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.

This article traces the development of possible worlds semantics through the work of: Wittgenstein, 1913-1921; Feys, 1924; McKinsey, 1945; Carnap, 1945-1947; McKinsey, Tarski and Jónsson, 1947-1952; von Wright, 1951; Becker, 1952; Prior, 1953-1954; Montague, 1955; Meredith and Prior, 1956; Geach, 1960; Smiley, 1955-1957; Kanger, 1957; Hintikka, 1957; Guillaume, 1958; Binkley, 1958; Bayart, 1958-1959; Drake, 1959-1961; Kripke, 1958-1965.

Temporal logic is one of the many areas in which a possible world semantics is adopted. Prior's Ockhamist and Peircean semantics for branching-time, though, depart from the genuine Kripke semantics in that they involve a quantification over histories, which is a second-order quantification over sets of possible worlds. In the paper, variants of the original Prior's semantics will be considered and it will be shown that all of them can be viewed as first-order (...) counterparts of the original semantics. (shrink)

_ Source: _Page Count 19 The theory of possible worlds has been minimally employed in the field of theory and philosophy of history, even though it has found a place as a tool in other areas of philosophy. Discussion has mostly focused on arguments concerning counterfactual history’s status as either useful or harmful. The theory of possible worlds can, however be used also to analyze historical writing. The concept of textual possible worlds offers an interesting (...) framework to work with for analyzing a historical text’s characteristics and features. However, one of the challenges is that the literary theory’s notion of possible worlds is that they are metaphorical in nature. This in itself is not problematic but while discussing about history, which arguably deals with the real world, the terminology can become muddled. The latest attempt to combine the literary and philosophical notions of possible worlds and apply it to historiography came from Lubomír Doležel in his _Possible Worlds of Fiction and History: The Postmodern Stage_. I offer some criticism to his usage of possible worlds to separate history and fiction, and argue that when historiography is under discussion a more philosophical notion of possible worlds should be prioritized over the metaphorical interpretation of possible worlds. (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)

Situation semantics was originally conceived as an alternative to extensional model theory and possible world semantics especially suited to the analysis of various problematic constructions, including naked-infinitive perception verbs (Barwise 1981) and belief-reports (Barwise and Perry 1981a, 1981b). In its earliest forms, the central ideas were.

The paper puts forward a theory of historical modalities that is framed in terms of possible continuations rather than possible worlds or histories. The proposal is tested as a semantic theory for a language with historical modalities, tenses, and indexicals.

This paper evaluates Stalnaker’s recent attempt to outline a realist interpretation of possible worlds semantics that lacks substantive metaphysical commitments. The limitations of his approach are used to draw some more general lessons about the non-representational artefacts of formal representations. Three key conclusions are drawn. Stalnaker’s account of possible worlds semantics’ non-representational artefacts does not cohere with his modal metaphysics. Invariance-based analyses of non-representational artefacts cannot capture a certain kind of artefact. Stalnaker must treat instrumentally those (...) aspects of possible worlds formalism governing the interaction between quantification and modality, under any analysis whatsoever of non-representational artefacts. (shrink)

This paper discusses the account of alethic modality as presented by Wilfrid Sellars in his earlier work from 1947 to 1958. Its aim is twofold. First, I discuss Sellars' analysis by exploring its historical relationship to Carnap's account of modality. I argue that Carnap's early syntactic treatment of modality profoundly influenced Sellars' own so-called ‘regulist' account of modality in terms of rules of inference. Furthermore, it is suggested that Sellars' lesser-known possible worlds analysis was influenced by Carnap's later semantic (...) account of modality. The second aim of the paper is a critical one. I raise a number of objections to Sellars’ account of modality and argue that his account confronts some serious limitations. I also argue that Sellars does not provide a satisfying explanation of the relationship between his regulist account and his possible worlds analysis. I offer such an explanation by arguing that his regulist account should be understood as a pragmatic account of what is conveyed by the use of modal sentences, whereas his possible worlds analysis is a semantic account of the asserted content of modal statements. That is, the regulist account and the possible worlds analysis have different explanatory targets. (shrink)

