This is a thorough treatment of first-order modal logic. The book covers such issues as quantification, equality (including a treatment of Frege's morning star/evening star puzzle), the notion of existence, non-rigid constants and function symbols, predicate abstraction, the distinction between nonexistence and nondesignation, and definite descriptions, borrowing from both Fregean and Russellian paradigms.

Fitch’s argument purports to show that for any unknown truth, p , there is an unknowable truth, namely, that p is true and unknown; for a contradiction follows from the assumption that it is possible to know that p is true and unknown. In earlier work I argued that there is a sense in which it is possible to know that p is true and unknown, from a counterfactual perspective; that is, there can be possible, non-actual knowledge, of the actual (...) situation, that in that situation, p is true and unknown. Here I further elaborate that claim and respond to objections by Williamson, who argued that there cannot be non-trivial knowledge of this kind. I give conditions which suffice for such non-trivial counterfactual knowledge. (shrink)

But Findlay's remark, like so much that has been written on the subject of time in the present century, was provoked in the first place by McTaggart's ...

This is a revised and expanded edition of a seminal work in the logic and philosophy of time, originally published in 1968. Arthur N. Prior (1914-1969) was the founding father of temporal logic, and his book offers an excellent introduction to the fundamental questions in the field. Several important papers have been added to the original selection, as well as a comprehensive bibliography of Prior's work and an illuminating interview with his widow, Mary Prior. In addition, the Polish logic which (...) made Prior's writings difficult for many readers has been replaced by standard logical notation. This new edition will secure the classic status of the book. (shrink)

Knowledge and its Limits presents a systematic new conception of knowledge as a kind of mental stage sensitive to the knower's environment. It makes a major contribution to the debate between externalist and internalist philosophies of mind, and breaks radically with the epistemological tradition of analyzing knowledge in terms of true belief. The theory casts new light on such philosophical problems as scepticism, evidence, probability and assertion, realism and anti-realism, and the limits of what can be known. The arguments are (...) illustrated by rigorous models based on epistemic logic and probability theory. The result is a new way of doing epistemology and a notable contribution to the philosophy of mind. (shrink)

We introduce and study hierarchies of extensions of the propositional modal and temporal languages with pairs of new syntactic devices: point of reference-reference pointer which enable semantic references to be made within a formula. We propose three different but equivalent semantics for the extended languages, discuss and compare their expressiveness. The languages with reference pointers are shown to have great expressive power (especially when their frugal syntax is taken into account), perspicuous semantics, and simple deductive systems. For instance, Kamp's and (...) Stavi's temporal operators, as well as nominals (names, clock variables), are definable in them. Universal validity in these languages is proved undecidable. The basic modal and temporal logics with reference pointers are uniformly axiomatized and a strong completeness theorem is proved for them and extended to some classes of their extensions. (shrink)

If it is an unknown truth that p, it is an unknowable truth that it is an unknown truth that p . It follows, by classical logic, that if all truths are knowable then all truths are known. This hardish fact makes life difficult for the verificationist who wishes to assert that all truths are knowable, but to deny that all truths are known. He might try rejecting classical logic . Dorothy Edgington has recently suggested a different way out . (...) She admits that there are unknowable truths in the sense of Fitch's argument, but interestingly revises the verificationist principle, to give it this form: if, in a situation s, it is a truth that p, then there is a possible situation s' in which it is known that, in s, p. Although the truth that, in s, it is an unknown truth that p cannot be known in s, it might be known in some possible situation other than s. I have argued elsewhere that this account faces difficulties of principle in explaining how the knower in s' can pick out the situations in thought with adequate specificity . I waive those objections here, to examine Edgington's application of her principle to a particular case of knowledge in one situation that something is an unknown truth in another. I shall argue that her account does not generalize to the full range of cases which it needs to cover. (shrink)

This is a companion paper to Braüner where a natural deduction system for propositional hybrid logic is given. In the present paper we generalize the system to the first-order case. Our natural deduction system for first-order hybrid logic can be extended with additional inference rules corresponding to conditions on the accessibility relations and the quantifier domains expressed by so-called geometric theories. We prove soundness and completeness and we prove a normalisation theorem. Moreover, we give an axiom system first-order hybrid logic.

