Between the end of the nineteenth century and the first twenty years of the twentieth century, stimulated by the impetuous development of logical studies and taking inspiration from Leibniz's idea of a characteristica universalis, the three founding fathers of the analytic tradition in philosophy, i.e., Frege, Russell, and Wittgenstein, started to talk of a logically perfect language, as opposed to natural languages, all feeling that the latter were inadequate to their (different) philosophical purposes. In the second half (...) of the twentieth century, however, the very idea of a logically perfect language ceased for various reasons to seem attractive to analytic philosophers. Thus, it might appear that this idea could be classified together with the many other bizarre ideas that from time to time surface in the history of philosophy-an idea that perhaps had a beneficial impact on the development of twentieth century logic, but which can now be put to rest. In this brief note, I contend that this conclusion may be too hasty. Indeed, if a well-known empirical hypothesis advanced in 1975 by Jerry Fodor turns out to be true, then there is a logically perfect language, after all. More precisely, I argue that, if it exists, Fodor's language of thought possesses the main characteristics a logically perfect language is required to have. (shrink)

For humanists the perfect language was a revived Classical Latin. For scholastics it was a practical logic adapted to the needs of education. Though they have long been portrayed as arch rivals, Alan Perreiah here argues that humanists and scholastics were working in complementary ways toward some of the same goals: most significantly, the early modern search for the perfect language. The study advances research on language pedagogy in the Renaissance by clarifying the connections between (...) truth and translation. (shrink)

Voice: Malagasy presents morphologically distinct verbs built from the same root which assign different grammatical cases to DPs with given theta roles, yielding Ss that are theta equivalent, and, with appropriate choice of DPs, logically equivalent, much like active and agented passive Ss in English. The problem is to derive and interpret such Ss so as to yield these judgments of semantic equivalence as theorems. Our solution, which is purely structural, invoking no notion of ‘subject’, ‘topic’, ‘pivot’, ‘trigger’, etc., (...) is simply an explicit syntactic and semantic interpretation of voice affixes. Deriving Ss built from verbs in different voices involves no A movement of DPs. Voice morphology determines the distinctive syntactic and semantic properties of nuclear clauses. This supports that “Variation of language is essentially morphological ...” (Chomsky 1995:7). (shrink)

The paper focuses on the inferential role of quantifiers in Frege, Peano and Russell. Two aspects of the early years of mathematical logic are discussed: the gradual perfection of the principles of reasoning with quantifiers, and the presumed conceptual impossibility of posing metatheoretical questions, as embodied in Jean van Heijenoort’s well-known dictum about “logic as calculus and logic as language.”.

The paper focuses on the inferential role of quantifiers in Frege, Peano and Russell. Two aspects of the early years of mathematical logic are discussed: the gradual perfection of the principles of reasoning with quantifiers, and the presumed conceptual impossibility of posing metatheoretical questions, as embodied in Jean van Heijenoort’s well-known dictum about “logic as calculus and logic as language.”.

We live in an ageing society, where people are living longer, and where decreases in the birth rate mean that the proportion of the population above retirement age is steadily increasing. An ageing population has considerable implications for health services and care provision. Consequently there is a growing interest among researchers, medical practitioners, and policy makers in older adults, their capabilities, and the changes in their cognitive functioning. This book offers an up-to-the-minute account of the latest methodological and theoretical issues (...) in cognitive ageing. Part of the Debates in Psychology series, it sets out the arguments surrounding the currently controversial questions in cognitive ageing. What is the appropriate methodology for understanding cognitive change? How many factors are necessary to understand the patterns of age-related change? What might these factors be? The topics and arguments are explored in a series of chapters by the leading researchers in the field. Each contributor offers their view of how cognitive ageing can be best understood, and together they cover a broad range of cognitive functions including language use, cognitive slowing, and memory loss. Each of the chapters stands alone as the latest review of work in the area. Taken together, the chapters form a coherent theoretical debate through which the reader will learn about the dynamic nature of cognitive ageing research, and about the direction this research will be taking in the future. Models of Cognitive Aging will be an invaluable resource for anyone with an interest in the elderly, and in their cognitive abilities. (shrink)

"De interpretatione" from Aristoteles. Aristotle (384-322 BCE) was a Greek philosopher born in Greece.

We present the propositional logic LEC for the two epistemic modalities of current and stable knowledge used by an agent who system-atically enriches his language. A change in the linguistic resources of an agent as a result of certain cognitive processes is something that commonly happens. Our system is based on the logic LC intended to formalize the idea that the occurrence of changes induces the passage of time. Here, the primitive operator C read as: it changes that, defines (...) the temporal succession of states of the world. The notion of current knowledge concerns variable components of the world and it may change over time. We represent it by the primitive operator k read as: the agent currently knows that, and assume that it has S5 properties. The second type of knowledge, symbolized by the primitive operator K read as: the agent stably knows that, relates to constant components of the world and it does not change. As a result of the axiomatic entanglement of C, K and k we show that stable knowledge satisfies axioms of S4.3. K and k modalities are not mutually definable, stable knowledge implies the current one and if the latter never changes, then it comes to be stable. The combination of K and k with the idea of an expanding language allows questioning of the so-called perfect recall principle. It cannot be maintained for both types of knowledge just because of changes in the vocabulary of the agent and possibly the growing spectrum of possible states of the world. We interpret LEC in the semantics of histories of epistemic changes and show that it is complete. Finally, we compare our logic with selected epistemic logics based on the concept of linear discrete time. (shrink)

