As emphasized by Alonzo Church and David Kaplan (Church 1974, Kaplan 1975), the philosophies of language of Frege and Russell incorporate quite different methods of semantic analysis with different basic concepts and different ontologies. Accordingly we distinguish between a Fregean and a Russellian tradition in intensional semantics. The purpose of this paper is to pursue the Russellian alternative and to provide a language of intensional logic with a model-theoretic semantics. We also discuss the so-called (...) Russell-Myhill paradox that threatens simple Russellian type theory if propositions satisfies very strict principles of individuation. One way of avoiding the paradox is to adopt a ramified rather than a simple theory of types. (shrink)

This is a thesis in formal semantics. It consists of two parts corresponding to the distinction, due to Richard Montague, between universal grammar and specific semantic theories. The first part concerns universal grammar and is intended to provide a precise and unified conceptual framework within which different theories of formal semantics can be represented and compared. ;The second part of the thesis is concerned with intensional logic, i.e., with the logical analysis of discourse involving so called oblique contexts. These (...) contexts are characterized by the apparent failure of certain classically valid principles of substitutivity. Two kinds of reactions among logicians to the appearance of oblique contexts in natural languages are distinguished: (1) the intensional point of view, according to which oblique contexts are seen as genuine counterexamples to classical logic and to the related semantical principle of extensionality: the principle that the denotation of an expression is a function of the denotations of its parts; and (2) the extensional point of view, according to which the conflict between oblique contexts and classical logic is only apparent. The extensional point of view therefore calls for analyses of oblique contexts that preserve the laws of classical logic and the principle of extensionality. In this thesis, we are concerned with the precise formulation of and comparison between different programs for the formal semantic representation of oblique contexts. In Chapter 5, we are concerned with Church's program of representing oblique contexts within a formal language whose semantics is fully extensional and based on Frege's distinction between sense and denotation. The ambiguity between the "direct" and "indirect" denotation of an expression A is avoided by letting A be replaced in oblique contexts by an expression which denotes A's ordinary sense. We provide a possible-worlds semantics for a version of Church's formal language with the following features: (i) Objectual quantification into oblique constructions is accounted for. The treatment of quantification requires for each entity x an essence of x, by which we mean a sense which determines x in those worlds in which x exists and is undefined in all other worlds. (ii) The variables range over actually existing entities only. It is allowed that entities of certain types are contingent, i.e., the same entity may exist in one world and fail to exist in other worlds. (iii) In order to combine a proper treatment of the cross-world identification of functions with varying domains, partial functions are allowed. (iv) Senses are allowed to be partially defined. For example, the sense of a proper name is undefined in a world in which the denotation of the name does not exist. (v) Senses of functions from objects of type a to objects of type b are identified with functions from senses of objects of type a to senses of objects of type b. In Chapters 6 and 7, we pursue the Russellian Alternative in intensional semantics, where a sense/denotation distinction is avoided. Apparent failures of substitutivity principles for singular terms are explained along the lines of Russell's theory of definite descriptions. Failures of substitutivity of coextensional sentences and predicates are explained by Russell's doctrine that sentences and predicate denote propositions and propositional functions , respectively. Russellian semantics is fully extensional in the sense that the Russellian denotation of a designator is a function of the Russellian denotations of its parts. In Chapter 6, a theory of Russellian propositions is developed within set theory. This theory is then applied in Chapter 7 to the task of providing a set-theoretic semantics for Russellian type theory. (shrink)

This paper sets out a predicative response to the Russell-Myhill paradox of propositions within the framework of Church’s intensional logic. A predicative response places restrictions on the full comprehension schema, which asserts that every formula determines a higher-order entity. In addition to motivating the restriction on the comprehension schema from intuitions about the stability of reference, this paper contains a consistency proof for the predicative response to the Russell-Myhill paradox. The models used to establish this (...) consistency also model other axioms of Church’s intensional logic that have been criticized by Parsons and Klement: this, it turns out, is due to resources which also permit an interpretation of a fragment of Gallin’s intensional logic. Finally, the relation between the predicative response to the Russell-Myhill paradox of propositions and the Russell paradox of sets is discussed, and it is shown that the predicative conception of set induced by this predicative intensional logic allows one to respond to the Wehmeier problem of many non-extensions. (shrink)