This collection is the final volume of a four book survey of the state of phenomenology fifty years after the death of Edmund Husserl. Its publication represents a landmark in the comprehensive treatment of contemporary phenomenology in all its vastness and richness. The diversity of the issues raised here is dazzling, but the main themes of Husserl's thought are all either explicitly treated, or else they underlie the ingenious approaches found here. Time, historicity, intentionality, eidos, meaning, possibility/reality, and teleology are (...) the main concerns of this collection devoted to studies in aesthetics, metaphysics and literary interpretation, written by such authors as, among others, R. Cobb-Stevens, C. Moreno Marquez, J. Swiecimski, Sitansu Ray and M. Kronegger. These original studies of phenomenological aesthetics and literary theory by scholars from all parts of the world were gathered by the World Institute for Advanced Phenomenological Research and Learn ing during the year 1988/89 during its assessment of the phenomeno logical movement, fifty years after Husserl's death. IX A -T. Tymieniecka (ed.), Analecta Husserliana, Vol. XXXVII, ix. (shrink)

Possible world semantics considers not only what an expression actually refers to but also what it might have referred to in counterfactual circumstances. This has proven exceptionally useful both inside and outside philosophy. The way this is achieved is by using intensions. An intension of an expression is a function that assigns to each possible world the reference of the expression in that world. However, the specific intension of terms has been subject to frequent (...) disputes. How is one to determine the intension of a term? Carnap has shown how the intension of a term depends on the type of that term. Two-dimensional semantics has shown how intensions also depend on the actual state of affairs. I will show how, in addition, intensions are no less dependent on metaphysical criteria of identity. Furthermore, I will reveal how these three factors interact to fix the exact intension of a term. In other words, I propose an outline of the overall mechanism by which intensions are being fixed. (shrink)

The canonical version of possible worlds semantics for story prefixes is due to David Lewis. This paper reassesses Lewis's theory and draws attention to some novel problems for his account.

In the tech report Artemov and Yavorskaya [4] an elegant formulation of the first-order logic of proofs was given, FOLP. This logic plays a fundamental role in providing an arithmetic semantics for first-order intuitionistic logic, as was shown. In particular, the tech report proved an arithmetic completeness theorem, and a realization theorem for FOLP. In this paper we provide a possible-world semantics for FOLP, based on the propositional semantics of Fitting [5]. We also give an (...) Mkrtychev semantics. Motivation and intuition for FOLP can be found in Artemov and Yavorskaya [4], and are not fully discussed here.This paper is dedicated to Sergei Artemov, an honored colleague and friend, who has made wonderful things for the rest of us to play with. (shrink)

Adams’s Thesis, the claim that the probabilities of indicative conditionals equal the conditional probabilities of their consequents given their antecedents, has proven impossible to accommodate within orthodox possible-world semantics. This essay proposes a modification to the orthodoxy that removes this impossibility. The starting point is a proposal by Jeffrey and Stalnaker that conditionals take semantic values in the unit interval, interpreting these (à la McGee) as their expected truth-values at a world. Their theories imply a false (...) principle, namely, that the probability of a conditional is independent of any proposition inconsistent with its antecedent. But they also point to something important, namely, that our uncertainty about conditionals is not confined to uncertainty about the facts (what the actual world is like) but also expresses uncertainty about the counterfacts (what the world would be like if one or another supposition were true). To capture this observation, this essay proposes that the semantic contents of conditionals be treated as sets of vectors of possible worlds, not singleton worlds, with the coordinates of each specifying the world that is or would be true under the supposition that it represents. The probabilities of truth for conditionals will then depend on the joint probabilities of the facts and counterfacts, the latter in turn depending on the mode of supposition. The implication of this treatment is that the probabilities of conditionals are conditional probabilities whenever the mode of supposition is evidential. (shrink)

