Possible worlds have found many applications in contemporary philosophy: from theories of possibility and necessity, to accounts of conditionals, to theories of mental and linguistic content, to understanding supervenience relationships, to theories of properties and propositions, among many other applications. Almost as soon as possible worlds started to be used in formal theories in logic, philosophy of language, philosophy of mind, metaphysics, and elsewhere, theorists started to wonder whether impossible worlds should be postulated as well. In many applications, possible worlds (...) face limitations that can be dealt with through postulating impossible worlds as well. This chapter examines some of the uses of impossible worlds, and philosophical challenges theories of impossible worlds face. (shrink)

The verb 'knows' is often taken to be context-sensitive in an interesting way. What 'knows' means seems to be sensitive to the epistemic features of the context, e.g. the epistemic standard in play, the set of relevant alternatives, etc. There are standard model-theoretic semantic frameworks which deal with both intensional operators and context-sensitive expressions. In this chapter, we provide a brief overview of the various moving parts of these frameworks, the roles of context and index, the need for double indexing, (...) and the relationship between semantic value and content. With the best version of the standard framework explicated we then return at the end to the treatment of ‘know’ as a context-sensitive intensional operator (contrasting it with an invariantist treatment). (shrink)

Like modal logic, temporal logic, and description logic, separation logic has become a popular class of logical formalisms in computer science, conceived as assertion languages for Hoare-style proof systems with the goal to perform automatic program analysis. In a broad sense, separation logic is often understood as a programming language, an assertion language and a family of rules involving Hoare triples. In this survey, we present similarities between separation logic as an assertion language and modal and temporal logics. Moreover, we (...) propose a selection of landmark results about decidability, complexity and expressive power. (shrink)

Le regain de faveur de la thématique des « mondes possibles » dans la philosophie contemporaine est pour l’essentiel un effet collatéral du développement de la logique modale au long du XXe siècle. C’est en effet initialement pour résoudre le problème soulevé par l’évaluation des systèmes modaux, élaborés entre les années trente et cinquante par des auteurs comme Clarence Lewis, Richard Feys ou Georg von Wright, qu’une sémantique...

The axiomatic presentation of modal systems and the standard formulations of natural deduction and sequent calculus for modal logic are reviewed, together with the difficulties that emerge with these approaches. Generalizations of standard proof systems are then presented. These include, among others, display calculi, hypersequents, and labelled systems, with the latter surveyed from a closer perspective.

Logic: the Basics is an accessible introduction to the core philosophy topic of standard logic. Focussing on traditional Classical Logic the book deals with topics such as mathematical preliminaries, propositional logic, monadic quantified logic, polyadic quantified logic, and English and standard ‘symbolic transitions’. With exercises and sample answers throughout this thoroughly revised new edition not only comprehensively covers the core topics at introductory level but also gives the reader an idea of how they can take their knowledge further and the (...) philosophical questions around logic. -/- Logic: the Basics is essential reading for first-year undergraduate philosophy students on standard introductory logic courses. (shrink)

This essay considers Kant’s theory of modality in light of a debate in contemporary modal metaphysics and modal logic concerning the Barcan formulas. The comparison provides a new and fruitful perspective on Kant’s complex and sometimes confusing claims about possibility and necessity. Two central Kantian principles provide the starting point for the comparison: that the possible must be grounded in the actual and that existence is not a real predicate. Both are shown to be intimately connected to the Barcan formulas, (...) and Kant’s views on what he distinguishes as three different kinds of modality are then considered in light of this connection. (shrink)

This book brings together papers from a conference that took place in the city of L'Aquila, 4–6 April 2019, to commemorate the 10th anniversary of the earthquake that struck on 6 April 2009. Philosophers and scientists from diverse fields of research debated the problem that, on 6 April 1922, divided Einstein and Bergson: the nature of time. For Einstein, scientific time is the only time that matters and the only time we can rely on. Bergson, however, believes that scientific time (...) is derived by abstraction, even in the sense of extraction, from a more fundamental time. The plurality of times envisaged by the theory of Relativity does not, for him, contradict the philosophical intuition of the existence of a single time. But how do things stand today? What can we say about the relationship between the quantitative and qualitative dimensions of time in the light of contemporary science? What do quantum mechanics, biology and neuroscience teach us about the nature of time? The essays collected here take up the question that pitted Einstein against Bergson, science against philosophy, in an attempt to reverse the outcome of their monologue in two voices, with a multilogue in several voices. (shrink)

Tarski's analysis of the concept of truth gives rise to a hierarchy of languages. Does this fragment the concept all the way to philosophical unacceptability? I argue it doesn't, drawing on a modification of Kaplan's theory of indexicals.