W. V. Quine famously defended two theses that have fallen rather dramatically out of fashion. The first is that intensions are “creatures of darkness” that ultimately have no place in respectable philosophical circles, owing primarily to their lack of rigorous identity conditions. However, although he was thoroughly familiar with Carnap’s foundational studies in what would become known as possible world semantics, it likely wouldn’t yet have been apparent to Quine that he was fighting a losing battle against intensions, due (...) in large measure to developments stemming from Carnap’s studies and culminating in the work of Kripke, Hintikka, and Bayart. These developments undermined Quine’s crusade against intensions on two fronts. First, in the context of possible world semantics, intensions could after all be given rigorous identity conditions by defining them (in the simplest case) as functions from worlds to appropriate extensions, a fact exploited to powerful and influential effect in logic and linguistics by the likes of Kaplan, Montague, Lewis, and Cresswell. Second, the rise of possible world semantics fueled a strong resurgence of metaphysics in contemporary analytic philosophy that saw properties and propositions widely, fruitfully, and unabashedly adopted as ontological primitives in their own right. This resurgence — happily, in my view — continues into the present day. -/- For a time, at any rate, Quine experienced somewhat better success with his second thesis: that higher-order logic is, at worst, confused and, at best, a quirky notational alternative to standard first-order logic. However, Quine notwithstanding, a great deal of recent work in formal metaphysics transpires in a higher-order logical framework in which properties and propositions fall into an infinite hierarchy of types of (at least) every finite order. Initially, the most philosophically compelling reason for embracing such a framework since Russell first proposed his simple theory of types was simply that it provides a relatively natural explanation of the paradoxes. However, since the seminal work of Prior there has been a growing trend to consider higher-order logic to be the most philosophically natural framework for metaphysical inquiry, many of the contributors to this volume being among the most important and influential advocates of this view. Indeed, this is now quite arguably the dominant view among formal metaphysicians. -/- In this paper, and against the current tide, I will argue in §1 that there are still good reasons to think that Quine’s second battle is not yet lost and that the correct framework for logic is first-order and type-free — properties and propositions, logically speaking, are just individuals among others in a single domain of quantification — and that it arises naturally out of our most basic logical and semantical intuitions. The data I will draw upon are not new and are well-known to contemporary higher-order metaphysicians. However, I will try to defend my thesis in what I believe is a novel way by suggesting that these basic intuitions ground a reasonable distinction between “pure” logic and non-logical theory, and that Russell-style semantic paradoxes of truth and exemplification arise only when we move beyond the purely logical and, hence, do not of themselves provide any strong objection to a type-free conception of properties and propositions. -/- Most of my arguments in §1 are largely independent of any specific account of the nature of properties and propositions beyond their type-freedom. However, I will in addition argue that there are good reasons to take propositions, at least, to be very fine-grained. My arguments are thus bolstered significantly if it can be shown that there are in fact well-defined examples of logics that are not only type-free but which comport with such a conception of propositions. It is the purpose of §2 to lay out a logic of this sort in some detail, drawing especially upon work by George Bealer and related work of my own. With the logic in place, it will be possible to generalize the line of argument noted above regarding Russell-style paradoxes and, in §3, apply it to two propositional paradoxes — the Prior-Kaplan paradox and the Russell-Myhill paradox — that are often taken to threaten the sort of account developed here. (shrink)