In the logic of theory change, the standard model is AGM, proposed by Alchourrón et al. (J Symb Log 50:510–530, 1985 ). This paper focuses on the extension of AGM that accounts for contractions of a theory by a set of sentences instead of only by a single sentence. Hansson (Theoria 55:114–132, 1989 ), Fuhrmann and Hansson (J Logic Lang Inf 3:39–74, 1994 ) generalized Partial Meet Contraction to the case of contractions by (possibly non-singleton) sets of sentences. In this (...) paper we present the possible worlds semantics for partial meet multiple contractions. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Possible Worlds in the Tahâfut al-tahâfut:Averroes on Plenitude and PossibilityTaneli Kukkonen1.It has become customary to credit John Duns Scotus with having first systematically laid out the basis for treating the modal terms as referring to synchronic alternative states of affairs. This has been viewed as constituting a genuine shift in modal paradigms, as no former model had included the idea of genuine synchronic alternative possibilities. Historians of modal (...) logic and contemporary logicians alike have found it interesting that certain key features of Duns Scotus's theory and subsequent late medieval work markedly resemble the so-called possible worlds semantics approach of modern modal theory.1Duns Scotus' innovations were not completely without precedent. Several key elements in Scotus' theory were foreshadowed by twelfth-century developments. Perhaps somewhat amusingly, one of the most important forerunners to the Latin discussion was one in whose context the expression "possible worlds" would have made sense in a very special way.2 This is the medieval Arabic debate on the eternity of the world and its modal status. In this paper I propose to take stock of the positions the Arabs reached, and to do so by way of [End Page 329] consulting one of the documents central to the debate, the Tahâfut al-tahâfut or the "Incoherence of the Incoherence," by Abû al-Walîd Ibn Rushd (the Latin "Averroes," 1126-1198). In the first part I examine Averroes' exposition of the received Aristotelian tradition; in the second I assess the revisions to modal theory suggested by al-Ghazâlî (1058-1111), in the latter's comprehensive critique of philosophical doctrine. Though the two inquiries are obviously complementary, they can be accomplished independently of each other.It will be seen that Averroes' and his formidable adversary's views on the interpretation of the modal concepts differ quite fundamentally. What makes the ensuing debate, often fraught with misunderstandings and misrepresentation, so engaging is that both parties, in spite of their differences, refer to a common Aristotelian backdrop in questions of terminology and mode of argumentation. Both Averroes and al-Ghazâlî are well-placed to present a considered and balanced account of what they take to be crucial in the issues involved. It is on account of this that the complex interplay between the old and the new comes to the fore with exceptional force and clarity in the Tahâfut debates.2.The Tahâfut al-tahâfut, first published in 1180, is a philosophical rejoinder to an attack on philosophy, Abû Hâmid al-Ghazâlî's Tahâfut al-falâsifa or "The Incoherence of the Philosophers" (1095). In that celebrated work al-Ghazâlî had claimed to expose certain philosophical doctrines as not only contrary to orthodox Muslim belief, but also internally incoherent.3 Averroes' reply in turn was written in order "to show the different degrees of assent and conviction attained by the assertions in The Incoherence of the Philosophers, and to prove that the greater part has not reached the degree of evidence and of truth."4 The work is thus of a doubly dialectical nature. Whereas al-Ghazâlî tries to show the philosophers' reasoning to be defective, Averroes has to show both that al-Ghazâlî is likewise lacking in intellectual rigor and that philosophy, properly understood, is innocent of the charges leveled at it. If the Islamic philosophers (al-Fârâbî and, above all, Avicenna) have in fact erred, this is only to the extent that they have misrepresented correct Aristotelian doctrine. [End Page 330]Averroes' presentation is appropriately delicate considering the complexity of the task at hand. Averroes quotes al-Ghazâlî exclusively in full, lengthy passages, with the result of incorporating almost all of the Tahâfut al-falâsifa in his own work. In so doing he gives us an adequate and comparably fair representation of al-Ghazâlî's views. Averroes then goes on to discuss what al-Ghazâlî says both in the philosophers' name and in his own, and points out their respective deviations from Aristotelian doctrine. The text thus comes laid out in three successive layers, with Averroes' own... (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.