This article examines the translator, Rongzom’s, scholastic philosophical defense of early Dzokchen or “Great Perfection.” As our earliest instance of religious apologia in Tibet, this examination contributes to a growing body of knowledge about the Tibetan assimilation of post-tenth century of Vajrayāna Buddhism and the indigenous response to the forces of cultural transformation shaping the late eleventh/early twelfth century Tibet. Traditional authorities and academics have identified Dzokchen as a Tibetan tradition of Buddhism that drew intense criticism at the time from (...) renaissance agents. This paper explores the primary Tibetan response by describing Rongzom’s philosophical defense of Great Perfection. As such, it illuminates the intellectual and ideological context of the milieu as it evinces Rongzom’s innovation and mastery of Indian systems of logic, language, and epistemology in the Dzokchen approach to the Buddhist path. (shrink)

This paper investigates a problem related to quantifiers which has some analogies to that of propositional completeness I give a definition of quantifier in many-valued logics generalizing the cases which already occur in first order many- valued logics. Though other definitions are possible, this particular one, which I call distribution quantifiers, generalizes the classical quantifiers in a very natural way, and occurs in finite numbers in every m-valued logic. We then call the problem of quantificationa2 completeness in m-valued logic the (...) problem of characterizing which are the quantifiers in a given language which can generate all other quantifiers in this language, using the connectives, as is the case, for example, of the universal and exis- tential quantifiers in classical logic, using negation. We are interested, in particular, in those many-valued quantifiers which closely mimic the behavior of existential an universal quantifiers in generating all other quantifiers using negation: these I call perfect quantifiers, as defined below. The main result of this paper is the characterization of all perfect quantifiers in 3-valued logics, which are complete if the logic is functionally complete. As a byproduct, we obtain the same result for the classical logic, which we include mainly for motivation. (shrink)

The Joint International Conference on Logic Programming, sponsored by the Association for Logic Programming, is a major forum for presentations of research, applications, and implementations in this important area of computer science. Logic programming is one of the most promising steps toward declarative programming and forms the theoretical basis of the programming language Prolog and its various extensions. Logic programming is also fundamental to work in artificial intelligence, where it has been used for nonmonotonic and commonsense reasoning, expert systems (...) implementation, deductive databases, and applications such as computer-aided manufacturing. Krzysztof R. Apt is project leader at the Centre for Mathematics and Computer Science in Amsterdam and part-time Professor in Computer Science at the University of Amsterdam. Topics covered: Theory Foundations. Programming Languages. Implementation. Programming Methodologies and Tools. Applications. Deductive Databases. Artificial Intelligence. Parallelism. (shrink)

The five English words—sentence, proposition, judgment, statement, and fact—are central to coherent discussion in logic. However, each is ambiguous in that logicians use each with multiple normal meanings. Several of their meanings are vague in the sense of admitting borderline cases. In the course of displaying and describing the phenomena discussed using these words, this paper juxtaposes, distinguishes, and analyzes several senses of these and related words, focusing on a constellation of recommended senses. One of the purposes of this paper (...) is to demonstrate that ordinary English properly used has the resources for intricate and philosophically sound investigation of rather deep issues in logic and philosophy of language. No mathematical, logical, or linguistic symbols are used. Meanings need to be identified and clarified before being expressed in symbols. We hope to establish that clarity is served by deferring the extensive use of formalized or logically perfect languages until a solid “informal” foundation has been established. Questions of “ontological status”—e.g., whether propositions or sentences, or for that matter characters, numbers, truth-values, or instants, are “real entities”, are “idealizations”, or are “theoretical constructs”—plays no role in this paper. As is suggested by the title, this paper is written to be read aloud. -/- I hope that reading this aloud in groups will unite people in the enjoyment of the humanistic spirit of analytic philosophy. (shrink)

ABSTRACT At the centre of Plato’s Euthydemus lie a series of arguments in which Socrates’ interlocutors, the sophists Euthydemus and Dionysodorus propose a radical account of truth (‘chopped logos’) according to which there is no such thing as falsehood, and no such thing as disagreement (here ‘counter-saying’). This account of truth is not directly refutable; but in response Socrates offers a revised account of ‘saying’ focussed on the different aspects of the verb (perfect and imperfect) to give a rich (...) account of saying, of truth and of knowledge. I argue that Socrates’ response has much to offer, notably in its amplification of the process of saying and cognition, and the development of virtue. (shrink)

Many books explain what is known about the universe. This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own thought processes. Yanofsky describes (...) simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve; perfectly formed English sentences that make no sense; different levels of infinity; the bizarre world of the quantum; the relevance of relativity theory; the causes of chaos theory; math problems that cannot be solved by normal means; and statements that are true but cannot be proven. He explains the limitations of our intuitions about the world -- our ideas about space, time, and motion, and the complex relationship between the knower and the known. Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there. (shrink)

