature of logic. It discusses the different definitions presupposed by those uses. And it examines the ontological and epistemic presuppositions circumvented or mooted by the use of schemata, as well as the ontological and epistemic presuppositions engendered by their use. In short, this paper is an introduction to the history and philosophy of schemata. (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)

This book features a unique selection of works presented at the 2019 annual international conference of the International Association for Computing and Philosophy (IACAP). Every contribution has been peer-reviewed, revised, and extended. The included chapters are thematically diverse; topics include epistemology, dynamic epistemic logic, topology, philosophy of science and computation, game theory and abductive inferences, automated reasoning and mathematical proofs, computer simulations, scientific modelling, applied ethics, pedagogy, human-robot interactions, and big data, algorithms, and artificial intelligence. The (...) volume is a testament to the value of interdisciplinary approaches to the computational and informational turn. We live in a time of tremendous development, which requires rigorous reflection on the philosophical nature of these technologies and how they are changing the world. How can we understand these technologies? How do these technologies change our understanding of the world? And how do these technologies affect our place as humans in the world? These questions, and more, are addressed in this volume which is of interest to philosophers, engineers, and computer scientists alike. (shrink)

Wittgenstein’s language games can be put into a wider service by virtue of elements they share with some contemporary opinions concerning logic and the semantics of computation. I will give two examples: manifestations of language games and their possible variations in logical studies, and their role in some of the recent developments in computer science. It turns out that the current paradigm of computation that Girard termed Ludics bears a striking resemblance to members of language games. Moreover, the kind (...) of interrelations that are emerging could be scrutinised from the viewpoint of logic that virtually necessitates game-theoretic conceptualisations, demonstrating the fact that the meaning of utterances may, in many situations, be understood as Wittgenstein’s language games of ‘showing or telling what one sees’. This provides motivation for the use of games in relation to logic and formal semantics that some commentators have called for. Many of the ideas can be traced to C.S. Peirce, for whom signs were vehicles of strategic communication. The conclusion about Wittgenstein is that the notions of saying and showing converge in his late philosophy. (shrink)

Paradox Lost covers ten of philosophy’s most fascinating paradoxes, in which seemingly compelling reasoning leads to absurd conclusions. The following paradoxes are included: The Liar Paradox, in which a sentence says of itself that it is false. Is the sentence true or false? The Sorites Paradox, in which we imagine removing grains of sand one at a time from a heap of sand. Is there a particular grain whose removal converts the heap to a non-heap? The Puzzle of the (...) Self-Torturer, in which a series of seemingly rational choices has us accepting a life of excruciating pain, in exchange for millions of dollars. Newcomb’s Problem, in which we seemingly maximize our expected profit by taking an unknown sum of money, rather than taking the same sum plus $1000. The Surprise Quiz Paradox, in which a professor finds that it is impossible to give a surprise quiz on any particular day of the week... but also that if this is so, then a surprise quiz can be given on any day. The Two Envelope Paradox, in which we are asked to choose between two indistinguishable envelopes, and it is seemingly shown that each envelope is preferable to the other. The Ravens Paradox, in which observing a purple shoe provides evidence that all ravens are black. The Shooting Room Paradox, in which a deadly game kills 90% of all who play, yet each individual’s survival turns on the flip of a fair coin. Each paradox is clearly described, common mistakes are explored, and a clear, logical solution offered. Paradox Lost will appeal to professional philosophers, students of philosophy, and all who love intellectual puzzles. (shrink)

Preference is a basic notion in human behaviour, underlying such varied phenomena as individual rationality in the philosophy of action and game theory, obligations in deontic logic (we should aim for the best of all possible worlds), or collective decisions in social choice theory. Also, in a more abstract sense, preference orderings are used in conditional logic or non-monotonic reasoning as a way of arranging worlds into more or less plausible ones. The field of preference (...) class='Hi'>logic (cf. Hansson [10]) studies formal systems that can express and analyze notions of preference between various sorts of entities: worlds, actions, or propositions. The art is of course to design a language that combines perspicuity and low complexity with reasonable expressive power. In this paper, we take a particularly simple approach. As preferences are binary relations between worlds, they naturally support standard unary modalities. In particular, our key modality ♦ϕ will just say that is ϕ true in some world which is at least as good as the current one. Of course, this notion can also be indexed to separate agents. The essence of this language is already in [4], but our semantics is more general, and so are our applications and later language extensions. Our modal language can express a variety of preference notions between propositions. Moreover, as already suggested in [9], it can “deconstruct” standard conditionals, providing an embedding of conditional logic into more standard modal logics. Next, we take the language to the analysis of games, where some sort of preference logic is evidently needed ([23] has a binary modal analysis different from ours). We show how a qualitative unary preference modality suffices for defining Nash Equilibrium in strategic games, and also the Backward Induction solution for finite extensive games. Finally, from a technical perspective, our treatment adds a new twist. Each application considered in this paper suggests the need for some additional access to worlds before the preference modality can unfold its true power.. (shrink)

