•  15
    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.
  •  480
    The Question of Logic
    Mind 133 (529): 1-36. 2023.
    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.
  •  53
    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 concep…Read more
  • Identitatea eta beharrezkotasuna
    In Agustin Arrieta Urtizberea (ed.), Egia motak, Universidad Del País Vasco, Servicio Editorial. 2001.
  •  161
    A Proof of Gamma
    In Katalin Bimbo (ed.), Essays in Honor of J. Michael Dunn, College Publications. pp. 261-265. 2022.
    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 subf…Read more
  •  85
    Gödel’s Theorem and Direct Self-Reference
    Review of Symbolic Logic 16 (2): 650-654. 2023.
    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.
  •  56
    The collapse of the Hilbert program: A variation on the gödelian theme
    Bulletin of Symbolic Logic 28 (3): 413-426. 2022.
    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 tha…Read more
  •  57
    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.
  •  1
    A Priori Knowledge, Necessity, and Contingency
    In Sven Bernecker & Fred I. Dretske (eds.), Knowledge: Readings in Contemporary Epistemology, Oxford University Press. 2000.
  •  1
    Naming and Necessity
    In John Heil (ed.), Philosophy of Mind: A Guide and Anthology, Oxford University Press. 2003.
  •  204
    Fregean Quantification Theory
    Journal of Philosophical Logic 43 (5): 879-881. 2013.
    Frege’s system of first-order logic is presented in a contemporary framework. The system described is distinguished by economy of expression and an unusual syntax.
  •  1581
    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 ref…Read more
  •  78
    This paper sketches a way of supplementing classical mathematics with a motivation for a Brouwerian theory of free choice sequences. The idea is that time is unending, i.e. that one can never come to an end of it, but also indeterminate, so that in a branching time model only one branch represents the ‘actual’ one. The branching can be random or subject to various restrictions imposed by the creating subject. The fact that the underlying mathematics is classical makes such perhaps delicate issue…Read more
  •  128
    Ungroundedness in Tarskian Languages
    Journal of Philosophical Logic 48 (3): 603-609. 2019.
    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 re…Read more
  •  1091
    Speaker’s Reference and Semantic Reference
    Midwest Studies in Philosophy 2 (1): 255-276. 1977.
    am going to discuss some issues inspired by a well-known paper ofKeith Donnellan, "Reference and Definite Descriptions,”2 but the interest—to me—of the contrast mentioned in my title goes beyond Donnellan's paper: I think it is of considerable constructive as well as critical importance to the philosophy oflanguage. These applications, however, and even everything I might want to say relative to Donnellan’s paper, cannot be discussed in full here because of problems of length. Moreover, although…Read more
  •  335
    History and Idealism: The Theory of R.G. Collingwood
    Collingwood and British Idealism Studies 23 (1): 9-29. 2017.
  •  177
    ‘And’ and ‘But’: A Note
    Thought: A Journal of Philosophy 6 (2): 102-105. 2017.
    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 i…Read more
  •  355
    Philosophical Troubles. Collected Papers Vol I (edited book)
    Oxford University Press. 2011.
    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…Read more
  •  126
    Nonstandard Models of Peano Arithmetic
    with S. Kochen
    L’Enseignement Mathematique (3-4): 211-231. 1982.
  •  147
    The Undecidability of Monadic Modal Quantification Theory
    Mathematical Logic Quarterly 8 (2): 113-116. 1962.
  •  396
    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 advoc…Read more