The program put forward in von Wright's last works defines deontic logic as ``a study of conditions which must be satisfied in rational norm-giving activity'' and thus introduces the perspective of logical pragmatics. In this paper a formal explication for von Wright's program is proposed within the framework of set-theoretic approach and extended to a two-sets model which allows for the separate treatment of obligation-norms and permission norms. The three translation functions connecting the language of deontic logic with the (...) language of the extended set-theoretical approach are introduced, and used in proving the correspondence between the deontic theorems, on one side, and the perfection properties of the norm-set and the ``counter-set'', on the other side. In this way the possibility of reinterpretation of standard deontic logic as the theory of perfection properties that ought to be achieved in norm-giving activity has been formally proved. The extended set-theoretic approach is applied to the problem of rationality of principles of completion of normative systems. The paper concludes with a plaidoyer for logical pragmatics turn envisaged in the late phase of Von Wright's work in deontic logic. (shrink)

Finally, the first book started Peirceana. Peirceana is expected as a new series that provides access to both Peirce’s mostly unpublished late works and secondary papers, in which ideas of this American philosopher are developed. This edition is opened with three volumes on Peirce’s manuscripts on “Logic of the Future.” The thinker gave this definition to his theory of existential graphs, i.e., a diagrammatical logical project that includes three sections. The sections can roughly correspond to propositional logic, first-order logic and (...) modal logic. The theory of existential graphs is a particular conception. It predicts ideas of proof theory, mathematics of continuity, and cognitive sciences. Besides, it has an impressive philosophical foundation and perfectly emphasizes the importance of diagrammatic notations. Since many writings are published here for the first time, the edition per se is a significant event for the history of logic. However, Peirceana can do more than this. It urges to think of how the logic of 20‒21st centuries would have looked like if Peirce’s intentions were discovered earlier. At the same time, it clarifies the ground for contemporary investigations. Today we have a bunch of papers about various non-classical modifications, extensions, restrictions, and applications of the original theory. Peirceana is projected as the publication that can gather specialists (logicians, philosophers, as well as IT and cognitive science scholars) who are interested in the development of Peirce’s approach. It lets the readers reconsider our ordinary logical conceptions (e.g., reasoning, logical and language analysis, and others) as well as the conventional understanding of the evolution of modern logic. The current paper has two objectives: firstly, it estimates this diplomatic partly critical edition with its several thoroughly elaborated introductions, and secondly, it briefly introduces the existential graphs theory. A set of examples demonstrates the basic principles of this system. (shrink)

The papers collected in this volume exemplify some of the trends in current approaches to logic, language and computation. Written by authors with varied academic backgrounds, the contributions are intended for an interdisciplinary audience. The first part of this volume addresses issues relevant for multi-agent systems: reasoning with incomplete information, reasoning about knowledge and beliefs, and reasoning about games. Proofs as formal objects form the subject of Part II. Topics covered include: contributions on logical frameworks, linear logic, and different (...) approaches to formalized reasoning. Part III focuses on representations and formal methods in linguistic theory, addressing the areas of comparative and temporal expressions, modal subordination, and compositionality. (shrink)

The logical form of a discourse—such as a proposition, a set of propositions, an argument, or an argumentation—is obtained by abstracting from the subject-matter of its content terms or by regarding the content terms as mere place-holders or blanks in a form. In a logically perfect language the logical form of a proposition, a set of propositions, an argument, or an argumentation is determined by the grammatical form of the sentence, the set of sentences, the argument-text, or (...) the argumentation-text expressing it. Two such discourse-texts are said to have the same grammatical form, in this sense, if a uniform one-one substitution of content words transforms the one exactly into the other. The sentence ‘Abe properly respects every agent who respects himself’ may be regarded as having the same grammatical form as the sentence ‘Ben generously assists every patient who assists himself’. (shrink)

The title of this volume -- Logic, God and Metaphysics -- is carefully chosen and, at the same time, descriptive of its main focus. In the twentieth century, the interests of most philosophers and theologians have fallen into only one of the three areas indicated -- logic, god or metaphysics. Since much of Anglo-American philosophy in this century has been analytic and antimetaphysical because of the influence of positivism, there have been few attempts at continuing metaphysical inquiry. In the early (...) part of the century, the logical atomists combined logic and metaphysics by arguing that the structure of reality is mirrored isomorphically in the structure of a formal, logically perfect, truth-functional language, but their effort was short-lived. Alfred North Whitehead and process philosophers have focused upon god and metaphysics but usually by adopting terminology and distinctions which are unique to certain systems -- making rigorous, logical analysis difficult or impossible. The papers included in this volume are illustrative of the application of careful, rigorous logical analysis to do critical philosophy of religion and what has been called constructive metaphysics. (shrink)