This introduction to modern work in analytic philosophy uses the example of the proper name to give a clear explanation of the logical theories of Gottlob Frege, and explain the application of his ideas to ordinary language. McCulloch then shows how meaning is rooted in the philosophy of mind and the question of intentionality, and looks at the ways in which thought can be "about" individual material objects.

An overview of different versions and applications of Lorenzen’s dialogue game approach to the foundations of logic, here largely restricted to the realm of manyvalued logics, is presented. Among the reviewed concepts and results are Giles’s characterization of Łukasiewicz logic and some of its generalizations to other fuzzy logics, including interval based logics, a parallel version of Lorenzen’s game for intuitionistic logic that is adequate for finite- and infinite-valued Gödel logics, and a truth comparison (...) class='Hi'>game for infinite-valued Gödel logic. (shrink)

This essay is a critique of the two chapters on jealousy in Jerome Neu's book A Tear is an Intellectual Thing. The rival — as anobject of both fear and hatred — is of central importance in romantic jealousy, but it is here argued that the role of the rival cannot be fully understood in Neu's account of jealousy and that shame (not noted by Neu) must be seen as central to the concept of jealousy if the role of (...) the rival is to be fully understood. (shrink)

-/- A schema (plural: schemata, or schemas), also known as a scheme (plural: schemes), is a linguistic template or pattern together with a rule for using it to specify a potentially infinite multitude of phrases, sentences, or arguments, which are called instances of the schema. Schemas are used in logic to specify rules of inference, in mathematics to describe theories with infinitely many axioms, and in semantics to give adequacy conditions for definitions of truth. -/- 1. What is a (...) Schema? 2. Uses of Schemas 3. The Ontological Status of Schemas 4. Schemas in the History of Logic Bibliography. (shrink)

I argue that the medieval form of dialectical disputation known as obligationes can be viewed as a logical game of consistency maintenance. The game has two participants, Opponent and Respondent. Opponent puts forward a proposition P; Respondent must concede, deny or doubt, on the basis of inferential relations between P and previously accepted or denied propositions, or, in case there is none, on the basis of the common set of beliefs. Respondent loses the game if he concedes (...) a contradictory set of propositions. Opponent loses the game if Respondent is able to maintain consistency during the stipulated period of time. The obligational rules are here formalised by means of familiar notational devices, and the application of some game-theoretical concepts, such as (winning) strategy, moves, motivation, allows for an analysis of some crucial properties of the game. In particular, the primacy of inferential (syntactic) relations over semantic aspects and the dynamic character of obligations are outlined. (shrink)

We develop a multi-agent deontic action logic to study the logical behaviour of two types of deontic conditionals: (1) conditional obligations, having the form "If group H were to perform action aH, then, in group F's interest, group G ought to perform action aG" and (2) conditional permissions, having the form "If group H were to perform action aH, then, in group F's interest, group G may perform action aG". First, we define a formal language for multi-agent deontic action (...) logic and a class of consequentialist models to interpret the formulas of the language. Second, we define a transformation that converts any strategic game into a consequentialist model. Third, we show that an outcome a* is a Nash equilibrium of a strategic game if and only if a conjunction of certain conditional permissions is true in the consequentialist model that results from the transformation of that strategic game. (shrink)

This paper introduces The Logic Game, a two-player strategy game designed to help students in introductory logic classes learn the truth conditions for the logical operators. The game materials can be printed using an ordinary printer on ordinary paper, takes 10-15 minutes to play, and the rules are fairly easy to learn. This paper includes a complete set of rules, a URL for a website hosting all of the game materials, and the results of (...) a study of the effectiveness of the Logic Game in three introductory logic classes. (shrink)