This paper contains an argument to the effect that possible worlds semantics renders semantic knowledge impossible, no matter what ontological interpretation is given to possible worlds. The essential contention made is that possible worlds semantic knowledge is unsafe and this is shown by a parallel with the preface paradox.

For many recent readers of Hegel, Wilfrid Sellars’s 1956 London lectures on the “Myth of the Given” have signaled an important rapprochement between Hegelian and analytic traditions in philosophy. Here I want to explore the ideas of another philosopher, also active in London in the 1950s, who consciously pursued such a goal: John N. Findlay. The ideas that Findlay brought to Hegel—sometimes converging with, sometimes diverging from those of Sellars—had been informed by his earlier study of the Austrian philosopher Alexius (...) Meinong, and transformations of Meinong’s ideas by his student, the logician Ernst Mally. These ideas that Findlay found Hegel-friendly are ones that have had a particular bearing on more recent analytic modal metaphysics, especially via the work of Findlay’s own former student, Arthur Prior. Given this, we might not be surprised at the similarities between the type of actualist interpretation of modal logic that Prior offered in opposition to David Lewis’s variant on Leibnizian possibilism, and Hegel’s approach to the category of “Actuality” [Wirklichkeit] at the end of the Objective Logic of The Science of Logic. But the similarities, I suggest, do not end there, as elements of Hegel treatment of predication in the Subjective Logic parallel similar elements found in the work of Mally and, more recently, “modal actualists” such as Prior and Stalnaker. In this paper I explore some puzzling features of Hegel’s treatment of predication in the Subjective Logic from the point of view of the need for a logic for thought about the modally complex actual world, as Hegel conceived it. (shrink)

This chapter provides an introduction to possible worlds semantics in both logic and the philosophy of language, including a discussion of some of the advantages and challenges for possible worlds semantics.

This paper explores early Australasian philosophy in some detail. Two approaches have dominated Western philosophy in Australia: idealism and materialism. Idealism was prevalent between the 1880s and the 1930s, but dissipated thereafter. Idealism in Australia often reflected Kantian themes, but it also reflected the revival of interest in Hegel through the work of ‘absolute idealists’ such as T. H. Green, F. H. Bradley, and Henry Jones. A number of the early New Zealand philosophers were also educated in the idealist tradition (...) and were influential in their communities, but produced relatively little. In Australia, materialism gained prominence through the work of John Anderson, who arrived in Australia in 1927, and continues to be influential. John Anderson had been a student of Henry Jones, who might therefore be said to have influenced both main strands of Australian philosophical thought. (shrink)

Relativized Metaphysical Modality (RMM: Murray and Wilson, 'Relativized metaphysical modality', Oxford Studies in Metaphysics, 2012; Murray, Perspectives on Modal Metaphysics, 2017) exploits 'two-dimensionalist' resources to metaphysical, rather than epistemological, ends: the second dimension offers perspective-dependence without contingency, diverting attacks on 'Classical' analyses of modals (in effect, analyses validating S5 and the Barcan Formulae). Here, we extend the RMM program in two directions. First, we harvest resources for RMM from Lewis's 1980 'Context--Index' (CI) framework: (a) the ban in CI on binding (...) into context-arguments (akin to Kaplan's 'monstrosity' ban) projects a bright line between perspective-dependence and contingency; and (b) CI-postulated connections among meaning, content, truth, argument-structure, context, and modality collectively generate a 'Generalized Humphrey Problem' for any non-Classical analysis (examples covered include appeals to accessibility, contingent domains, and counterpart relations). Second, we sharpen the tools of RMM-based metaphysical analysis, and extend their domain of coverage across familiar anomalies for Classical modals: we revisit earlier RMM-based bulwarks for S5 (against 'Chisholm's Paradox' for moderate flexibility of essence, and nomological necessitarianism); and we now similarly shore up the Barcan Formulae (against the apparent contingency of existence and nonexistence). (shrink)