The standard semantics for counterfactuals ensures that any counterfactual with a true antecedent and true consequent is itself true. There have been many recent attempts to amend the standard semantics to avoid this result. I show that these proposals invalidate a number of further principles of the standard logic of counterfactuals. The case against the automatic truth of counterfactuals with true components does not extend to these further principles, however, so it is not clear that rejecting the latter (...) should be a consequence of rejecting the former. Instead I consider how one might defuse putative counterexamples to the truth of true-true counterfactuals. (shrink)

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)

Providing a possible worlds semantics for a logic involves choosing a class of possible worlds models, and setting up a truth definition connecting formulas of the logic with statements about these models. This scheme is so flexible that a danger arises: perhaps, any (reasonable) logic whatsoever can be modelled in this way. Thus, the enterprise would lose its essential tension. Fortunately, it may be shown that the so-called incompleteness-examples from modal logic resist possible worlds modelling, even (...) in the above wider sense. More systematically, we investigate the interplay of truth definitions and model conditions, proving a preservation theorem characterizing those types of truth definition which generate the minimal modal logic. (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)

In the paper we will study the notions of possible-worlds semantics, fiction, and creativity. The intention is to show how the notion of possible-worlds semantics allows us to generate a fresh interpretation of the notions of fiction and creativity. To do this, we have to consider the philosophy of logic. Possible-worlds semantics can be used in interpreting modal notions. The intention is to interpret the notions of fiction and creativity as modal notions. However, the (...) analysis shows that the notions of fiction and creativity are multimodal notions. (shrink)

The goal of this paper is to argue for the fruitfulness for linguistic theory of an approach to semantics that has been developed primarily by logicians and philosophers. That the theory of possible worlds semantics has been extremely fruitful for logic and philosophy is widely if not universally accepted, and I will not try to convince remaining skeptics on that score. But the goals of linguistics are sufficiently different from those of philosophy and logic that there are (...) independent and highly reasonable grounds for skepticism about the appropriateness of such a theory for linguistics, and I will address what seem to me the most important of these in addition to offering positive evidence in favor of such an approach to semantics. (shrink)

If a possible-worlds semantic theory for modal logics is pure, then the assertion of the theory, taken at face-value, can bring no commitment to the existence of a plurality of possible worlds (genuine or ersatz). But if we consider an applied theory (an application of the pure theory) in which the elements of the models are required to be possible worlds, then assertion of such a theory, taken at face-value, does appear to bring commitment to the existence (...) of a plurality of possible worlds. Or at least that is so if the applied theory is adequate. For an applied possible-worlds semantic theory that is constrained to contain only one-world models is bound to deliver results on validity, soundness and completeness that are apt to seem disastrous. I attempt to steer a course between commitment to the existence of a plurality of possible worlds and commitment to such a disastrous applied possible-worlds semantics by noting, and developing, the position of one who asserts such a theory at face-value but who remains agnostic about the existence of other (non-actualized) possible worlds. Thus, a novel interpretation of applied possible-worlds semantics is offered on which we may lay claim to whatever benefits such a theory offers while avoiding realism about (other) possible worlds. Thereby, the contention that applied possible-worlds semantics gives us reason to be realists about possible worlds is (further) undermined. (shrink)