This paper develops an account of Wittgenstein’s method of language-games as a method of logic that exhibits important continuities with Russell’s and the early Wittgenstein’s conceptions of logic and logical analysis as the method of philosophy. On the proposed interpretation, the method of language-games is a method for isolating and modeling aspects of the uses of linguistic expressions embedded in human activities that enables one to make perspicuous complex uses of expressions by gradually building up the complexity (...) of clarificatory models. Wittgenstein’s introduction of the language-game method constitutes an attempt to overcome certain limitations of calculus-based logical methods, and to respond in this way to problems with Russell’s and his own early philosophy of logic. The method is nevertheless compatible with the employment of calculus-based methods in logic and philosophy, and makes no exclusive claim to being the correct method. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Theologian's Doubts:Natural Philosophy and the Skeptical Games of GhazālīLeor HaleviIn the history of skeptical thought, which normally leaps from the Pyrrhonists to the rediscovery of Sextus Empiricus in the sixteenth century, Abū Ḥāmid Muḥammad al-Ghazālī (1058-1111) figures as a medieval curiosity. Skeptical enough to merit passing acknowledgment, he has proven too baffling to be treated fully alongside pagan, atheist, or materialist philosophers. As a theologian defending certain (...) Muslim dogmas, Ghazālī has not met what historians consider the mark of the true skeptic, a mind doubting the possibility of all systems of knowledge. But what is fascinating about him is that he brought into practical operation the tools of what I call "functional skepticism."1He denied the claims to truth of Aristotelian physics—whose basis he showed to rest on groundless belief—then turned and argued for the possibility of the Resurrection tooth and nail. The scholarly debate on The Incoherence of the Philosophers (Tahāfut al-falāsifa) has concentrated on the extent to which Ghazālī qua Ashcarite theologian was seduced into Aristotelian philosophy despite himself.2 In my view this debate has been misguided in the attempt to distill the [End Page 19] essence of Ghazālī from the book's eclectic theology; I will argue for a different view of Ghazālī on the basis of a close reading of key passages. In the unusual sections where Ghazālī applies Aristotelian language to a world not following the ordinary laws of physics, some have found Ghazālī slipping, unconsciously perhaps, into an Aristotelian frame of mind. I will show that, as a skeptical theologian with a dialogic imagination, he was rather deconstructing Aristotelian discourse while playing a Wittgensteinian sort of language game.Natural Philosopher or Speculative Theologian?The disagreement about the extent to which philosophy infected Ghazālī is ancient. Ghazālī might have studied philosophy only in order to refute it. He himself defended his philosophizing with the claim that one cannot deconstruct a system of thought until one has understood it so deeply as to elaborate upon its fundamental principles.3 His Maqāṣid al-falāsifa was in fact received, especially in trans-Pyrenean Europe, as a philosopher's genuine summary of the object of philosophy.4 The book strikes me as suspiciously creative in its representation of philosophical discourse, but it appears in any case as an expert and surprisingly unbiased treatment.5 Arabic readers knew that Ghazālī had also written a polemical treatise against philosophy, Tahāfut al-falāsifa, but they still wondered about his engagement with the ideas he challenged. Abū Bakr Ibn al-cArabī, for example, commented that Ghazālī had been unable to extricate himself from philosophy.6 Other philosophers pondered whether or not he had been a closeted member of their charmed circle and sought in his writings traces of esoteric philosophy.7Averroës's own sober sense of distance between philosophy and theology was partially a reaction to what he perceived as Ghazālī's dangerous and carefree mixture of the two sciences.8 He attacked Ghazālī's book in The Incoherence [End Page 20] of the Incoherence to restore philosophy's sense of purity, an aim he sought to accomplish by separating religious concerns from the philosopher's field of inquiry.9 Ironically, such a separation is precisely what Ghazālī might have wished to provoke by crisscrossing and blurring the line between religion and philosophy.The modern debate on chapter 17 of Tahāfut al-falāsifa has concentrated on defining Ghazālī as either a natural philosopher or an occasionalist theologian. In his defense of the possibility of miracles Ghazālī presented two theories of causation, one denying the logical basis of Aristotelian notions of natural causality, and the other more or less adopting these notions. Jointly, the two theories have seemed incompatible, and for this reason scholars have attempted to sort Ghazālī out of the apparent confusion. In 1978 L. E. Goodman argued persuasively that Ghazālī exploited rather than denied the philosophers' ideas of causality. In two articles Michael Marmura challenged Goodman, contending... (shrink)