In their correspondence in 1902 and 1903, after discussing the Russell paradox, Russell and Frege discussed the paradox of propositions considered informally in Appendix B of Russell’s Principles of Mathematics. It seems that the proposition, p, stating the logical product of the class w, namely, the class of all propositions stating the logical product of a class they are not in, is in w if and only if it is not. Frege believed that this paradox was avoided (...) within his philosophy due to his distinction between sense (Sinn) and reference (Bedeutung). However, I show that while the paradox as Russell formulates it is ill-formed with Frege’s extant logical system, if Frege’s system is expanded to contain the commitments of his philosophy of language, an analogue of this paradox is formulable. This and other concerns in Fregean intensional logic are discussed, and it is discovered that Frege’s logical system, even without its naive class theory embodied in its infamous Basic Law V, leads to inconsistencies when the theory of sense and reference is axiomatized therein. (shrink)

Russell's "new contradiction" about "the totality of propositions" has been connected with a number of modal paradoxes. M. Oksanen has recently shown how these modal paradoxes are resolved in the set theory NFU. Russell's paradox of the totality of propositions was left unexplained, however. We reconstruct Russell's argument and explain how it is resolved in two intensional logics that are equiconsistent with NFU. We also show how different notions of possible worlds are represented in (...) these intensional logics. (shrink)

Deleuze’s “transcendental empiricism” and the “empirical side” of Whitehead’s metaphysics are paradoxical unless placed in the context of their unorthodox readings of empiricism. I explore this context focusing on their engagements with Hume. Both subvert presumptions of a categorical gap between external nature and internal human experience and open possibilities for a speculative empiricism that is non-reductive while still affirming experience as source for philosophical thinking. Deleuze and Whitehead follow Hume in beginning with events of sensation as primary but do (...) not presume the logic of (human) subjects and objects (of nature) as necessary structuring polarities for their interpretation. This challenges a basic distinction (between inner and outer or between self and world) that seems inherent in the ordinary concept of experience, thus earning the moniker speculative. The speculative empiricist studies how these abstractions arise from events of experience prior to their consolidation in representation. This includes a critical component: to what extent do unexamined assumptions about conceptual abstraction hinder, block, or prefigure experiential attention? This critical component has existential implications for how we attend to the affective, intuitive, and preconceptual. (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)

Some philosophers have claimed that sentences like all bachelors are unmarried are analytic, where this is to say that they are true in virtue of meaning, and that anyone who understands one can know that it is true. Some have claimed in addition that the notion of analyticity can be used to solve problems in epistemology. However, in the last century the work of Quine and Putnam led many to doubt such claims, and to suspect that there is no analyticity, (...) only an illusion of analyticity to be explained. ;I think that there is something to Quine and Putnams objections. Moreover, I think that they are of help in formulating a better account of analyticity. The core of this dissertation is an account of the analytic/synthetic distinction which uses recent developments in the philosophy of language-including Russellian semantics, distinctions between different kinds of meaning, two-dimensional modal logic and the distinction between analyticity, necessity and a priority---to defend a theory which covers both the traditional necessary analytic truths such as all vixens are female and Kaplans examples of the contingent analytic such as I am here now, dthat □ = and Snow is white iff actually, now, snow is white. ;This account is used to provide solutions to problems in philosophical logic concerning the correct accounts of vagueness, inconsistency and modality. I also show how it can be used to provide a solution to the Liar paradox. (shrink)

This is a critical discussion of Nino B. Cocchiarella’s book “Formal Ontology and Conceptual Realism.” It focuses on paradoxes of hyperintensionality that may arise in formal systems of intensional logic.

Possible worlds semantics (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 POSSIBLE WORLDS, PHILOSOPHICAL ISSUES IN.. (shrink)