Saul Kripke did more than anyone else to bring possible worlds into the contemporary philosophical discourse, first with his more formal work on the model theory for modal logic in the 1960s, and then with his more philosophical lectures on reference and modality, delivered in January 1970, that used the possible worlds apparatus informally to clarify the relations between semantic issues about names and metaphysical issues about individuals and kinds. Possible worlds semantics have been widely applied (...) since then, both in philosophy and in other fields such as linguistic semantics and pragmatics, theoretical computer science, and game theory. Kripke’s work, along with that of David Lewis, stimulated an ongoing debate about the nature and metaphysical status of possible worlds. Kripke himself has had little to say about the issues raised in this debate, in print, beyond what he said in Naming and Necessity and in brief remarks in a preface to a later edition of the lectures, published in 1980. But there is a clear view of the nature of possible worlds, and of the status of an explanation of modality in terms of possible worlds, implicit in the lectures and the preface. -/- The central focus of the post–Naming and Necessity debate about possible worlds has been a contrast between David Lewis’s modal realism and various versions of actualism. On this general issue, it is clear enough where Kripke stands: His criticisms of what he describes as the “other countries” picture of possible worlds are an explicit rejection of Lewis’s realism about possible worlds. But the rejection of modal realism raises a range of further questions: What exactly are possible worlds (or possible states of the world, which Kripke suggests would be less misleading terminology)? What contribution do they make to the explanation of modal discourse, and of the distinctive facts that modal discourse is used to state? Does the slogan “necessity is truth in all possible worlds” provide, or point to, a reductive analysis of necessity? Are possible worlds, in some sense, prior to modal operators and modal auxiliaries? If not, in what sense are they explanatory? How are possible worlds, or counterfactual situations, specified? How do they contribute to our understanding of specific meta- physical questions about the relations between particular individuals and their qualitative characteristics, the kinds to which they belong, and the matter of which they are constituted? How are we to understand the possible existence of individuals that do not actually exist? What is the status of the domains of individuals in merely possible worlds? -/- My aim in this chapter is to spell out the views about some of these foundational questions that are expressed or at least implicit in Kripke’s lectures. In Section 2, I discuss the general contrast between modal realism and actualism and questions about the kind of explanation that possible worlds provide for modal discourse and modal facts. In Section 3, I look at Kripke’s views about how possible worlds are specified, in particular at the role of individuals in specifying possible worlds. In Section 4, I consider the problems about merely possible individuals. (shrink)

The chapter looks at an aspect of David Lewis’s work on language that has been important for the foundation and history of formal semantics as a discipline practiced by both linguists and philosophers of language: a referential semantics over possible worlds that is connected to linguistically plausible syntactic structures. Lewis’s original contributions are placed within their historical context: Church’s typed lambda calculus, Carnapian intensions, the categorial grammars of Ajdukiewicz, and Chomsky’s theories of the relation between syntax (...) and semantics. Relying on Lewis’s letters, the chapter identifies the works of Stenius, Davidson, and Katz as triggering Lewis’s interest in formal theories of natural language semantics and clarifies the relation between his and Montague’s contributions to the foundation of the discipline. (shrink)

Conditional structures lie at the heart of the sciences, humanities, and everyday reasoning. It is hence not surprising that conditional logics – logics specifically designed to account for natural language conditionals – are an active and interdisciplinary area. The present book gives a formal and a philosophical account of indicative and counterfactual conditionals in terms of Chellas-Segerberg semantics. For that purpose a range of topics are discussed such as Bennett’s arguments against truth value based semantics for indicative conditionals.

This paper is about possible worlds semantics for propositional attitude sentences. In particular I shall focus on belief reports in English such as "Lusina believes that tofu is nutritious." It is well-known that possible worlds semantics for such reports suffers from the so-called _problem of equivalence_ . In this paper I shall examine some attempts to deal with this problem and argue that they are unsatisfactory.

Providing a possible worlds semantics for a logic involves choosing a class of possible worlds models, and setting up a truth definition connecting formulas of the logic with statements about these models. This scheme is so flexible that a danger arises: perhaps, any logic whatsoever can be modelled in this way. Thus, the enterprise would lose its essential 'tension'. Fortunately, it may be shown that the so-called 'incompleteness-examples' from modal logic resist possible worlds modelling, even in (...) the above wider sense. More systematically, we investigate the interplay of truth definitions and model conditions, proving a preservation theorem characterizing those types of truth definition which generate the minimal modal logic. (shrink)