The perfect fit of syntactic derivability and logical consequence in first-order logic is one of the most celebrated facts of modern logic. In the present flurry of attention given to the semantics of natural language, surprisingly little effort has been focused on the problem of logical inference in natural language and the possibility of its completeness. Even the traditional theory of the syllogism does not give a thorough analysis of the restricted syntax it uses.My objective is to (...) show how a theory of inference may be formulated for a fragment of English that includes a good deal more than the classical syllogism. The syntax and semantics are made as formal and as explicit as is customary for artificial formal languages. The fragment chosen is not maximal but is restricted severely in order to provide a clear overview of the method without the cluttering details that seem to be an inevitable part of any grammar covering a substantial fragment of a natural language. (Some readers may feel the details given here are too onerous.). (shrink)

What is the source of logical and mathematical truth? This book revitalizes conventionalism as an answer to this question. Conventionalism takes logical and mathematical truth to have their source in linguistic conventions. This was an extremely popular view in the early 20th century, but it was never worked out in detail and is now almost universally rejected in mainstream philosophical circles. Shadows of Syntax is the first book-length treatment and defense of a combined conventionalist theory of logic and mathematics. It (...) argues that our conventions, in the form of syntactic rules of language use, are perfectly suited to explain the truth, necessity, and a priority of logical and mathematical claims, as well as our logical and mathematical knowledge. (shrink)

In this paper we study connections between game theoretical concepts and results, and features of IF-predicate logic, extending observations from J. van Benthem (2001) for IF-propositional logic. We highlight how both characteristics of perfect recall can fail in the semantic games for IF-formulas, and we discuss the four Thompson transformations in relation with IF-logic. Many (strong) equivalence schemes for IF-logic correspond to one or more of the transformations. However, we also find one equivalence that does not fit in this (...) picture, by the type of imperfect recall involved. We point out that the connection between the transformations and logical equivalence schemes is less direct in IF-first order logic than in the propositional case. The transformations do not generate a reduced normal form for IF-logic, because the IF-language is not flexible enough. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviews 85 RUSSELL’S CONTRIBUTION TO PHILOSOPHY OF LANGUAGE James Connelly Philosophy, Trent U. Peterborough, on k9l 1z6, Canada [email protected] Graham Stevens. The Theory of Descriptions: Russell and the Philosophy of Language. Basingstoke, uk: Palgrave Macmillan, 2011. Pp. xiii, 197. isbn: 978-0230 -20116-3. £50; us$85. ver the past decade, Graham Stevens has built his reputation as a lucid, durable, and oftentimes ground-breaking historian of analytic philosophy. His latest (...) book, entitled TheTheory of Descriptions: Russell and the Philosophy of Language, will only add to that burgeoning scholarly legacy. If it has not been established already, this book will doubtless cement Stevens’ place amongst the leading Russell scholars in the world today. It may very well herald Stevens ’ arrival on the scene as a noteworthy contributor to contemporary philosophy of language as well. The central goal of the book is “to bring the historical and purely philosophical analyses of [Russell’s] work into closer alignment” (p. 3). Stevens hopes to overcome a “striking disparity” (p. 2) in the ways that Russell’s contributions to the philosophy of language have been conceived by expositors of his philosophy, on the one hand, versus philosophers of language, on the other. In particular, though contemporary philosophers of language would tend to view Russell’s enormous contribution to that subject as being “undeniable” (p. 1), and to be “bewildered” (p. 94) by any suggestion to the contrary, expositors of Russell’s philosophy have nevertheless been at pains to emphasize that Russell “was not engaged in the philosophical study of language” (p. 2). As Stevens notes, this situation is especially puzzling since “these two groups [of scholars] overlap to a considerable extent” (p. 2). Stevens’ strategy for overcoming this disparity is two-pronged. First he aims to tackle, head on, the fallacious arguments of Monk,1 Dummett,2 and others, to the effect that Russell was not engaged in the philosophy of language. According to Stevens, such arguments have principally appealed to either (1) ______ 1 Ray Monk, “What Is Analytical Philosophy?”. 2 Michael Dummett, Frege: Philosophy of Language. l= 86 Reviews Russell’s dismissal of ordinary language philosophy, (2) his early, non-linguistic, conception of the nature of propositions, or (3) his view that natural language was inherently defective for philosophical purposes, and so called for replacement by a “logically perfect language”. In regards to (1), Stevens argues in a word that “[o]rdinary language philosophy has had its day” (p. 176). Over the past several decades, in other words, leading philosophers of language have come to agree with Russell in viewing ordinary language philosophy as “an outdated, and rather eccentric, relic of mid-twentieth century British philosophy” (ibid.).The classic Russell– Strawson debate over the question whether ordinary language lacks an exact logic3 has been settled decisively in Russell’s favour, as philosophers of language have transformed “the attempt to systematically specify the semantics of large regions of natural language” (ibid.) into a “central project” (ibid.). In regards to (2), moreover, Stevens notes that by this line of reasoning, absurdly, David Kaplan would not qualify as a philosopher of language since he “explicitly invokes the Russellian non-linguistic conception of a proposition as the conception appropriate for providing the content of properly context-situated indexical sentences” (p. 170). And, of course, Kaplan is not at all unique amongst contemporary philosophers of language in appealing to a Russellian conception of propositional content, as the examples of Nathan Salmon,4 Scott Soames,5 and many others show. In regards to (3), finally, Stevens argues that Russell’s dim view of natural language was grounded in his conception of logical form as non-linguistic, and that that conception, in turn, derives simply from the poverty of syntactic theory available to Russell, prior to the Chomskyian revolution in linguistics during the second half of the twentieth century. In light of the conceptual and analytic resources made available by this revolution, however, there exists “no insurmountable obstacle to assimilating Russell ’s notion of logical form to something akin to the modern notion of lf” (p. 172), where lf is conceived as one of four levels of syntactic representation within Chomsky’s Government and Binding Theory... (shrink)