Au cours des dernières décennies, les travaux portant sur les pratiques humaines réelles ont pris de l'importance dans différents domaines de la philosophie, sans pour autant atteindre une position dominante. À ce jour, ce type de tournant pratique n'a cependant pas encore pénétré la philosophie de la logique. En première partie, j'esquisse ce que serait (ou pourrait être) une philosophie de la logique centrée sur l'étude des pratiques, en insistant en particulier sur sa pertinence et sur la manière de la (...) conduire. En deuxième partie, j'illustre cette approche centrée sur les pratiques au moyen d une étude de cas : le rôle joué par les langages formels en logique, en particulier dans les pratiques des logiciens. Ma thèse est que les langages formels jouent un rôle opératoire fondamental dans le travail des logiciens en tant que technologie pratique du crayon et du papier, génératrice de processus cognitifs - et qui plus spécifiquement vient contrebalancer certains de nos schémas cognitifs « spontanés » peu adéquats à la recherche en logique (ainsi que dans d'autres domaines). Cette thèse sera appuyée sur des données empiriques venant de la recherche en psychologie du raisonnement. Avec cette analyse j'espère montrer qu'une philosophie de la logique centrée sur l'étude des pratiques peut être fructueuse, en particulier si elle est complétée par les réflexions méthodologiques nécessaires. (shrink)

Logical omniscience states that the knowledge set of ordinary rational agents is closed for its logical consequences. Although epistemic logicians in general judge this principle unrealistic, there is no consensus on how it should be restrained. The challenge is conceptual: we must find adequate criteria for separating obvious logical consequences (consequences for which epistemic closure certainly holds) from non-obvious ones. Non-classical game-theoretic semantics has been employed in this discussion with relative success. On the one hand, with urn semantics [15], (...) an expressive fragment of classical game semantics that weakens the dependence relations between quantifiers occurring in a formula, we can formalize, for a broad array of examples, epistemic scenarios in which an individual ignores the validity of some first-order sentence. On the other hand, urn semantics offers a disproportionate restriction of logical omniscience. Therefore, an improvement of this system is needed to obtain a better solution of the problem. In this paper, I argue that our linguistic competence in using quantifiers requires a sort of basic hypothetical logical knowledge that can be formulated as follows: when inquiring after the truth-value of ∀xφ, an individual might be unaware of all substitutional instances this sentence accepts, but at least she must know that, if an element a is given, then ∀xφ holds only if φ(x/a) is true. This thesis accepts game-theoretic formalization in terms of a refinement of urn semantics. I maintain that the system so obtained (US+) affords an improved solution of the logical omniscience problem. To do this, I characterize first-order theoremhood in US+. As a consequence of this result, we will see that the ideal reasoner depicted by US+ only knows the validity of first-order formulas whose Herbrand witnesses can be trivially found, a fact that provides strong evidence that our refinement of urn semantics captures a relevant sense of logical obviousness. (shrink)

While previous writing on the philosophy of sport has tended to see sport as a kind of testing ground for philosophical theories devised to deal with other kinds of problems—of ethics, aesthetics, or logical categorization—here Steven Connor offers a new philosophical understanding of sport in its own terms. In order to define what sport essentially is and means, Connor presents a complete grammar of sport, isolating and describing its essential elements, including the characteristic spaces of sport, the nature of (...) sporting time, the importance of sporting objects like bats and balls, the methods of movement in sport, the role of rules and chance, and what it really means to cheat and to win. Defined as games that involve bodily exertion and exhaustion, sports simultaneously require constraint and the ability to overcome it. Sport, argues Connor, is a fundamental feature of modern humans. It is shown to be one of the most powerful ways in which we negotiate the relationship between the human and natural worlds. Encompassing a huge range of different sports, and enlisting the help of Hegel, Freud, Wittgenstein, Heidegger, Adorno, Sartre, Ayer, Deleuze, and Serres, _A Philosophy of Sport _will inform, surprise, and delight thoughtful athletes and sporty philosophers alike. (shrink)