Tässä artikkelissa käsittelen Descartesin ikuisten totuuksien välttämättömyyteen liittyvää ongelmaa. Teoksessa Mietiskelyjä ensimmäisestä filosofiasta (1641–1642) Descartes nostaa esiin käsitteen ikuisista totuuksista, käyttäen esimerkkinään kolmiota. Kolmion muuttumattomaan ja ikuiseen luontoon kuuluu esimerkiksi, että sen kolme kulmaa ovat yhteenlaskettuna 180°. Se on totta kolmiosta, vaikka yhtään yksittäistä kolmiota ei olisi koskaan ollutkaan olemassa. Eräät ajattelemieni asioiden piirteet ovat siis Descartesin mukaan ajattelustani riippumattomia. Ikuisia totuuksia ovat ainakin matemaattiset ja geometriset tosiseikat sekä ristiriidan laki. Samoin Descartesin kuuluisa lause “ajattelen, siis olen” lukeutuu ikuisten totuuksien (...) joukkoon. Descartesin ikuiset totuudet olisivatkin siis loogisesti välttämättömiä. Niillä on kyseinen olemus riippumatta ulkoisten kohteiden olemassaolosta tai siitä, ajattelenko niitä lainkaan. Kuitenkin kirjeenvaihdossaan Descartes pitää itsepintaisesti kiinni käsityksestään, että ikuiset totuudet ovat Jumalan vapaasti luomia ja Jumala olisi voinut luoda ne erilailla. Näin ollen luodut ikuiset totuudet eivät tarkkaan ottaen olisikaan välttämättömiä vaan kontingentteja. Ne voisivat olla myös toisella tavalla. Artikkelin alkuun esittelen Descartesin modaalista metafysiikkaa sekä luotujen ikuisten totuuksien kontingenttiudesta seuraavia tulkinnallisia vaikeuksia. Tämän jälkeen pureudun kolmeen erilaiseen ratkaisuyritykseen kommentaarikirjallisuudessa (Frankfurt 1977; Curley 1984 & Bennett 1994) ja osoitan, miksi ne eivät riitä vastaamaan ongelmaan. Lopussa vedän johtopäätöksiä ja luonnostelen mahdollisen ratkaisun. (shrink)

While art and science still functioned side-by-side during the Renaissance, their methods and perspectives diverged during the nineteenth century, creating a still enduring separation between the "two cultures". Recently, artists and scientists again collaborate more frequently, as promoted most radically by the ArtScience movement. This approach aims at a true synthesis between the intuitive, imaginative methods of art and the rational, rule-governed methods of science. To prepare the grounds for a theoretical synthesis, this paper surveys the fundamental commonalities and differences (...) between science and art. Science and art are united in their creative investigation, where coherence, pattern or meaning play a vital role in the development of concepts, while relying on concrete representations to experiment with the resulting insights. On the other hand, according to the standard conception, science seeks an understanding that is universal, objective and unambiguous, while art focuses on unique, subjective and open-ended experiences. Both offer prospect and coherence, mystery and complexity, albeit with science preferring the former and art, the latter. The paper concludes with some examples of artscience works that combine all these aspects. (shrink)

The relevance of any logical analysis lies in its ability to solve paradoxes and trace conceptual troubles back; with this respect, the task of epistemic logic is to handle paradoxes in connection with the concept of knowledge. Epistemic logic is currently introduced as the logical analysis of crucial concepts within epistemology, namely: knowledge, belief, truth, and justification. An alternative approach will be advanced here in order to enlighten such a discourse, as centred upon the word assertion and displayed in terms (...) of utterance. Insofar as epistemic modalities express some attitudes, the intentionality of discourse will be emphasized within an illocutionary modal logic. Two large views will range over the whole study: declarative and epistemic sentences have one and the same logic (assertion logic); the plurality of languages games doesn’t entail any logical pluralism. -/- La valeur d'une analyse logique réside dans sa capacité à résoudre des paradoxes et à comprendre l'origine de nos problèmes conceptuels ; à ce titre, le rôle d'une logique épistémique est de traiter des paradoxes liés au concept de connaissance. On présente généralement la logique épistémique comme une analyse logique de concepts centraux en épistémologie : connaissance, croyance, vérité, justification. Une autre approche sera proposée ici en vue de clarifier ce genre de discours, centrée sur la notion d'assertion et décrite en termes d'énonciation. Parce que les modalités épistémiques expriment des attitudes, c'est l'intentionnalité du discours qui sera mise en valeur dans le cadre d'une logique modale illocutoire. Deux thèses transversales parcourront l'ensemble du travail : les énoncés déclaratifs et épistémiques partagent la même logique (logique assertorique) ; la pluralité des jeux de langages n'implique pas un pluralisme logique. (shrink)