The logics of the modal operators and of the quantifiers show striking analogies. The analogies are so extensive that, when a special class of entities (possible worlds) is postulated, natural and non-arbitrary translation procedures can be defined from the language with the modal operators into a purely quantificational one, under which the necessity and possibility operators translate into universal and existential quantifiers. In view of this I would be willing to classify the modal operators as ‘disguised’ quantifiers, and I (...) think that wholehearted acceptance of modal language should be considered to carry ontological commitment to something like possible worldsConsidered as two languages for describing the same subject matter, modal and purely quantificational languages show interesting differences. The operator variables of the purely quantificational languages give them more power than the modal languages, but at least some of the functions performed by the apparatus of operator variables are also performed, in a more primitive and less versatile way, by actuality operators in modal languages.A final note. Quine has written much on the inter-relations of quantifiers, identity, and the concept of existence. These, he holds, form a tightly knit conceptual system which has been evolved to a high point of perfection, but which might conceivably change yet further.29 He has also dropped hints about the possibility of a simpler, primitive or defective version of the system, in which the quantifiers are not backed up in their accustomed way by the concept of identity. He has dubbed the resulting concept a ‘pre-individuative’ concept of existence, or a concept of ‘entity without identity.’ What would a pre-individuative concept of existence be like? Quine has sometimes suggested that one might be embodied in the use of mass nouns, but the identity concept is used in connection with stuff as well as with things: “is that the same coffee that was in the cup last night?” I would submit that modality provides a better case. In view of the comparative weakness of modal languages, compared to the explicitly quantificational ones Quine takes as canonical, there is surely a sense in which the concept of existence embodied in that disguised existential quantifier, the possibility operator, is a defective one. And as we have seen, one of the differences between modal operators and explicit quantifiers is that modal operators cannot be joined with the identity predicate in the way quantifiers with operator variables can. Surely, then, there is a sense in which ordinary speech, as opposed to the metaphysical theorizing of a Leibniz or a David Lewis, conceives of possible worlds as entities without identity. (shrink)

Bringing elementary logic out of the academic darkness into the light of day, Paul Tomassi makes logic fully accessible for anyone attempting to come to grips with the complexities of this challenging subject. Including student-friendly exercises, illustrations, summaries and a glossary of terms, _Logic_ introduces and explains: * The Theory of Validity * The Language of Propositional Logic * Proof-Theory for Propositional Logic * Formal Semantics for Propositional Logic including the Truth-Tree Method * The Language of Quantificational Logic (...) including the Theory of Descriptions. _Logic _is an ideal textbook for any logic student: perfect for revision, staying on top of coursework or for anyone wanting to learn about the subject. Related downloadable software for Macs and PCs is available for this title at www.logic.routledge.com. (shrink)

An overcomplete logic is a logic that ‘ceases to make the difference’: According to such a logic, all inferences hold independently of the nature of the statements involved. A negation-inconsistent logic is a logic having at least one model that satisfies both some statement and its negation. A negation-incomplete logic has at least one model according to which neither some statement nor its negation are satisfied. Paraconsistent logics are negation-inconsistent yet non-overcomplete; paracomplete logics are negation-incomplete yet non-overcomplete. A paranormal logic (...) is simply a logic that is both paraconsistent and paracomplete. -/- Despite being perfectly consistent and complete with respect to classical negation, nearly every normal modal logic, in its ordinary language and interpretation, admits to some latent paranormality: It is paracomplete with respect to a negation defined as an impossibility operator, and paraconsistent with respect to a negation defined as non-necessity. In fact, as it will be shown here, even in languages without a primitive classical negation, normal modal logics can often be alternatively characterized directly by way of their paranormal negations and related operators. So, instead of talking about ‘necessity’, ‘possibility’, and so on, modal logics could be seen just as devices tailored for the study of (modal) negation. This paper shows how and to what extent this alternative characterization of modal logics can be realized. (shrink)

Historically, George Boole’s philosophy of logic has been regarded as the very opposite of Gottlob Frege’s, insofar as Frege is characterized as a strong logical anti-psychologist. Although there are significant differences between Frege’s and Boole’s views on logic, there are also significant similarities, which provide support for our representation of Frege’s philosophy of logic as weakly psychologistic. Both Boole and Frege aspire to capture the essence of a pure and ideally perfect language that may faithfully express correct reasoning, (...) but Boole’s trust in the power of natural language is stronger than Frege’s. Although we cannot adequately defend this claim, we submit that a thorough examination of the differences between Frege’s and Boole’s views on symbolic and natural languages may lead to a more interesting comparison of their stances on logic and thinking than the often repeated contrast in their attitudes toward psychologism. (shrink)