Could it ever be right to say that a language---as opposed to a speaker of the language---makes, or presupposes or somehow commits itself to certain claims? Such as that certain kinds of objects exist, or that things are a certain way? It can be tempting to think not, to think that languages are just the neutral media through which speakers make claims. Yet certain, surprisingly diverse, phenomena---analyticity, racial epithets, object-involving direct reference, arithmetic, and semantic paradoxes like the Liar---have pushed philosophers (...) towards views according to which languages can have presuppositions or commitments of their own---to things like the existence of numbers, the marital status of bachelors, the existence of water, and even to contradictions or morally abhorrent views. In this paper I want to present some recent data from linguistics that supports a less commonly discussed, and rather surprising version of this idea: namely that English presupposes the existence of locations or places. In section one I do some work to clarify what this claim could possibly mean by identifying some central ways in which languages have been thought to presuppose various things about the world. In section two I present the core of the linguistic data and theory from the work of Susan Rothstein. In section three I compare it to some older work by David Kaplan, arguing that the significance of the new results is greater for the issue at hand, and then in the final section I examine the philosophical significance of this work. One might attempt to draw quite impressive conclusions: such as that the existence of space is analytic, and hence a priori. I will argue that such a conclusion here would be over hasty, and that what we really have is just a surprising fact about our not-so-neutral natural language. (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)

We present a new logic -based approach to the reasoning about knowledge which is independent of possible worlds semantics.? k is a non- Fregean logic whose models consist of propositional universes with subsets for true, false and known propositions. Knowledge is, in general, not closed under rules of inference; the only valid epistemic principles are the knowledge axiom K i??? and some minimal conditions concerning common knowledge in a group. Knowledge is explicit and all forms of the (...) logical omniscience problem are avoided. Various stronger epistemic properties such as positive and/or negative introspection, the K-axiom, closure under logical connectives, etc, can be restored by imposing additional semantic constraints. This yields corresponding sublogics for which we present sound and complete axiomatizations. As a useful tool for general model constructions we study abstract versions of some 3-valued logics in which we interpret truth as knowledge. We establish a connection between? k and the well-known syntactic approach to explicit knowledge proving a result concerning equi-expressiveness. Furthermore, we discuss some self - referential epistemic statements, such as the knower paradox, as relaxations of variants of the liar paradox and show how these epistemic "paradoxes" can be solved in? k. Every specific? k - logic is defined as a certain extension of some underlying classical abstract logic. (shrink)

The Russell-Myhill paradox puts pressure on the Russellian structured view of propositions by showing that it conflicts with certain prima facie attractive ontological and logical principles. I describe several versions of RMP and argue that structurists can appeal to natural assumptions about metaphysical grounding to provide independent reasons for rejecting the ontological principles used in these paradoxes. It remains a task for future work to extend this grounding-based approach to all variants of RMP.

We present a new logic-based approach to the reasoning about knowledge which is independent of possible worlds semantics. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\in_K}$$\end{document} is a non-Fregean logic whose models consist of propositional universes with subsets for true, false and known propositions. Knowledge is, in general, not closed under rules of inference; the only valid epistemic principles are the knowledge axiom Kiφ → φ and some minimal conditions concerning common knowledge in a group. (...) Knowledge is explicit and all forms of the logical omniscience problem are avoided. Various stronger epistemic properties such as positive and/or negative introspection, the K-axiom, closure under logical connectives, etc. can be restored by imposing additional semantic constraints. This yields corresponding sublogics for which we present sound and complete axiomatizations. As a useful tool for general model constructions we study abstract versions of some 3-valued logics in which we interpret truth as knowledge. We establish a connection between \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\in_K}$$\end{document} and the well-known syntactic approach to explicit knowledge proving a result concerning equi-expressiveness. Furthermore, we discuss some self-referential epistemic statements, such as the knower paradox, as relaxations of variants of the liar paradox and show how these epistemic “paradoxes” can be solved in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\in_K}$$\end{document}. Every specific \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\in_K}$$\end{document}-logic is defined as a certain extension of some underlying classical abstract logic. (shrink)

