This paper contains an argument to the effect that possibleworldssemantics renders semantic knowledge impossible, no matter what ontological interpretation is given to possibleworlds. The essential contention made is that possibleworlds semantic knowledge is unsafe and this is shown by a parallel with the preface paradox.
This chapter provides an introduction to possibleworldssemantics in both logic and the philosophy of language, including a discussion of some of the advantages and challenges for possibleworldssemantics.
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 possibleworldssemantics for partial meet multiple contractions. (shrink)
The standard view of clauses embedded under attitude verbs or modal predicates is that they act as terms standing for propositions, a view that faces a range of philosophical and linguistic difficulties. Recently an alternative has been explored according to which embedded clauses act semantically as predicates of content-bearing objects. This paper argues that this approach faces serious problems when it is based on possibleworlds-semantics. It outlines a development of the approach in terms of truthmaker theory (...) instead. (shrink)
A century ago, Charles S. Peirce proposed a logical approach to modalities that came close to possible-worldssemantics. 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 An appendix is included that provides a transcription with commentary of Peirce’s unpublished manuscript on modality from (...) 1901. (shrink)
This paper evaluates Stalnaker’s recent attempt to outline a realist interpretation of possibleworldssemantics 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 possibleworldssemantics’ 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 possibleworlds formalism governing the interaction between quantification and modality, under any analysis whatsoever of non-representational artefacts. (shrink)
Philosophers have long analyzed the truth-condition of counterfactual conditionals in terms of the possible-worldssemantics advanced by Lewis  and Stalnaker . In this paper, I argue that, from the perspective of philosophical semantics, the causal modeling semantics proposed by Pearl  and others (e.g., Briggs ) is more plausible than the Lewis-Stalnaker possible-worldssemantics. I offer two reasons. First, the possible-worldssemantics has suffered from a specific type of (...) counterexamples. While the causal modeling semantics can handle such examples with ease, the only way for the possible-worldssemantics to do so seems to cost it its distinctive status as a philosophical semantics. Second, the causal modeling semantics, but not the possible-worldssemantics, has the resources enough for accounting for both forward-tracking and backtracking counterfactual conditionals. (shrink)
Are transcendental phenomenology and possibleworldssemantics, two seemingly disparate, perhaps even incompatible philosophical traditions, actually complementary? Have two well-known representatives of each tradition, J.N. Mohanty and J. Hintikka, misinterpreted the other's philosophical "program" in such a way that they did not recognize the complementarity? Charles Harvey 1 has recently argued that the answer to both questions is "yes." Here I intend to argue that the answer to the first is unclear, whereas the answer to the second (...) is "no." Mohanty (at least) rightly cites fundamental differences between transcendental phenomenology and possibleworldssemantics. (shrink)
Of late, evidentiality has received great attention in formal semantics. In this paper I develop ‘evidentiality-informed’ truth conditions for modal operators such as must and may . With language data drawn from Luoping Nase (a Tibeto-Burman language spoken in the P.R. of China and belonging to the Yi Nationality), I illustrate that epistemic modals clash with clauses articulating first-hand information. I then demonstrate that existing models such as Kratzer’s graded possible-worldssemantics fail to provide accurate truth (...) conditions for modals tagging clauses with first-hand information. As a remedy I propose a fuzzy version of possible-worldssemantics with various grades of belief and knowledge. In addition to preserving the expressive power of graded possible-worldssemantics, the fuzzy model will be shown to supply appropriate truth conditions for epistemic modals appended to evidential clauses (i.e. clauses expressing first-hand information). (shrink)
This paper is about possibleworldssemantics 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 possibleworldssemantics 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.
This chapter begins with a discussion of Kant's theory of judgment-forms. It argues that it is not true in Kant's logic that assertoric or apodeictic judgments imply problematic ones, in the manner in which necessity and truth imply possibility in even the weakest systems of modern modal logic. The chapter then discusses theories of judgment-form after Kant, the theory of quantification, Frege's Begriffsschrift, C. I. Lewis and the beginnings of modern modal logic, the proof-theoretic approach to modal logic, possible (...) world semantics, correspondence theory, and modality and quantification. (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-worldssemantics (...) for predicates of sentences has not been developed very far. By introducing possible-worldssemantics 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 the paper we will study the notions of possible-worldssemantics, fiction, and creativity. The intention is to show how the notion of possible-worldssemantics 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-worldssemantics 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)
This paper is predicated on the idea that some modal operators are better understood as quantificational expressions over worlds that determine not only first-order facts but modal facts also. In what follows, we will present a framework in which these two types of facts are brought closer together. Structural features will be located in the worlds themselves. This result will be achieved by decomposing worlds into parts, where some of these parts will have “modal import” in the (...) sense that they will determine structure on other worldly parts. The main upshot of this will be a clearer grasp of the interaction between modal notions. (shrink)
McCall (1984) offered a semantics of counterfactual conditionals based on “real possibleworlds” that avoids using the vague notion of similarity between possibleworlds. I will propose an interpretation of McCall’s counterfactuals in a formal framework based on Baltag-Moss-Solecki events and protocols. Moreover, I will argue that using this interpretation one can avoid an objection raised by Otte (1987).