This paper tries to determine the philosophical nature of language, its functions, structure and content. It also explains the concept of natural language, ordinary and ideal language i.e. how there is a need of artificial perfect logical language without errors and unclearness in that language. This paper further shows the logical form of language with its syntactical, semantical, innate and acquired criteria for the evaluation of the languages. It deals with the analysis of (...) language to clear what is unclear, to know what is unknown, to make definite what is vague. In this paper I used the method; logical method for interpretation and argumentation, analytical method for simplification, and critical method to investigate the real domain of language. This paper does not deal with ordinary functions of the language but it deals with the conceptual and modular functions of the language. The fundamental aim of this written up is to determine the analytical approach of Wittgenstein to sketch the ‘language as a tool to discuss the state of affairs or facts of the worlds that is also what philosophy does. This paper describes the contributions of rationalism and empiricism in the field of knowing the truths of language. (shrink)

Lambek elegantly characterized part of natural language. As is well-known, his substructural logic L, and its non-associative version NL, handle basic function/argument composition well, but not scope taking and syntactic displacement—at least, not in their full generality. In previous work, I propose $$\text {NL}_\lambda $$, which is NL supplemented with a single structural inference rule (“abstraction”). Abstraction closely resembles the traditional linguistic rule of quantifier raising, and characterizes both semantic scope taking and syntactic displacement. Due to the unconventional form (...) of the abstraction inference, there has been some doubt that $$\text {NL}_\lambda $$ should count at a legitimate substructural logic. This paper argues that $$\text {NL}_\lambda $$ is perfectly well-behaved. In particular, it enjoys cut elimination and an interpolation result. In addition, perhaps surprisingly, it is decidable. Finally, I prove that it is sound and complete with respect to the usual class of relational frames. (shrink)

What relationship is there between violence and language?* What happens when language is the main target of attack? We should perhaps begin by defining the inner logic of violence, and then tackle the question of the monstrous hybrid it has created with language. In one of the texts that make up the collection entitled Difficile Liberte’, Lévinas remarks that violent action is an ‘action where one acts as if one were the only actor: as if the rest (...) of the universe existed only to receive the action; thus every action is violent that we suffer without wholeheartedly collaborating in it’. So violence has two characteristics. On the one hand, it is fed by a fundamental illusion, that is, a fiction of the will that imagines it is so super-powerful and autonomous that it thinks that by itself it can decide the fate of ‘the rest of the universe’. On the other hand, it is never an authentic action, because it prevents others from owning it and becoming co-actors themselves. Thinking perhaps of Spinoza, Lévinas suggests that violence comes into being from the moment when individuals decide to stop being part of the ordinary world of actions and think, ‘like an empire within an empire’, they are the unique cause of their acts and gestures. This subjective decision is clearly a control decision that contradicts the requirement of common sense, which is to be understood here as a sense of the community. It leads inexorably to consigning others to the world of effects in order more easily to turn them into eternal victims. In Dostoevsky's The Idiot, Prince Mishkin perfectly embodies the figure of the other who continually ‘receives’ the action. But when interplay between the will and its own mirrors becomes excessive, individuals always end up confusing the reality of the world with the exaggerated trust they put in their own prejudices. Since the analyses of the psychiatrist Minkowski at least, we know quite well that the more the certainty naturally accompanying the prejudice increases and expands until it borders on madness, the more violence is likely to grow. (shrink)

Yuval Steinitz has argued that, since it is logically possible that there are logically necessary beings, it follows that there is at least one logically necessary being. Steinitz switches the Leibnitzean ontological argument's concern from perfect beings to logically necessary beings. My paper has two primary aims. First, I argue that Steinitz's quick treatment is insufficient to establish the validity of his argument. Secondly, I argue that the correct approach to logical necessity must account for (...) those possible situations in which the meanings of some of the terms in our language might have been different; on such an approach, the premise of Steinitz's argument is false. My remarks here are intended to add to the prima facie plausibility of Hume's claim that logic has no existential implications. (shrink)

We discuss games of both perfect and imperfect information at two levels of structural detail: players’ local actions, and their global powers for determining outcomes of the game. We propose matching logical languages for both. In particular, at the ‘action level’, imperfect information games naturally model a combined ‘dynamic-epistemic language’ – and we find correspondences between special axioms and particular modes of playing games with their information dynamics. At the ‘outcome level’, we present suitable notions of game equivalence, (...) plus some simple representation results. (shrink)

The notion of language in e-Learning is still not very clear from a technical as well as semantic point of view. In the era of Information Technology, it is more and more important to unify the principles of language used and its semantic meaning to be more simple and precise when taking into consideration online educational courses. During the last years, e-Learning courses have begun to be popular around the world as during an internet era, we tend to (...) find consolidated information sources on internet rather than in traditional courses which require our physical presence. The crucial issue which makes an e- Learning course function is the language used to transmit all the information to the students in a clear and effective manner. For such language to be considered effective, it is necessary to adjust it to the general standards adopted in an international environment. The notion of a language used in e-Learning also faces some problems as it should be so concise as to be accessible for everybody regardless of gender, nationality, and intellectual level. It is hard to standardise its principles, thus over the years many scientists have tried to unify the top requirements a perfect e-Learning course should have. Nowadays, most of the population should stop considering e-Learning as an alternative form of education and focus on developing new models and structures for education and learning that fully exploit the opportunities of today’s digital revolution. With a laptop, a mobile device and Wi-Fi, you can manage your own e-Learning course, and take courses yourself, at any time and place, in any language. A typical model of an e-Learning course is based on guided self-study with a linear progression through modules consisting of recorded lectures, course literature, written assignments and multiple-choice self-tests. Technology has got an even better solution which consists of standardising the learning process and adopting it to a commonly known level of difficulty which might be expected when considering its use by an average person. (shrink)

