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175A Proof of GammaIn 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
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175The Road to GödelIn Jonathan Berg (ed.), Naming, Necessity and More: Explorations in the Philosophical Work of Saul Kripke, Palgrave-macmillan. 2014.
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174Semantical Analysis of Modal Logic II. Non-Normal Modal Propositional CalculiIn J. W. Addison (ed.), The theory of models, North-holland Pub. Co.. pp. 206-20. 1965.
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156The Undecidability of Monadic Modal Quantification TheoryMathematical Logic Quarterly 8 (2): 113-116. 1962.
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133Ungroundedness in Tarskian LanguagesJournal 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
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99Gödel’s Theorem and Direct Self-ReferenceReview 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.
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87Fine Kit. Model theory for modal logic. Part I—the de re/de dicto distinction. Journal of philosophical logic, vol. 7 , pp. 125–156.Fine Kit. Model theory for modal logic—part II. The elimination of de re modality. Journal of philosophical logic, vol. 7 , pp. 277–306.Fine Kit. Model theory for modal logic—part III. Existence and predication. Journal of philosophical logic, vol. 10 , pp. 293–307 (review)Journal of Symbolic Logic 50 (4): 1083-1093. 1985.
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86Free Choice Sequences: A Temporal Interpretation Compatible with Acceptance of Classical MathematicsIndagationes Mathematicae 30 (3): 492-499. 2019.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
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73Mathematical Incompleteness Results in First-Order Peano Arithmetic: A Revisionist View of the Early HistoryHistory and Philosophy of Logic 43 (2): 175-182. 2021.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.
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66Wittgenstein, Russell, and Our Concept of the Natural NumbersIn Carl Posy & Yemima Ben-Menahem (eds.), Mathematical Knowledge, Objects and Applications: Essays in Memory of Mark Steiner, Springer. pp. 137-155. 2023.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
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63The collapse of the Hilbert program: A variation on the gödelian themeBulletin 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
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46Review: Kit Fine, Failures of the Interpolation Lemma in Quantified Modal Logic (review)Journal of Symbolic Logic 48 (2): 486-488. 1983.
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40Deduction-preserving ‘Recursive Isomorphisms’ between TheoriesFundamenta Mathematicae 61 141-163. 1967.
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23Correction to: Wittgenstein, Russell, and our Concept of the Natural NumbersIn Carl Posy & Yemima Ben-Menahem (eds.), Mathematical Knowledge, Objects and Applications: Essays in Memory of Mark Steiner, Springer. 2023.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.
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8A priori knowledge, necessity, and contingencyIn Paul K. Moser (ed.), A priori knowledge, Oxford University Press. 1987.
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3Selection from Naming and NecessityIn Tim Crane & Katalin Farkas (eds.), Metaphysics: a guide and anthology, Oxford University Press Uk. 2004.
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2C. The Mental-Physical ContrastIn David M. Rosenthal (ed.), The Nature of Mind, Oxford University Press. pp. 236. 1991.
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1Naming and NecessityIn John Heil (ed.), Philosophy of Mind: A Guide and Anthology, Oxford University Press. 2003.
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1A Priori Knowledge, Necessity, and ContingencyIn Sven Bernecker & Fred I. Dretske (eds.), Knowledge: Readings in Contemporary Epistemology, Oxford University Press. 2000.
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Identitatea eta beharrezkotasunaIn Agustin Arrieta Urtizberea (ed.), Egia motak, Universidad Del País Vasco, Servicio Editorial. 2001.
Saul Kripke
(1940 - 2022)
New York City, New York, United States of America
Areas of Interest
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