If we want to retain classical logic and standard syntax in light of the liar, we are forced to restrict the T-schema. The traditional philosophical justification for this is sentential – liar sentences somehow malfunction. But the standard formal way of implementing this is conditional, our T-sentences tell us that if “p” does not malfunction, then “p” is true if and only if p. Recently Bacon and others have pointed out that conditional T-restrictions like this flirt with incoherence. If (...) we want to keep the “malfunction” motivation, our only other option is to non-conditionally restrict the T-schema, but Field and others have given powerful philosophical and technical arguments against this kind of approach. Here I argue that if we really take the philosophical motivation for restricting T-sentences seriously, we can explain why conditional restrictions fail, answer Field's argument, and reason in a coherent way about truth using a non-conditional restriction strategy. This cracks the door open for a fully classical response to the liar and related paradoxes. In closing, I argue that, when properly understood, this kind of “restriction” is not really a restriction at all. If this is right, then the holy grail of liar studies (classical logic, naïve truth, and standard syntax) may yet be attainable. (Note for readers: when this paper was first put online, the typesetters had changed some instances of corners to brackets, leading to confusion. The paper has now been corrected online by PPR, so please make sure you have the corrected version before reading or citing.). (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Signs of Logic: Peircean Themes on the Philosophy of Language, Games, and CommunicationRobert W. BurchAhti-Veikko Pietarinen Signs of Logic: Peircean Themes on the Philosophy of Language, Games, and Communication Dordrecht, The Netherlands: Springer, 2006. xiv + 496 pp.This compendious volume of fourteen of Pietarinen's essays on Peirce, plus a three-page set of "Final Words" relating to the work of Robert Aumann, is a "must-have" (...) for both the Peirce scholar and any other philosopher who wishes to relate Peirce's thinking on language and logic to other major thinkers and logical themes of the twentieth century (and beyond). The essays extend or complement discussions of Peirce's logic and philosophy of language that have come to be expected from the "Finnish school" of philosophers, which includes Hintikka and Hilpinen, as well as Pietarinen.Nine of the essays (Chapters 3, 4, 5, 7, 8, 10, 12, 13, and 14), comprising about two-thirds of the entire book, are revised and expanded versions of essays that Pietarinen has previously published. The remaining one-third (approximately) of the book is brand new. Chapters 1 and 2 serve as general introductions to the book's major interests. Chapter 6 is on evidence for constructivism in Peirce, as well as several other topics. Chapter 9 compares Peirce's ideas with Wilfred Hodges's "dialogue foundations" and contains a small philosophical dialogue, which has Peirce, Wittgenstein, and Hodges as its characters. Chapter 11 concerns evolutionary semantics and language [End Page 577] games. And the cursory Chapter 15 of "Final Words" predicts that the game-theoretical approach to semantics and Peirce scholarship has an exploding future, like an erupting volcano.From the foregoing one can gather, correctly, that each essay in the book is separately conceived and that the book is not a single continuous line of argumentative development of one or even of a few themes. Still, the essays are similar to one another in two ways, which ways are closely related to each other. First, they all concern the Peircean doctrine that semeiotic and semeiosis constitute the heartland of logic, and that this heartland is vastly richer than the sort of pure mathematical calculi that might mistakenly be taken for logic itself (and were in fact so taken for much of the twentieth century). Second, they all deal with the Peircean insistence that semeiosis is inherently a form of Praxis in which interchanges occur between or among various "agents" or "actors," one of which might be nature itself; so that at the very least logic is dialogic, and so that more generally one may justifiably speak of semeiosis as involving something like a "game." These lines of exploration will surprise no seasoned Peirce scholar, but the special genius of the Finnish "school" of Peirce interpretation from Hintikka forward is to have spotlighted in dramatic fashion the game-theoretical nature of many elements in Peirce's semeiotic.In these essays Pietarinen amply exhibits two attainments of mind that are indispensable for the serious Peirce scholar. One is the object of what we might call "The Eisele Imperative" after the vehement urgings of Carolyn Eisele: this is the possession of some significant degree of sophistication in mathematics. Pietarinen's mathematical skills are plainly sufficient for his discussions of logic and game theory. For example, his Chapter 5 is an excellent technical discussion of Peirce's existential graphs, and his Chapter 7 is an admirable technical discussion of certain aspects of game theory and generalized quantifiers. Another crucial skill needed by the serious Peirce scholar is the object of what we might call "The Pietarinen Corrective" after the practices exemplified in these essays: this is the possession of extremely broad knowledge of recent and contemporary philosophy, especially philosophy of language, logic, metaphysics, epistemology, and philosophy of science.Indeed, the breadth of Pietarinen's acquaintance with twentieth century logic and philosophy of language, both "analytic" and "continental," is breathtaking. This allows him scope for comparisons of Peirce's views with an extraordinarily wide, and not always easily anticipated, range of philosophers and philosophic traditions. Pietarinen's range of reference is so extensive that it would be pointless to attempt to discuss in... (shrink)

What is the relation or connection between formalizations of induction and the actual inductive inferences of scientists? Building from recent works in the philosophy of logic, this paper argues that these formalizations of induction are best viewed as models and not literal descriptions of inductive inferences in science. Three arguments are put forward to support this claim. First, I argue that inductive support is the kind of phenomenon that can be justifiably modeled. Second, I argue that these formalizations (...) have the features that define models—that they have representors, artefacts, and idealizations. Third, I argue that these formalizations being models explains their plurality and revisability. (shrink)

In this article, we reflect on the use of formal methods in the philosophy of science. These are taken to comprise not just methods from logic broadly conceived, but also from other formal disciplines such as probability theory, game theory, and graph theory. We explain how formal modelling in the philosophy of science can shed light on difficult problems in this domain.