An aim of science is to find truths about reality. These truths are collected together to form systematic knowledge structures called theories. Theories are intended to create a truthful picture of the reality behind the study. Together with all the other fields of science we get a scientific picture or a world view. This scientific world view is open in the sense that not all truths are known by scientists and not all present day theories are true. So, there is (...) no reason to assume that any field of science has been or will be completed; science is essentially progressive, or an open ended approach. Science is not the only method of picturing, but the view that science is the best human method for knowledge acquisition is well justified. Knowledge is not all we humans are looking for; we need to make our lives meaningful. The meaningfulness may be achieved through science, art, or practical activity. It is interesting to compare literature and science. Both are expressed linguistically, but the aims of literature and science seem to be very different. We are looking for the theoretical interconnection between science and literature, but the proper dialogue can be found not through science, literature or philosophy, but through pedagogy. (shrink)

This paper charts some early history of the possible worlds semantics for modal logic, starting with the pioneering work of Prior and Meredith. The contributions of Geach, Hintikka, Kanger, Kripke, Montague, and Smiley are also discussed.

Graham Solomon, to whom this collection is dedicated, went into hospital for antibiotic treatment of pneumonia in Oc- ber, 2001. Three days later, on Nov. 1, he died of a massive stroke, at the age of 44. Solomon was well liked by those who got the chance to know him—it was a revelation to?nd out, when helping to sort out his a?airs after his death, how many “friends” he had whom he had actually never met, as his email included correspondence (...) with philosophers around the world running sometimes to hundreds of messages. He was well respected in the philosophical community more broadly. He was for several years a member of the editorial board for the Western Ontario Series in Philosophy of Science. While he was employed at Wilfrid Laurier University in Waterloo, Ontario, several of us at the University of Wat- loo always regarded our own department as a sort of second academic home for him. We therefore decided that it would be appropriate to hold a memorial conference in his honour. Thanks to the generous?nancial support of the Humphrey Conference Fund, we were able to do so in May 2003. Many of the papers in this volume were presented at that conf- ence. (shrink)

Charles Peirce incorporates modality into his Existential Graphs by introducing the broken cut for possible falsity. Although it can be adapted to various modern modal logics, Zeman demonstrates that making no other changes results in a version that he calls Gamma-MR, an implementation of Jan Łukasiewicz's four-valued Ł-modal system. It disallows the assertion of necessity, reflecting a denial of determinism, and has theorems involving possibility that seem counterintuitive at first glance. However, the latter is a misconception that arises from overlooking (...) the distinction between the intermediate truth values that are assigned to possibly true propositions as either X-contingent or Y-contingent. Any two propositions having the same ITV are possible together, while any two propositions having different ITVs, including those that are each other's negation, are possible individually yet not possible together. Porte shows that Ł-modal can be translated into classical logic by defining a constant for each ITV such that its implication of another proposition asserts the latter's possibility, while its conjunction with another proposition asserts the latter's necessity. These are expressed in the Alpha part of EG without broken cuts, simplifying derivations and shedding further light on Łukasiewicz's system, as long as graphs including either of the constants are properly interpreted. Ł-modal and Gamma-MR thus capture the two-sided nature of possibility as the limit between truth and falsity in Peirce's triadic conception. (shrink)

The possible worlds semantics is articulated as one of the most relevant logical and philosophical theories of our time. The famous possible worlds form and have been part of the philosophical jargon of authors of the so-called analytical tendency in the last decades. It has also been a theory suitable for the treatment and approach of many topics and problems that have afflicted philosophers of all time. In this paper, we will focus on the origin, preparation and consolidation of PWS (...) and its central notions by hand of some of its main representatives. (shrink)