The main objective of this paper is to examine how theories of truth and reference that are in a broad sense Fregean in character are threatened by antinomies; in particular by the Epimenides paradox and versions of the so-called Russell-Myhill antinomy, an intensional analogue of Russell’s more well-known paradox for extensions. Frege’s ontology of propositions and senses has recently received renewed interest in connection with minimalist theories that take propositions (thoughts) and senses (concepts) as the (...) primary bearers of truth and reference. In this paper, I will present a rigorous version of Frege’s theory of sense and denotation and show that it leads to antinomies. I am also going to discuss ways of modifying Frege’s semantical and ontological framework in order to avoid the paradoxes. In this connection, I explore the possibility of giving up the Fregean assumption of a universal domain of absolutely all objects, containing in addition to extensional objects also abstract intensional ones like propositions and singular concepts. I outline a cumulative hierarchy of Fregean propositions and senses, in analogy with Gödel’s hierarchy of constructible sets. In this hierarchy, there is no domain of all objects. Instead, every domain of objects is extendible with new objects that, on pain of contradiction, cannot belong to the given domain. According to this approach, there is no domain containing absolutely all propositions or absolutely all senses. (shrink)

The Logic of Metaphor uses techniques from possible worlds semantics to provide formal truth-conditions for many grammatical classes of metaphors. It gives logically precise and practically useful syntactic and semantic rules for generating and interpreting metaphors. These rules are implemented in a working computer program. The book treats the lexicon as a conceptual network with semantics provided by an intensional predicate calculus. It gives rules for finding analogies in such networks. It shows how to syntactically and semantically (...) analyze texts containing metaphors and how to use structural similarities between parts of possible worlds to provide truth-conditions for metaphors. Meanings for metaphors are linked to the modal logics of identity and indiscernibility. The book shows how to extend deductive and abductive inference systems to handle metaphors. It shows how to handle novel metaphorical word-senses. The Logic of Metaphor will be useful to philosophers, logicians, linguists, and computer scientists. (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)

The Russell-Myhill Antinomy, also known as the Principles of Mathematics Appendix B Paradox, is a contradiction that arises in the logical treatment of classes and "propositions", where "propositions" are understood as mind-independent and language-independent logical objects. If propositions are treated as objectively existing objects, then they can be members of classes. But propositions can also be about classes, including classes of propositions. Indeed, for each class of propositions, there is a proposition stating that all propositions in that class (...) are true. Propositions of this form are said to "assert the logical product" of their associated classes. Some such propositions are themselves in the class whose logical product they assert. For example, the proposition asserting that all-propositions-in-the- class-of-all-propositions-are-true is itself a proposition, and therefore it itself is in the class whose logical product it asserts. However, the proposition stating that all-propositions-in-the-null-class-are-true is not itself in the null class. Now consider the class w, consisting of all propositions that state the logical product of some class m in which they are not included. This w is itself a class of propositions, and so there is a proposition r, stating its logical product. The contradiction arises from asking the question of whether r is in the class w. It seems that r is in w just in case it is not. This antinomy was discovered by Bertrand Russell in 1902, a year after discovering a simpler paradox usually called Russell's paradox ". It was discussed informally in Appendix B of his 1903 Principles of Mathematics . In 1958, the antinomy was independently rediscovered by John Myhill, who found it to plague the "Logic of Sense and Denotation" developed by Alonzo Church. (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.

Dramatization and comedy are recurring themes in Deleuze's work in the 1960′s and, from his book on Nietzsche in 1962 through The Logic of Sense in 1969, remarks on humor and comedy are closely bound to ethical and political concerns. In Nietzsche and Philosophy, he speaks of the “true” and “false” senses of the tragic in order to frame his interpretation of Nietzsche as a whole, but the distinction acquires its immediate importance from its bearing on the question, “what is (...) justice?” In 1967, in Coldness and Cruelty, he describes legal critique as possible only in terms of irony and comedy. And, in 1969, in The Logic of Sense, the series on humor is followed and explicated by the series “On the Moral Problem in Stoic Philosophy.” This final discussion makes clear what binds these disparate discussions together: comedy is a mode of dramatization that facilitates a morally relevant experience that does not necessarily or immediately engender an act of judgment. For Deleuze, comedy is a demonstration that provokes an experience of wonder at a world that is not organized by the concepts and judgments of subjectivity. (shrink)