I have been working on meta-philosophy for quite some time and was pleasantly surprised to encounter, mid-May 2017, someone who shares this commitment (apart from his many other interests and specializations) for very similar reasons as my own. He is Dr Desh Ray Sirswal from India and one of his numerous websites, blogs, journals, etc is - http://drsirswal.webs.com/ I let him speak for himself. “My objective is to achieve an intellectual detachment from all philosophical systems, and not to solve (...) specific philosophical problems but to become sensitively aware of what it is when we philosophize.” Copyright© Desh Raj Sirswal . I commence by dealing with the teaching of philosophy, because the contents of what is being taught at under-graduate level is for most people who are slightly informed about the subject what philosophy is about. This usually consists of the history of Ideas of Western Philosophy. Although an increasing number of faculties now broaden the scope to the ‘philosophies’ of Asia, the Far East and the Middle East. This international broadening of what is being included in curricula of or as philosophy is another index that Western Philosophy is in need of subject-matter as its traditional subject-matter have all but died out. Apart from the History of Philosophical ideas, the subject often is presented in terms of so-called branches, for example metaphysics, ontology, epistemology, ethics, logic, and so on. A number of authors suggest that both ways of teaching the discipline is very selective because of the departments adherence to some form of either ‘analytical’ or ‘continental’ philosophy. Apart from the traditional lecture-style the teaching of philosophy is dealt with by means of some variation on the Oxbridge ‘tutorial’-style. Tutorials are often acclaimed as being an amazing, to be highly regarded innovation. Some studies and research of it however revealed that is not at all very comprehensive but is restricted to a number of items concerning reasoning, argumentation and critical re-viewing and thinking. This approach forms part of the attempt by contemporary research universities to teach aspects of ‘research’. This brings us to my next section on methods of doing philosophy. I suggest that the doing of philosophy resembles certain aspects and contexts of some of the steps and stages of doing theorizing. This is the rationale for including the next section on theorizing, its steps, stages and other aspects such as the use of metaphors, imaginary experiments, heuristic devices, etc. The next section deals with the changing nature of traditional philosophy as it lost most of its subject-matter to other disciplines that have been socio-culturally differentiated. And the search for new philosophical subject-matter such as Experimental Philosophy or XPhi, the involvement of philosophers in inter-disciplinary studies, especially the latest fad of cognitive studies or sciences and of course the fabrication of philosophies of all areas of human behaviour and kinds of socio-cultural activities for example sport, the arts, sciences, cognition, sex, violence, gender, race, religion, etc etc. I then turn to the question about how, where and why one could perhaps do philosophy against the background of the above. In this investigation I make explicit some of the self-imposed limits of the discourse. Some of these restrictions have been created because of the absolute institutionalization of the discipline as just another subject of universities. This institutionalization of course requires that those involved in the discipline of institutionalized philosophy must be professionals. This absolute requirement lays down the condition that to be a philosopher one must be a professional and an academic. The conditions of institutionalization and professionalization have far reaching consequences for the philosophical discourse, its subject-matter, methods, principles, values, aims, purposes and norms. One of these is the need to publish and to publish often especially in peer-reviewed journals and in their required, institutionalized format. Because of these institutionalized restrictions of what philosophy is, what it must be like, what it may be like and what it may not be like I explore the lack of self-cognition of academically institutionalized philosophy and the associated absence of critical, meta-cognition and self-awareness of professional philosophers. I question the values of doing that type of philosophy, philosophy-on-demand and because of demand and suggest that it is preferable to engage with the more original, creative-thinking philosophers’ work. All of the above are of course intersubjectively determined and this is why I finally explore the nature and operation of different forms of intersubjectivity, for example of common sense, everyday existence, that of the different sciences, the arts, etc and the roles or functions of these things in the creation or constitution of alternative discourses, their realities, life-worlds or perspectives on ‘the world, reality, and existence’. This is the phantom, the ghost of the deceased discourse of philosophy that I chased, encountered and describe. -/- . (shrink)