The primary aim is the reconstruction of the main argument of the second chapter of Anselm’s Proslogion. To be proved is the statement that God, or something than which nothing greater can be thought, exists in reality. I proceed by a piecemeal analysis of every sentence of the Latin original and its subsequent translation into a formal second-order language with choice operator. Reconstructing Anselm’s reasoning demands interpretative input and additions. For example, the formula ‘quod maius est’ has to be (...) suitably interpreted and expanded. Furthermore, I try to explicate Anselm’s maius predicate in terms of a perfection predicate and to develop a general proof for Anselm’s theorem, i.e. the statement that something/that than which something greater cannot be thought has all greater-making attributes. (shrink)

We suggest that developing automata theoretic foundations is relevant for knowledge theory, so that we study not only what is known by agents, but also the mechanisms by which such knowledge is arrived at. We define a class of epistemic automata, in which agents’ local states are annotated with abstract knowledge assertions about others. These are finite state agents who communicate synchronously with each other and information exchange is ‘perfect’. We show that the class of recognizable languages has good (...) closure properties, leading to a Kleene-type theorem using what we call regular knowledge expressions. These automata model distributed causal knowledge in the following way: each agent in the system has a partial knowledge of the temporal evolution of the system, and every time agents synchronize, they update each other’s knowledge, resulting in a more up-to-date view of the system state. Hence we show that these automata can be used to solve the satisfiability problem for a natural epistemic temporal logic for local properties. Finally, we characterize the class of languages recognized by epistemic automata as the regular consistent languages studied in concurrency theory. (shrink)

We are used to the idea that computers operate on numbers, yet another kind of data is equally important: the syntax of formal languages, with variables, binding, and alpha-equivalence. The original application of nominal techniques, and the one with greatest prominence in this paper, is to reasoning on formal syntax with variables and binding. Variables can be modelled in many ways: for instance as numbers (since we usually take countably many of them); as links (since they may `point' to a (...) binding site in the term, where they are bound); or as functions (since they often, though not always, represent `an unknown'). None of these models is perfect. In every case for the models above, problems arise when trying to use them as a basis for a fully formal mechanical treatment of formal language. The problems are practical—but their underlying cause may be mathematical. The issue is not whether formal syntax exists, since clearly it does, so much as what kind of mathematical structure it is. To illustrate this point by a parody, logical derivations can be modelled using a Gödel encoding (i.e., injected into the natural numbers). It would be false to conclude from this that proof-theory is a branch of number theory and can be understood in terms of, say, Peano's axioms. Similarly, as it turns out, it is false to conclude from the fact that variables can be encoded e.g., as numbers, that the theory of syntax-with-binding can be understood in terms of the theory of syntax-without-binding, plus the theory of numbers (or, taking this to a logical extreme, purely in terms of the theory of numbers). It cannot; something else is going on. What that something else is, has not yet been fully understood. In nominal techniques, variables are an instance of names, and names are data. We model names using urelemente with properties that, pleasingly enough, turn out to have been investigated by Fraenkel and Mostowski in the first half of the 20th century for a completely different purpose than modelling formal language. What makes this model really interesting is that it gives names distinctive properties which can be related to useful logic and programming principles for formal syntax. Since the initial publications, advances in the mathematics and presentation have been introduced piecemeal in the literature. This paper provides in a single accessible document an updated development of the foundations of nominal techniques. This gives the reader easy access to updated results and new proofs which they would otherwise have to search across two or more papers to find, and full proofs that in other publications may have been elided. We also include some new material not appearing elsewhere. (shrink)

The main aim of the present paper is to understand the debate between Descartes and Leibniz about eternal truths as providing the structure of several possible dialogues involving counter-logic . According to this analysis the positions of Descartes and Leibniz are understood as constituting dual and dynamic perspectives in relation to the availability of some specific choices that should provide norms of rationality. Each of these dialogues has both a universal, monological aspect (given by the winning strategy) and a contextual, (...) dialogical one (given by the play level). I conclude with the suggestion that a notion of rationality that contains both the universal and the contextual aspects does not yield a specific logic, but rather a frame of normative rationality. The conception of such a frame seems to be closely linked to the notion of a universal perfectible language discussed by Olga Pombo. The central idea is that the Leibniz’s notion of rationality is a fondateur de discursivité if we use Marcelo Dascal´s quote of Foucault. (shrink)

