Reference and Existence, Saul Kripke's John Locke Lectures for 1973, can be read as a sequel to his classic Naming and Necessity. It confronts important issues left open in that work -- among them, the semantics of proper names and natural kind terms as they occur in fiction and in myth; negative existential statements; the ontology of fiction and myth. In treating these questions, he makes a number of methodological observations that go beyond the framework of his earlier book -- (...) including the striking claim that fiction cannot provide a test for theories of reference and naming. In addition, these lectures provide a glimpse into the transition to the pragmatics of singular reference that dominated his influential paper, " Speaker's Reference and Semantic Reference " -- a paper that helped reorient linguistic and philosophical semantics. Some of the themes have been worked out in later writings by other philosophers -- many influenced by typescripts of the lectures in circulation -- but none have approached the careful, systematic treatment provided here. The virtuosity of Naming and Necessity -- the colloquial ease of the tone, the dazzling, on-the-spot formulations, the logical structure of the overall view gradually emerging over the course of the lectures -- is on display here as well. (shrink)
are synthetic a priori judgements possible?" In both cases, i~thas usually been t'aken for granted in fife one case by Kant that synthetic a priori judgements were possible, and in the other case in contemporary,'d-". philosophical literature that contingent statements of identity are ppss. ible. I do not intend to deal with the Kantian question except to mention:ssj~".
Frege's theory of indirect contexts and the shift of sense and reference in these contexts has puzzled many. What can the hierarchy of indirect senses, doubly indirect senses, and so on, be? Donald Davidson gave a well-known 'unlearnability' argument against Frege's theory. The present paper argues that the key to Frege's theory lies in the fact that whenever a reference is specified (even though many senses determine a single reference), it is specified in a particular way, so that giving a (...) reference implies giving a sense; and that one must be 'acquainted' with the sense. It is argued that an indirect sense must be 'immediately revelatory' of its reference. General principles for Frege's doctrine of sense and reference are sated, for both direct and indirect quotation, to be understood iteratively. I also discuss Frege's doctrine of tensed and first person statements in the light of my analysis. The views of various other authors are examined. The conclusion is to ascribe to Frege an implicit doctrine of acquaintance similar to that of Russell. (shrink)
Writers on presupposition, and on the ‘‘projection problem’’ of determining the presuppositions of compound sentences from their component clauses, traditionally assign presuppositions to each clause in isolation. I argue that many presuppositional elements are anaphoric to previous discourse or contextual elements. In compound sentences, these can be other clauses of the sentence. We thus need a theory of presuppositional anaphora, analogous to the corresponding pronominal theory.
Despite the renown of ‘On Denoting’, much criticism has ignored or misconstrued Russell's treatment of scope, particularly in intensional, but also in extensional contexts. This has been rectified by more recent commentators, yet it remains largely unnoticed that the examples Russell gives of scope distinctions are questionable or inconsistent with his own philosophy. Nevertheless, Russell is right: scope does matter in intensional contexts. In Principia Mathematica, Russell proves a metatheorem to the effect that the scope of a single occurrence of (...) a description in an extensional context does not matter, provided existence and uniqueness conditions are satisfied. But attempts to eliminate descriptions in more complicated cases may produce an analysis with more occurrences of descriptions than featured in the analysand. Taking alternation and negation to be primitive (as in the first edition of Principia), this can be resolved, although the proof is non-trivial. Taking the Sheffer stroke to be primitive (as proposed by Russell in the second edition), with bad choices of scope the analysis fails to terminate. (shrink)
This important new book is the first of a series of volumes collecting essential work by an influential philosopher. It presents a mixture of published and unpublished works from various stages of Kripke's storied career. Included here are seminal and much discussed pieces such as “Identity and Necessity,” “Outline of a Theory of Truth,” and “A Puzzle About Belief.” More recent published work include “Russell's Notion of Scope” and “Frege's Theory of Sense and Reference” among others. Several of the works (...) included here are published for the first time, including both older works “Two Paradoxes of Knowledge,” “Vacuous Names and Fictional Entities,” “Nozick on Knowledge” as well as newer “The First Person” and “Unrestricted Exportation.” “A Puzzle on Time and Thought” was written for this volume. The publication of this volume—which ranges over epistemology, linguistics, pragmatics, philosophy of language, history of analytic philosophy, theory of truth, and metaphysics—represents a major event in contemporary analytic philosophy. This collection aims to be a testament to one of philosophy's greatest living figures. (shrink)
Under the influence of Quine’s famous manifesto, many philosophers have thought that logical theories are scientific theories that can be ‘adopted’ and tested as scientific theories. Here we argue that this idea is untenable. We discuss it with special reference to Putnam’s proposal to ‘adopt’ a particular non-classical logic to solve the foundational problems of quantum mechanics in his famous paper ‘Is Logic Empirical?’ (1968), which we argue was not really coherent.