ABSTRACTHegel's Phenomenology of Spirit provides a fascinating picture of individual minds caught up in “recognitive” relations so as to constitute a realm—“spirit”—which, while necessarily embedded in nature, is not reducible to it. In this essay I suggest a contemporary path for developing Hegel's suggestive ideas in a way that broadly conforms to the demands of his own system, such that one moves from logic to a philosophy of mind. Hence I draw on Hegel's “subjective logic”, understood in the light of (...) modern modal logic, in an attempt to model the way minds might be thought as connected by way of shared intentional contents. Here, we should not be surprised at some of the parallels that emerge between the approaches of Hegel and the modal logician Arthur Prior, as Prior had testified to the influence of his teacher, John N. Findlay, who himself had strong Hegelian leanings. In the final section, Robert Stalnaker's version of possible-world semantics is suggested as a framework within which Hegel's recognitive account of the mind might be understood. (shrink)

Here, I suggest a hitherto relatively unexplored way beyond the opposed Aristotelian realist and Kantian idealist approaches that divide recent interpretations of the categories or “thought determinations” of Hegel’s Logic, by locating his idealism within the terrain of recent debates in modal metaphysics. In particular, I return to the outlook of the first philosopher to attempt to bring Hegel into the analytic conversation, John Niemeyer Findlay, and consider Hegel’s idealism as instantiating the metaphysical position that, following the work of Findlay’s (...) former student, Arthur Prior, has come to be called “modal actualism”. (shrink)

This chapter presents a new semantics for inductive empirical knowledge. The epistemic agent is represented concretely as a learner who processes new inputs through time and who forms new beliefs from those inputs by means of a concrete, computable learning program. The agent’s belief state is represented hyper-intensionally as a set of time-indexed sentences. Knowledge is interpreted as avoidance of error in the limit and as having converged to true belief from the present time onward. Familiar topics are re-examined within (...) the semantics, such as inductive skepticism, the logic of discovery, Duhem’s problem, the articulation of theories by auxiliary hypotheses, the role of serendipity in scientific knowledge, Fitch’s paradox, deductive closure of knowability, whether one can know inductively that one knows inductively, whether one can know inductively that one does not know inductively, and whether expert instruction can spread common inductive knowledge—as opposed to mere, true belief—through a community of gullible pupils. (shrink)

This article includes a basic overview of possible world semantics and a relatively comprehensive overview of three central philosophical conceptions of possible worlds: Concretism (represented chiefly by Lewis), Abstractionism (represented chiefly by Plantinga), and Combinatorialism (represented chiefly by Armstrong).

If □ is conceived as an operator, i.e., an expression that gives applied to a formula another formula, the expressive power of the language is severely restricted when compared to a language where □ is conceived as a predicate, i.e., an expression that yields a formula if it is applied to a term. This consideration favours the predicate approach. The predicate view, however, is threatened mainly by two problems: Some obvious predicate systems are inconsistent, and possible-worlds semantics for predicates of (...) sentences has not been developed very far. By introducing possible-worlds semantics for the language of arithmetic plus the unary predicate □, we tackle both problems. Given a frame (W, R) consisting of a set W of worlds and a binary relation R on W, we investigate whether we can interpret □ at every world in such a way that □ $\ulcorner A \ulcorner$ holds at a world ᵆ ∊ W if and only if A holds at every world $\upsilon$ ∊ W such that ᵆR $\upsilon$ . The arithmetical vocabulary is interpreted by the standard model at every world. Several 'paradoxes' (like Montague's Theorem, Gödel's Second Incompleteness Theorem, McGee's Theorem on the ω-inconsistency of certain truth theories, etc.) show that many frames, e.g., reflexive frames, do not allow for such an interpretation. We present sufficient and necessary conditions for the existence of a suitable interpretation of □ at any world. Sound and complete semi-formal systems, corresponding to the modal systems K and K4, for the class of all possible-worlds models for predicates and all transitive possible-worlds models are presented. We apply our account also to nonstandard models of arithmetic and other languages than the language of arithmetic. (shrink)

In this chapter, the author takes up aspects of Richard Rorty's account of Georg Wilhelm Friedrich Hegel in the light of such developments. In an autobiographical essay Rorty recounted an early phase of his intellectual life in which he became disillusioned with the Platonist "quest for certainty" that he had harbored up to that time. Rorty's parallel vision of Hegel as providing a philosophical form of this redescriptive path to freedom and thereby as providing a philosophical narrative without a "moral" (...) or any "aspect of eternity" is one that, of course, stands in stark contrast to the usual picture of Hegel's philosophy. Rorty had been obviously attracted to the strongly anti‐Cartesian dimensions of Hegel's account of "Anerkennung" in which mindedness is treated not as a fixed human capacity but as having a history in virtue of being dependent on historically variable forms of social interaction. (shrink)