Stephen Barker argues that a possibleworldssemantics for the counterfactual conditional of the sort proposed by Stalnaker and Lewis cannot accommodate certain examples in which determinism is true and a counterfactual Q > R is false, but where, for some P, the compound counterfactual P > (Q > R) is true. I argue that the completeness theorem for Lewis’s system VC of counterfactual logic shows that Stalnaker–Lewis semantics does accommodate Barker’s example, and I argue that (...) its doing so should be understood as showing that the example is an exception to Lewis’s Time’s Arrow requirements. (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)
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 possibleworlds (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 possibleworlds, then assertion of such a theory, taken at face-value, does appear to bring commitment (...) to the existence of a plurality of possibleworlds. 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 possibleworlds and commitment to such a disastrous applied possible-worldssemantics 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) possibleworlds. Thus, a novel interpretation of applied possible-worldssemantics is offered on which we may lay claim to whatever benefits such a theory offers while avoiding realism about (other) possibleworlds. Thereby, the contention that applied possible-worldssemantics gives us reason to be realists about possibleworlds is (further) undermined. (shrink)
A century ago, Charles S. Peirce proposed a logical approach to modalities that came close to possible-worldssemantics. 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 charts some early history of the possibleworldssemantics 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.
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 possibleworldssemantics 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)
Providing a possibleworldssemantics for a logic involves choosing a class of possibleworlds 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 (...) class='Hi'>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)
Providing a possibleworldssemantics for a logic involves choosing a class of possibleworlds 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 possibleworlds (...) 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)
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)
Possibleworldssemantics (PWS) is a family of methods that have been used to analyze a wide variety of intensional phenomena, including modality, conditionals, tense and temporal adverbs, obligation, and reports of informational and cognitive content. PWS spurred the development of philosophical logic and led to new applications of logic in computer science and artiﬁcial intelligence. It revolutionized the study of the semantics of natural languages. PWS has inspired analyses of many concepts of philosophical importance, and (...) the concept of a possible world has been at the heart of important philosophical systems. (See also POSSIBLEWORLDS, PHILOSOPHICAL ISSUES IN.. (shrink)
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 possibleworlds. 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)
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 possibleworlds. It reveals the subtle hierarchical internal structure of a Kripkean world that has not been discovered before. (shrink)
The general issue addressed in this dissertation is: what do the models of formal model-theoretic semantics represent? In chapter 2, I argue that those of first-order classical logic represent meaning assignments in possibleworlds. This motivates an inquiry into what the interpretations of first-order quantified model logic represent, and in Chapter 3 I argue that they represent meaning assignments in possible universes of possibleworlds. A possible universe is unpacked as one way model (...) reality might be. The problem arises here as to how we are to understand the distinction between the actual and the possible as it relates to modal reality. ;Along with the development of the main arguments in Chapters 2 and 3, the dissertation assesses the status of semantic accounts or logical properties and relations. Specifically, what does the model-theoretic account of a logically possible situation add to the syntactic account ? ;Proofs of invalidity in terms of the models of formal semantics do not establish that it is possible for the premises to be true and the conclusion false, since a formal model is merely given by a consistent set of sentences. Unless there is some way to generate a non-formal model from a formal one, such proofs do not really go beyond syntactic notions. The dissertation ends by concluding that there is no way to generate a non-formal model from a formal one without relying on logical intuitions that are syntactical. ;Hence efforts to construct a semantic basis for model logic independent of syntactic commitments are misguided. However, in classical logic the independence of the semantic account from the syntactic one is grounded on the intuition that it is metaphysically possible for there to be a denumerably infinite totality of objects. (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)
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)
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.
The development of possibleworldssemantics 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.
“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 possibleworlds-like objects. This theory predates most of the prominent pioneering texts in possibleworldssemantics 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)
In this paper it is argued that the conjunction of linguistic ersatzism, the ontologically deflationary view that possibleworlds are maximal and consistent sets of sentences, and possible world semantics, the view that the meaning of a sentence is the set of possibleworlds at which it is true, implies that no actual speaker can effectively use virtually any language to successfully communicate information. This result is based on complexity issues that relate to our (...) finite computational ability to deal with large bodies of information and a strong, but well motivated, assumption about the cognitive accessibility of meanings of sentences ersatzers seem to be implicitly committed to. It follows that linguistic ersatzism, possible world semantics, or both must be rejected. (shrink)
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 possibleworlds. Hence, after a brief explanation of some philosophical matters I take a look at possibleworlds 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)
Formalized physical theories are not, as a rule, stated in intensional languages. Yet in talking about them we often treat them as if they were. We say for instance: 'Consider what would happen if instead of p's being true q were. In such a case r would be likely.' If we say this sort of thing, p, q and r appear to stand for the meanings of sentences of the theory, but meanings in some intensional sense. Now it is very (...) easy to extend the syntax of the formal theory by adding all sorts of intensional operators, e.g. a modal operator; and it is possible to extend the semantics by adding a set of possibleworlds and evaluating the modal formulae in the usual way. But this procedure is open to the criticism that we are extending the theory by adding something which is not already there. In particular the criticism will be that the possibleworlds required by the semantics seem to have no connection with the intended interpretations of the original physical theory. The aim of this paper is to shew how a set of possibleworlds is already implicit in the intended interpretations of a formally presented physical theory and that these interpretations induce, in a comparatively direct way, an intensional semantics which corresponds to the original one. (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)
This paper describes and compares the first step in modern semantic theory for deontic logic which appeared in works of Stig Kanger, Jaakko Hintikka, Richard Montague and Saul Kripke in late 50s and early 60s. Moreover, some further developments as well as systematizations are also noted.