In his paper on the incompleteness theorems, Gödel seemed to say that a direct way of constructing a formula that says of itself that it is unprovable might involve a faulty circularity. In this note, it is proved that ‘direct’ self-reference can actually be used to prove his result.
This paper is dedicated to the memory of Mike Dunn. His untimely death is a loss not only to logic, computer science, and philosophy, but to all of us who knew and loved him. The paper gives an argument for closure under γ in standard systems of relevance logic (first proved by Meyer and Dunn 1969). For definiteness, I chose the example of R. The proof also applies to E and to the quantified systems RQ and EQ. The argument uses (...) semantic tableaux (with one exceptional rule not satisfying the subformula property). It avoids the previous arguments’ use of cutting down inconsistent sets of formulas to consistent sets. Like all tableau arguments, it extends partial valuations to total valuations. (shrink)
The Hilbert program was actually a specific approach for proving consistency, a kind of constructive model theory. Quantifiers were supposed to be replaced by ε-terms. εxA(x) was supposed to denote a witness to ∃xA(x), or something arbitrary if there is none. The Hilbertians claimed that in any proof in a number-theoretic system S, each ε-term can be replaced by a numeral, making each line provable and true. This implies that S must not only be consistent, but also 1-consistent. Here we (...) show that if the result is supposed to be provable within S, a statement about all Pi-0-2 statements that subsumes itself within its own scope must be provable, yielding a contradiction. The result resembles Gödel's but arises naturally out of the Hilbert program itself. (shrink)
Several writers have assumed that when in “Outline of a Theory of Truth” I wrote that “the orthodox approach” – that is, Tarski’s account of the truth definition – admits descending chains, I was relying on a simple compactness theorem argument, and that non-standard models must result. However, I was actually relying on a paper on ‘pseudo-well-orderings’ by Harrison. The descending hierarchy of languages I define is a standard model. Yablo’s Paradox later emerged as a key to interpreting the result.
Traditionally, many writers, following Kleene (1952), thought of the Church-Turing thesis as unprovable by its nature but having various strong arguments in its favor, including Turing’s analysis of human computation. More recently, the beauty, power, and obvious fundamental importance of this analysis, what Turing (1936) calls “argument I,” has led some writers to give an almost exclusive emphasis on this argument as the unique justification for the Church-Turing thesis. In this chapter I advocate an alternative justification, essentially presupposed by Turing (...) himself in what he calls “argument II.” The idea is that computation is a special form of mathematical deduction. Assuming the steps of the deduction can be stated in a first order language, the Church-Turing thesis follows as a special case of Gödel’s completeness theorem (first order algorithm theorem). I propose this idea as an alternative foundation for the Church-Turing thesis, both for human and machine computation. Clearly the relevant assumptions are justified for computations presently known. Other issues, such as the significance of Gödel’s 1931 Theorem IX for the Entscheidungsproblem, are discussed along the way. (shrink)
This important new book is the first of a series of volumes collecting the essential articles by the eminent and highly influential philosopher Saul A. Kripke. It presents a mixture of published and unpublished articles from various stages of Kripke's storied career.
Wittgenstein gave a clearly erroneous refutation of Russell’s logicist project. The errors were ably pointed out by Mark Steiner. Nevertheless, I was motivated by Wittgenstein and Steiner to consider various ideas about the natural numbers. I ask which notations for natural numbers are ‘buck-stoppers’. For us it is the decimal notation and the corresponding verbal system. Based on the idea that a proper notation should be ‘structurally revelatory’, I draw various conclusions about our own concept of the natural numbers.
This book was inadvertently published with the addition of the editor’s name, C. J. Posy, as co-author of the chapter. His name has been removed now and the author’s name Saul A. Kripke has been updated in the chapter.
Most philosophers seem to be under a misleading impression about the difference between ‘and’ and ‘but’. They hold that they are truth-functional equivalents but that ‘but’ adds a Gricean ‘conventional implicature’ to ‘and’. Frege thought that the implicature attached to ‘but’ was that the second clause is unlikely given the first; others have simply said they express a contrast between the two. Though the second formulation may seem more general, in practice writers seem to agree with Frege's idea. The present (...) note will argue against this conventional view. Indeed, ‘and’ and ‘but’ may both convey conflicting implicatures; and the traditional characterization of the implicature of ‘but’ is outright mistaken, or at least misleading. (shrink)
In the Handbook of Mathematical Logic, the Paris-Harrington variant of Ramsey's theorem is celebrated as the first result of a long ‘search’ for a purely mathematical incompleteness result in first-order Peano arithmetic. This paper questions the existence of any such search and the status of the Paris-Harrington result as the first mathematical incompleteness result. In fact, I argue that Gentzen gave the first such result, and that it was restated by Goodstein in a number-theoretic form.