In this paper I argue against the commonly received view that Kripke's formal Possible World Semantics (PWS) reflects the adoption of a metaphysical interpretation of the modal operators. I consider in detail Kripke's three main innovations vis-à-vis Carnap's PWS: a new view of the worlds, variable domains of quantification, and the adoption of a notion of universal validity. I argue that all these changes are driven by the natural technical development of the model theory and its related notion of validity: (...) they are dictated by merely formal considerations, not interpretive concerns. I conclude that Kripke's model theoretic semantics does not induce a metaphysical reading of necessity, and is formally adequate independently of the specific interpretation of the modal operators. (shrink)

“The Craft of Formal Logic” is Arthur Prior’s unpublished textbook, written in 1950–51, in which he developed a theory of modality as quantification over possible worlds-like objects. This theory predates most of the prominent pioneering texts in possible worlds semantics and anticipates the significance of its basic concept in modal logic. Prior explicitly defines modal operators as quantifiers of ‘entities’ with modal character. Although he talks about these ‘entities’ only informally, and hesitates how to name them, using alternately the phrases (...) ‘possible states of affairs’, ‘chances’, ‘cases’ or ‘peculiar objects’, he is nevertheless very clear that they should be the fundamental concept of any theory of modality as a form of quantity. Without the assumption that modal operators quantify over such modal objects, the modal system will be incapable of distinguishing an actually true proposition from a necessarily true one. Due to the fact that Prior never made any direct reference to this theory in his subsequently published papers, it remained largely unknown. The comparison of “The Craft” with some of his papers on tense logic suggests that this early theory of modality underlies his later work on temporality. (shrink)

Turingin testi, interrogatiivimalli ja tekoäly.

In the 1930s, C. I. Lewis, who was responsible for the revival of modal logic in the era of modern symbolic logic, characterized ‘intensional’ approaches to logic as typical of post-Leibnizian ‘continental philosophy’, in contrast to the ‘extensionalist’ approaches dominant in the British tradition. Indeed Lewis’s own work in this area had been inspired by the logic of his teacher, the American ‘Absolute Idealist’, Josiah Royce. Hegel’s ‘Subjective Logic’ in Book III of hisScience of Logic, can, I suggest, be considered (...) as an intensional modal logic, and this paper explores parallels between it and a later variety of modal logic—tenselogic, as developed by Arthur Prior in the 1950s and 60s. Like Lewis, Prior too had been influenced in this area by a teacher with strong Hegelian leanings—John N. Findlay. Treated as anintensional(with an ‘s’) logic, Hegel’s subjective logic can be used as a framework for addressing issues ofintentionality(with a ‘t’)—the mind’s capacity to be intentionally directed to objects. In this way, I suggest that the structures of his subjective logic can clarify what is at issue in the ‘Psychology’ section of theEncyclopaediaPhilosophy of Subjective Spirit. (shrink)

The revolution in semantics in the late 1960s and 1970s overturned an earlier competing paradigm, ‘translational’ semantics. I revive and defend Prior’s translational semantics for modals and tense-modals. I also show how to extend Prior’s propositional modal semantics to quantificational modal logic, and use the resulting semantics to formalize Prior’s own counterexample to the Barcan Formula.

We give a reading of binary necessity statements of the form “ϕ is necessary for ψ” in terms of proofs. This reading is based on the idea of interpreting such statements as “Every proof of ψ uses ϕ”.