Las nociones epistémicas modales se definen como aquellos conceptos epistémicos que, como el de cognoscibilidad o el de indudabilidad, incluyen una nota modal. Segun se defiende en este trabajo, la semántica de mundos posibles y algunas de sus extensiones (especialmente las llevadas a cabo para logica temporal, logica epistemica y logica condicional) son instrumentos adecuados para deshacer el nudo de las intensionalidades superpuestas en estas nociones especialmente esquivas al análisis. Para mostrarlo, se proporcionan una serie de análisis sucesivos de la (...) nocion de cognoscibilidad que a partir de una interpretación naif van salvando una serie de presuposiciones, problemas y paradojas hasta dar con una analisis que se presume satisfactorio.“Modal epistemic notions” are those epistemic concepts which in some way or another has a modal element. These modal epistemic notions, although they could appear intuitively clear, they turn out to be particularly obscure, slippery, when one subjects them to a formal analysis. In this paper we will try to show that possible world semantics (and its extensions for epistemic, temporal and conditional logic) is an appropriate instrument for the explanation ofthese notions. Four successive analysis of the notion of “knowability” are given, ranging from a naive account to an analysis that gets to the bottom ofthe problem. (shrink)

In this paper, I shall consider the challenge that Quine posed in 1947 to the advocates of quantified modal logic to provide an explanation, or interpretation, of modal notions that is intuitively clear, allows “quantifying in”, and does not presuppose, mysterious, intensional entities. The modal concepts that Quine and his contemporaries, e.g. Carnap and Ruth Barcan Marcus, were primarily concerned with in the 1940’s were the notions of (broadly) logical, or analytical, necessity and possibility, rather than the metaphysical modalities that (...) have since become popular, largely due to the influence of Kripke. In the 1950’s modal logicians responded to Quine’s challenge by providing quantified modal logic with model-theoretic semantics of various types. In doing so they also, explicitly or implicitly addressed Quine’s interpretation problem. Here I shall consider the approaches developed by Carnap in the late 1940’s, and by Kanger, Hintikka, Montague, and Kripke in the 1950’s, and discuss to what extent these approaches were successful in meeting Quine’s doubts about the intelligibility of quantified modal logic. (shrink)

Actualism is the doctrine that the only things there are, that have being in any sense, are the things that actually exist. In particular, actualism eschews possibilism, the doctrine that there are merely possible objects. It is widely held that one cannot both be an actualist and at the same time take possible world semantics seriously — that is, take it as the basis for a genuine theory of truth for modal languages, or look to it (...) for insight into the modal structure of reality. For possible world semantics, it is supposed, commits one to possibilism. In this paper I take issue with this view. To the contrary, I argue that one can take possible world semantics seriously without any commitment to possible worlds or possibilism and hence remain in full compliance with actualist scruples. Moreover, one can do so without without invoking either "ersatz" worlds or haecceities. (shrink)

In the paper there is presented the semantic interpretation of idealism/ realism controversy which is one of the most essential issues in Ingarden’s phenomenological project of ontology. The procedure of semantic paraphrase which is contemporary developed by Wolen´ ski, is the main interpretative tool. In the central part of the paper, there is formulated the formal theory of the semantic framework underlying idealism/realism discourse. Finally, there are formulated some notes showing that intentional conception of negation may be used for defending (...) various idealistic positions. (shrink)

"Jim would still be alive if he hadn't jumped" means that Jim's death was a consequence of his jumping. "x wouldn't be a triangle if it didn't have three sides" means that x's having a three sides is a consequence its being a triangle. Lewis takes the first sentence to mean that Jim is still alive in some alternative universe where he didn't jump, and he takes the second to mean that x is a non-triangle in every alternative universe where (...) it doesn't have three sides. Why did Lewis have such obviously wrong views? Because, like so many of his contemporaries, he failed to grasp the truth that it is the purpose of the present paper to demonstrate, to wit: No coherent doctrine assumes that statements about possible worlds are anything other than statements about the dependence-relations governing our world. The negation of this proposition has a number of obviously false consequences, for example: all true propositions are necessarily true (there is no modal difference between "2+2=4" and "Socrates was bald"); all modal terms (e.g. "possible," "necessary") are infinitely ambiguous; there is no difference between laws of nature (e.g. "metal expands when heated") and accidental generalizations (e.g. "all of the coins in my pocket are quarters"); and there is no difference between the belief that 1+1=2 and the belief that arithmetic is incomplete. Given that possible worlds are identical with mathematical models, it follows that the concept of model-theoretic entailment is useless in the way of understanding how inferences are drawn or how they should be drawn. Given that the concept of formal-entailment is equally useless in these respects, it follows that philosophers and mathematicians have simply failed to shed any light on the nature of the consequence-relation. Q's being either a formal or a model-theoretic consequence of P is parasitic on its bearing some third, still unidentified relation to P; and until this relation has been identified, the discipline of philosophical logic has yet to begin. (shrink)