The split in our thinking between "masculine" and "feminine" is probably as old as language itself. Human beings seem to have a natural tendency to divide things into pairs: good/bad, light/dark, subject/object and so on. It is not surprising, then, that the male/female or masculine/feminine dichotomy is used to classify things other than men and women. Many languages actually classify all nouns as "masculine" or "feminine" (although not very consistently: for example, the Spanish masculine noun pollo means "hen", while (...) the feminine polla is slang for "penis"). This is perfectly natural; it is part of the way categorisation works in language. This does not, however, mean that it is right. It is probably unimportant whether a table or a chair is thought of as masculine or feminine. It may not even be very important these days whether we think of the sun as male and the moon as female (like the ancient Greeks) or vice versa (like most of the German tribes). However, when we start associating abstract concepts like Reason or Nature with men and women, we run into serious difficulties. (shrink)

The split in our thinking between "masculine" and "feminine" is probably as old as language itself. Human beings seem to have a natural tendency to divide things into pairs: good/bad, light/dark, subject/object and so on. It is not surprising, then, that the male/female or masculine/feminine dichotomy is used to classify things other than men and women. Many languages actually classify all nouns as "masculine" or "feminine" (although not very consistently: for example, the Spanish masculine noun pollo means "hen", while (...) the feminine polla is slang for "penis"). This is perfectly natural; it is part of the way categorisation works in language. This does not, however, mean that it is right. It is probably unimportant whether a table or a chair is thought of as masculine or feminine. It may not even be very important these days whether we think of the sun as male and the moon as female (like the ancient Greeks) or vice versa (like most of the German tribes). However, when we start associating abstract concepts like Reason or Nature with men and women, we run into serious difficulties. (shrink)

Frege's invention of the predicate calculus has been the most influential event in the history of modern logic. The calculus’ place in logic is so central that many philosophers think, in fact, of it when they think of logic. This book challenges the position in contemporary logic and philosophy of language of the predicate calculus claiming that it is based on mistaken assumptions. Ben-Yami shows that the predicate calculus is different from natural language in its fundamental semantic charac.

Originally published in 1973, this book shows that methods developed for the semantics of systems of formal logic can be successfully applied to problems about the semantics of natural languages; and, moreover, that such methods can take account of features of natural language which have often been thought incapable of formal treatment, such as vagueness, context dependence and metaphorical meaning. Parts 1 and 2 set out a class of formal languages and their semantics. Parts 3 and 4 show that (...) these formal languages are rich enought to be used in the precise description of natural languages. Appendices describe some of the concepts discussed in the text. (shrink)

Some apparently valid arguments crucially rely on context change. To take a kind of example first discussed by Frege, ‘Tomorrow, it’ll be sunny’ taken on a day seems to entail ‘Today, it’s sunny’ taken on the next day, but the first sentence taken on a day sadly does not seem to entail the second sentence taken on the second next day. Mid-argument context change has not been accounted for by the tradition that has extensively studied the distinctive logical properties of (...) context-dependent languages, for that tradition has focussed on arguments whose premises and conclusions are taken at the same context. I first argue for the desiderability of having a logic that accounts for mid-argument context change and I explain how one can informally understand such context change in a standard framework in which the relation of logical consequence holds among sentences. I then propose a family of simple temporal “intercontextual” logics that adequately model the validity of certain arguments in which the context changes. In particular, such logics validate the apparently valid argument in the Fregean example. The logics lack many traditional structural properties (reflexivity, contraction, commutativity etc.) as a consequence of the logical significance acquired by the sequence structure of premises and conclusions. The logics are however strong enough to capture in the form of logical truths all the valid arguments of both classical logic and Kaplan-style “intracontextual” logic. Finally, I extend the framework by introducing new operations into the object language, such as intercontextual conjunction, disjunction and implication, which, contrary to intracontextual conjunction, disjunction and implication, perfectly match the metalinguistic, intercontextual notions of premise combination, conclusion combination and logical consequence by representing their respective two operands as taken at different contexts. (shrink)

Originally published in 1973, this book shows that methods developed for the semantics of systems of formal logic can be successfully applied to problems about the semantics of natural languages; and, moreover, that such methods can take account of features of natural language which have often been thought incapable of formal treatment, such as vagueness, context dependence and metaphorical meaning. Parts 1 and 2 set out a class of formal languages and their semantics. Parts 3 and 4 show that (...) these formal languages are rich enought to be used in the precise description of natural languages. Appendices describe some of the concepts discussed in the text. (shrink)

Lambek elegantly characterized part of natural language. As is well-known, his substructural logic L, and its non-associative version NL, handle basic function/argument composition well, but not scope taking and syntactic displacement—at least, not in their full generality. In previous work, I propose \, which is NL supplemented with a single structural inference rule.ion closely resembles the traditional linguistic rule of quantifier raising, and characterizes both semantic scope taking and syntactic displacement. Due to the unconventional form of the abstraction inference, (...) there has been some doubt that \ should count at a legitimate substructural logic. This paper argues that \ is perfectly well-behaved. In particular, it enjoys cut elimination and an interpolation result. In addition, perhaps surprisingly, it is decidable. Finally, I prove that it is sound and complete with respect to the usual class of relational frames. (shrink)