The paper is a brief survey of the most important semantic constructions founded on the concept of possible world. It is impossible to capture in one short paper the whole variety of the problems connected with manifold applications of possible worlds. Hence, after a brief explanation of some philosophical matters I take a look at possible worlds from rather technical standpoint of logic and focus on the applications in formal semantics. In particular, I would like to focus on the fruitful (...) marriage of possible world semantics and algebra and its evolution leading to very general construction of Wójcicki called referential semantics and some of its refinements. The presentation is informal and sketchy; the main purpose is to put in one place a short, and readable I hope, description of the most important constructions and to point out the main sources of these solutions. (shrink)

A Leibnizian semantics proposed by Becker in 1952 for the modal operators has recently been reviewed in Copeland’s paper The Genesis of Possible World Semantics (Copeland in J Philos Logic 31:99–137, 2002 ), with a remark that “neither the binary relation nor the idea of proving completeness was present in Becker’s work”. In light of Frege’s celebrated Sense-Determines-Reference principle, we find, however, that it is Becker’s semantics, rather than Kripke’s semantics, that has captured the true spirit of Frege’s semantic program. (...) Furthermore, for Kripke’s possible world semantics to fit in Frege’s framework of senses , worlds and referents , it will have to be thoroughly reformulated. By introducing the notion of a hi-world into the picture, we manage to keep the key ingredients of Becker’s semantics intact, while at the same time solve a fatal problem that used to shadow Becker’s original semantics—it had not been able to make sense of inhomogeneous modality. The resulting generalized Beckerian semantics provides, in effect, a Beckerian analysis of the Kripkean possible worlds. It reveals the subtle hierarchical internal structure of a Kripkean world that has not been discovered before. (shrink)

This article opposes a view widely accepted in studies concerning the history of modal logic, according to which (i) the approach of C. I. Lewis towards constructing modern modal logic was purely syntactical (i.e. limited to the construction of axiomatic systems S1-S5 of propositional modal logic), and (ii) the notion of a possible world was incorporated into modern logic and philosophy mainly by authors such as Rudolf Carnap and Saul Kripke. The article presents Lewis' definition of a possible world, and (...) his formulation of the truth-conditions of statements containing strict implication as their main connective in terms of possible worlds. The main question of the article is whether it is possible to consider Lewis' work in this area as an early stage of the development of possible world semantics, and if so, in what sense? The article concludes by answering affirmatively, due to soundness and completeness proofs with respect to S5 using Lewis' semantics. (shrink)

Charles Sanders Peirce was one of the United States’ most original and profound thinkers, and a prolific writer. Peirce’s game theory-based approaches to the semantics and pragmatics of signs and language, to the theory of communication, and to the evolutionary emergence of signs, provide a toolkit for contemporary scholars and philosophers. Drawing on unpublished manuscripts, the book offers a rich, fresh picture of the achievements of a remarkable man.

Arthur Prior was one of the logicians who participated in the invention of the possible worlds’ semantics. The ontology, which is connected with his systems of modal logic, is unique. Prior tried to reduce the number of abstract entities as much as possible. Hence he did not elect to introduce possible worlds and possibilia into his ontology. In addition, he held a reductionist view, which is called modal actualism by Fine or modalism by Melia. Prior was inspired by various authors (...) but this paper mainly discusses the influence of two prominent sources, Wittgenstein and logicians from Warsaw School. Prior acknowledged Wittgenstein’s influence, when he discuss the view that possible worlds consist of propositions. The second important feature of Prior’s concept is the denial of the real existence of possible worlds and the denial of the existence of entities which are in them. It was probably enabled by Prior’s adoption of some systems of logic invented by logicians from the Warsaw school, especially Lesniewski’s and Łukasiewicz’s systems. (shrink)

A century ago, Charles S. Peirce proposed a logical approach to modalities that came close to possible-worlds semantics. This paper investigates his views on modalities through his diagrammatic logic of Existential Graphs. The contribution of the GAMMA part of EGs to the study of modalities is examined. Some ramifications of Peirce's remarks are presented and placed into a contemporary perspective. An appendix is included that provides a transcription with commentary of Peirce's unpublished manuscript on modality from 1901.

This paper gives an overview of logico-philosophical issues of time and determinism. After a brief review of historical roots and 20th century developments, three current research areas are discussed: the definition of determinism, space-time indeterminism, and the temporality of individual things and their possibilities.

The paper re-evaluates Prior's tenets about indeterminism and relativity from the point of view of the current state of the debate. We first discuss Prior's claims about indeterministic tense logic and about relativity separately and confront them with new technical developments. Then we combine the two topics in a discussion of indeterministic approaches to space-time logics. Finally we show why Prior would not have to "dig his heels in" when it comes to relativity: We point out a way of combining (...) the existential import of the distinction between past, present, and future with a frame-relative notion of the present. (shrink)