Intensional logic is the technical study of such intensional phenomena in human reasoning as modality, knowledge, or flow of time. These all require a richer semantic picture than standard truth values in one static environment. Such a picture is provided by so-called possible worlds semantics, a paradigm which is surveyed in this book, both as to its external sources of motivation and as to the internal dynamics of the resulting program. In particular, Manual of Intensional (...) Logic presents the major classical topics, including modal logic, tense logic, and conditional logic, all of which illustrate motivations coming from philosophy and linguistics. The Book also discusses recent computational applications in computer science and AI. Finally, Manual of Intensional Logic takes up recent developments in the study of language and information making themselves felt in the area. The Book examines the role of partial information--with illustrations drawn from different branches of Intensional Logic--and various influences stemming from current theories of the semantics of natural language, involving generalized quantifiers and theories of types. (shrink)

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)

The present essay is a critical study of Barwise and Perry’s book, emphasizing the logical and model-theoretical aspects of their work. I begin by presenting the authors’ criticism of the classical view of logic and semantics within the tradition of Frege, Russell and Tarski. In this connection, I discuss the so-called Frege argument (“the slingshot”). I try to show that the argument appears inconclusive, not only from a situation-theoretic perspective, but also from such alternative perspectives as orthodox Fregean (...) semantics or Russellian semantics. I then discuss the ontology of situation semantics and the way it is modeled within set theory. In particular, I compare the notion of an abstract situation with that of a possible world. The last two sections concern the model-theoretic aspects of the authors’ theory. In Section 7, I discuss how the “partial” perspective of situation semantics differs from that of classical model theory. Finally, in Section 8, different model-theoretic accounts of attitude reports within situation semantics are discussed, in particular the “relations to situations”-approach presented by the authors in Chapter 9 of S & A. The usual problems of “logical omniscience” that appear in standard Hintikka-style epistemic logic are avoided in situation semantics. I argue, however, that situation semantics is faced with analogous counter-intuitive results, unless the expressive power of the language under study is suitably restricted. (shrink)

In this paper I rehearse two central failings of traditional possible world semantics. I then present a much more robust framework for intensional logic and semantics based liberally on the work of George Bealer in his book Quality and Concept. Certain expressive limitations of Bealer's approach, however, lead me to extend the framework in a particularly natural and useful way. This extension, in turn, brings to light associated limitations of Bealer's account of predication. In response, I develop a (...) more general and intuitively more adequate account of the logical form of predication. (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 possible worlds 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 possible worlds 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 possible worlds 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)

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)

Metaphysically possible worlds have many uses. Epistemically possible worlds promise to be similarly useful, especially in connection with propositions and propositional attitudes. However, I argue that there is a serious threat to the natural accounts of epistemically possible worlds, from a version of Russell’s paradox. I contrast this threat with David Kaplan’s problem for metaphysical possible world semantics: Kaplan’s problem can be straightforwardly rebutted, the problems I raise cannot. I argue that although (...) there may be coherent accounts of epistemically possible worlds with fruitful applications, any such an account must fundamentally compromise the basic idea behind epistemic possibility. (shrink)

“There are no gaps in logical space,” David Lewis writes, giving voice to sentiment shared by many philosophers. But different natural ways of trying to make this sentiment precise turn out to conflict with one another. One is a *pattern* idea: “Any pattern of instantiation is metaphysically possible.” Another is a *cut and paste* idea: “For any objects in any worlds, there exists a world that contains any number of duplicates of all of those objects.” We use resources (...) from model theory to show the inconsistency of certain packages of combinatorial principles and the consistency of others. (shrink)