We analyze a recent trend in epistemic logic which consists in studying construction of knowledge from the agents’ observational abilities. It is based on the intuition that an agent’s knowledge comes from three possible sources: her observations, communication with other agents, and inference. The approaches mainly focus on the former two and suppose that the object of observations are propositional variables and that agents learn from public announcements. This allows to model knowledge in a more compact and intuitive way (...) than with Hintikka’s semantics. However, the semantics that one can find in the literature come with some counter-intuitive validities such as common knowledge of visibilities or the knowledge operator distributing over disjunctions. We propose a solution of each of these two issues and illustrate them with well-known toy examples of epistemic logic. (shrink)

In "A Problem in Possible-World Semantics," David Kaplan presented a consistent and intelligible modal principle that cannot be validated by any possible world frame (in the terminology of modal logic, any neighborhood frame). However, Kaplan's problem is tempered by the fact that his principle is stated in a language with propositional quantification, so possible world semantics for the basic modal language without propositional quantifiers is not directly affected, and the fact that on (...) careful inspection his principle does not target the world part of possible world semantics—the atomicity of the algebra of propositions—but rather the idea of propositional quantification over a complete Boolean algebra of propositions. By contrast, in this paper we present a simple and intelligible modal principle, without propositional quantifiers, that cannot be validated by any possible world frame precisely because of their assumption of atomicity (i.e., the principle also cannot be validated by any atomic Boolean algebra expansion). It follows from a theorem of David Lewis that our logic is as simple as possible in terms of modal nesting depth (two). We prove the consistency of the logic using a generalization of possible world semantics known as possibility semantics. We also prove the completeness of the logic (and two other relevant logics) with respect to possibility semantics. Finally, we observe that the logic we identify naturally arises in the study of Peano Arithmetic. (shrink)

Metaphysicians of modality are increasingly critical of possible-worlds talk, and increasingly happy to accept irreducibly modal properties – and in particular, irreducible dispositions – in nature. The aim of this paper is to provide the beginnings of a modal semantics which uses, instead of possible-worlds talk, the resources of such an 'anti-Humean' metaphysics. One central challenge to an anti-Humean view is the context-sensitivity of modal language. I show how that challenge can be met and a systematic modal (...) semantics provided, given an independently plausible metaphysics of dispositional properties or potentialities. (shrink)

The development of possible worlds semantics for modal claims has led to a more general application of that theory as a complete semantics for various formal and natural languages, and this view is widely held to be an adequate (philosophical) interpretation of the model theory for such languages. We argue here that this view generates a self-referential inconsistency that indicates either the falsity or the incompleteness of PWS.

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 (EGs). 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.

Standard approaches to possible-world semantics allow us to define necessity and logical truth, but analyticity is considerably more difficult to account for. The source of this difficulty lies in the received model-theoretical conception of a language interpretation. In intuitive terms, analyticity amounts to truth in virtue of meaning alone, i.e. solely in virtue of the interpretation of linguistic expressions. In other words, an analytic sentence should remain true under all variations of ‘extralinguistic reality’ as long as the (...) interpretation is kept constant. However, the received conception of an interpretation as a mapping from language to a model frame hinders keeping the interpretation constant while varying other components of the model. To make room for analyticity, the concept of an interpretation should therefore be revised. The latter should be made richer in content than it has usually been assumed. As a by-product, this revision also gives us a one-dimensional analogue of the influential two-dimensional account of a priori. We are thus able to map out the network of formal connections between the notions of analyticity, apriority, logical truth and necessity. (shrink)