Hybrid languages have both modal and first-order characteristics: a Kripke semantics, and explicit variable binding apparatus. This paper motivates the development of hybrid languages, sketches their history, and examines the expressive power of three hybrid binders. We show that all three binders give rise to languages strictly weaker than the corresponding first-order language, that full first-order expressivity can be gained by adding the universal modality, and that all three binders can force the existence of infinite models and have undecidable satisfiability (...) problems. (shrink)

The paradox of knowability poses real difficulities to our understanding of truth. It does so by claiming that if we assume a truth is knowable, we can demonstrate that it is known. This demonstration threatens our understanding of truth in two quite different ways, only one of which has been recognized to this point in the literature on the paradox. Jonathan Kvanvig first unearths the ways in which the paradox is threatening, and then delineates an approach to the paradox that (...) solves both of the problems raised by the paradox for our understanding of truth. His book will be of interest throughout philosophy, but especially to logicians and epistemologists. (shrink)

In this paper, I propose a solution to Fitch’s paradox that draws on ideas from Edgington (Mind 94:557–568, 1985), Rabinowicz and Segerberg (1994) and Kvanvig (Noûs 29:481–500, 1995). After examining the solution strategies of these authors, I will defend the view, initially proposed by Kvanvig, according to which the derivation of the paradox violates a crucial constraint on quantifier instantiation. The constraint states that non-rigid expressions cannot be substituted into modal positions. We will introduce a slightly modified syntax and semantics (...) that will help underline this point. Furthermore, we will prove results about the consistency of verificationism and the principle of non-omniscience by model-theoretical means. Namely, we prove there exists a model of these principles, and delineate certain constraints they pose on a structure in which they are true. (shrink)

The purpose of the present paper is to challenge some received assumptions about the logical analysis of modal English, and to show that these assumptions are crucial to certain debates in current philosophy of language. Specifically, I will argue that the standard analysis in terms of quantified modal logic mistakenly fudges important grammatical distinctions, and that the validity of Kripke's modal argument against description theories of proper names crucially depends on ensuing equivocations.

The title reflects my conviction that, viewed semantically,modal logic is fundamentally dialogical; this conviction is based on the key role played by the notion of bisimulation in modal model theory. But this dialogical conception of modal logic does not seem to apply to modal proof theory, which is notoriously messy. Nonetheless, by making use of ideas which trace back to Arthur Prior (notably the use of nominals, special proposition symbols which ‘name’ worlds) I will show how to lift the dialogical (...) conception to modal proof theory. I argue that this shift to hybrid logic has consequences for both modal and dialogical logic, and I discuss these in detail. (shrink)

Natural language provides motivation for studying modal backwards-looking operators such as “now”, “then” and “actually” that evaluate their argument formula at some previously considered point instead of the current one. This paper investigates the expressive power over models of both propositional and first-order basic modal language enriched with such operators. Having defined an appropriate notion of bisimulation for first-order modal logic, I show that backwards-looking operators increase its expressive power quite mildly, contrary to beliefs widespread among philosophers of language and (...) formal semanticists. That in turn presents a strong argument for the use of operator-based systems in the semantics of natural language, instead of systems with explicit quantification over worlds and times that have become a de-facto standard for such applications. The popularity of such explicit-quantification systems is shown to be based on the misinterpretation of a claim by Cresswell, which led many philosophers and linguists to assume that introducing “now” and “then” is expressively equivalent to explicitly quantifying over worlds and times. (shrink)

The paradox of knowability threatens to draw a logical equivalence between the believable claim that all truths are knowable and the obviously false claim that all truths are known. In this paper we evaluate prominent proposals for resolving the paradox of knowability. For instance, we argue that Neil Tennant’s restriction strategy, which aims principally to restrict the main quantifier in ‘all truths are knowable’, does not get to the heart of the problem since there are knowability paradoxes that the restriction (...) does nothing to thwart. We argue that Jon Kvanvig’s strategy, which aims to block the paradox by appealing to the special role of quantified epistemic expressions in modal contexts, has grave errors. We offer here a new proposal founded on Kvanvig’s insight that quantified expressions play a special role in modal contexts. On an articulation of this special role provided by Stanley and Szabo, we propose a solution to the knowability paradoxes. Introduction.. (shrink)