In this article, we discuss a simple argument that modal metaphysics is misconceived, and responses to it. Unlike Quine's, this argument begins with the simple observation that there are different candidate interpretations of the predicate ‘could have been the case’. This is analogous to the observation that there are different candidate interpretations of the predicate ‘is a member of’. The argument then infers that the search for metaphysical necessities is misguided in much the way the ‘set-theoretic pluralist’ claims that the (...) search for the true axioms of set theory is. We show that the obvious responses to this argument fail. However, a new response has emerged that purports to prove, from higher-order logical principles, that metaphysical possibility is the broadest kind of possibility applying to propositions, and is to that extent special. We distill two lines of reasoning from the literature, and argue that their import depends on premises that any ‘modal pluralist’ should deny. Both presuppose that there is a unique typed hierarchy, which is what the modal pluralist, in the context of higher-order logic, should disavow. In other words, both presupposes that there is a unique candidate for what higher-order claims could mean. We consider the worry that, in a higher-order setting, modal pluralism faces an insuperable problem of articulation, collapses into modal monism, is vulnerable to the Russell-Myhill paradox, or even contravenes the truism that there is a unique actual world, and argue that these worries are misplaced. We also sketch the bearing of the resulting ‘Higher-Order Pluralism’ on the theory of content. One theme of the discussion is that, if Higher-Order Pluralism is correct, then there is no fixed metatheory from which to characterize higher-order reality. (shrink)

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.

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)

The paradox of knowability and the debate about it are shortly presented. Some assumptions which appear more or less tacitly involved in its discussion are made explicit. They are embedded and integrated in a Russellian framework, where a formal paradox, very similar to the Russell-Myhill paradox, is derived. Its solution is provided within a Russellian formal logic introduced by A. Church. It follows that knowledge should be typed. Some relevant aspects of the typing of knowledge are (...) pointed out. (shrink)

The analytic/synthetic distinction looks simple. It is a distinction between two different kinds of sentence. Synthetic sentences are true in part because of the way the world is, and in part because of what they mean. Analytic sentences - like all bachelors are unmarried and triangles have three sides - are different. They are true in virtue of meaning, so no matter what the world is like, as long as the sentence means what it does, it will be true. -/- (...) This distinction seems powerful because analytic sentences seem to be knowable in a special way. One can know that all bachelors are unmarried, for example, just by thinking about what it means. But many twentieth-century philosophers, with Quine in the lead, argued that there were no analytic sentences, that the idea of analyticity didn't even make sense, and that the analytic/synthetic distinction was therefore an illusion. Others couldn't see how there could fail to be a distinction, however ingenious the arguments of Quine and his supporters. -/- But since the heyday of the debate, things have changed in the philosophy of language. Tools have been refined, confusions cleared up, and most significantly, many philosophers now accept a view of language - semantic externalism - on which it is possible to see how the distinction could fail. One might be tempted to think that ultimately the distinction has fallen for reasons other than those proposed in the original debate. -/- In Truth in Virtue of Meaning, Gillian Russell argues that it hasn't. Using the tools of contemporary philosophy of language, she outlines a view of analytic sentences which is compatible with semantic externalism and defends that view against the old Quinean arguments. She then goes on to draw out the surprising epistemological consequences of her approach. (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.

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.

Philosophers have long analyzed the truth-condition of counterfactual conditionals in terms of the possible-worlds semantics advanced by Lewis [13] and Stalnaker [23]. In this paper, I argue that, from the perspective of philosophical semantics, the causal modeling semantics proposed by Pearl [17] and others (e.g., Briggs [3]) is more plausible than the Lewis-Stalnaker possible-worlds semantics. I offer two reasons. First, the possible-worlds semantics 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-worlds semantics to do so seems to cost it its distinctive status as a philosophical semantics. Second, the causal modeling semantics, but not the possible-worlds semantics, has the resources enough for accounting for both forward-tracking and backtracking counterfactual conditionals. (shrink)

Fitch´s problem and the "knowability paradox" involve a couple of argumentations that are to each other in the same relation as Cantor´s uncollected multitudes theorem and Russell´s paradox. The authors exhibit the logical nature of the theorem and of the paradox and show their philosophical import, both from an anti-realist and from a realist perspective. In particular, the authors discuss an anti-realist solution to Fitch´s problem and provide an anti-realist interpretation of the problematic statement "It is knowable that r (...) is known and yet unknown". Then, it is argued that the knowability paradox has a solution even if one adopts a realist point of view. The authors provide a solution that takes into account the ambiguity of the term 'knowability' by deploying a temporal possible world semantics for epistemic modalities. (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)

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)

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)