This bibliography records Hilary Putnam’s contributions to mathematics, logic, their philosophy, and related matters. Needless to say, the border between those works that, strictly speaking, address logic and mathematics, and those that address other areas of philosophy, is fuzzy when dealing with a philosopher as systematic and as wide-ranging as Putnam. Thus, we have had to make some decisions – decisions that might not be the same decisions that the reader would have made if given the same task. For example, we have included many (but not all) of the more philosophical papers on truth, but have only included papers on confirmation when they directly address mathematical or logical, rather than scientific, issues and concerns. Nevertheless, we hope that this bibliography will be useful to readers interested in Putnam’s extensive and important work in mathematics and logic.

We have given original publication information, and (with the exception of Putnam’s PhD dissertation) noted reprints only when they occur in collections of Putnam’s essays also included on this list (i.e. those that contain a significant number of papers on mathematics and logic).

 

(1951):

The Meaning of the Concept of Probability in Application to Finite Sequences, PhD Dissertation, University of California – Los Angeles, 1951. Reprinted New York: Garland, 1991; London, Routledge: 2011.

(1956):

“Mathematics and the Existence of Abstract Entities”, Philosophical Studies 7(6): 81–88.

(1957a):

“Arithmetic Models for Consistent Formulae of Quantification Theory”, Journal of Symbolic Logic 22(1): 110–111.

(1957b):

“Decidability and Essential Undecidability”, Journal of Symbolic Logic 22(1): 39–54.

(1957c):

“Eine Unableitbarkeitsbeweismethode für den Intuitionistischen Aussagenkalkül” (w/ George Kreisel), Archiv für Mathematische Logik und Grundlagenforschung 3(1–2): 74–78.

(1957d):

“Review of Hughes Leblac”, An Introduction to Deductive Logic, Philosophical Review 66(4): 551–554.

(1957e):

“Three-Valued Logic”, Philosophical Studies 8(5): 73–80. Reprinted in (1975a): 166–173.

(1958a):

“Elementary Logic and Foundations of Set Theory”, in Philosophy in the Mid-Century (Raymond Klibansky, ed.), Florence: La Nuova Italia Editrice: 56–61.

(1958b):

“Feasible Computational Methods in the Propositional Calculus” (w/ Martin Davis), Troy, NY: Rensselaer Polytechnical Institute, Research Division.

(1958c):

“Formalization of the Concept ‘About’ ”, Philosophy of Science 25(2): 125–130.

(1958d):

“Reduction of Hilbert’s Tenth Problem”, (w/ Martin Davis), Journal of Symbolic Logic 23(2): 183–187.

(1959):

“Review of Raphael Robinson, “Arithmetical Representation of Recursively Enumerable Sets””, Journal of Symbolic Logic 24(2): 170–171.

(1960a):

“A Computing Procedure for Quantification Theory” (w/ Martin Davis), Journal of the Association of Computing Machinery 7(3): 201–215.

(1960b):

“An Unsolvable Problem in Number Theory”, Journal of Symbolic Logic 25(3): 220–232.

(1960c):

“Exact Separation of Recursively Enumerable Sets Within Theories” (w/ Raymond Smullyan), Proceedings of the American Mathematical Society 11(4): 574–577.

(1960d):

“Minds and Machines”, in Dimensions of Mind, (Sydney Hook, ed.), New York: New York University Press: 138–164. Reprinted in (1975b): 362–385.

(1960e):

“Review of Ernest Nagel and James E. Newman, Gödel’s Proof”, Philosophy of Science 27(2): 205–207.

(1961a):

“The Decision Problem for Exponential Diophantine Equations” (w/ Martin Davis & Julia Robinson), Annals of Mathematics 74(3): 425–436.

(1961b):

“Some Issues in the Theory of Grammar”, in The Structure of Language and Its Mathematical Aspects: Proceedings of a Symposium in Applied Mathematics (Roman Jakobson ed.), Providence, Rhode Island: American Mathematical Society: 25–42. Reprinted in (1975b): 85–106.

(1961c):

“Uniqueness Ordinals in Higher Constructive Number Classes”, in Essays on the Foundations of Mathematics Dedicated to A. A. Fraenkel on his Seventieth Anniversary (Yoshua Bar-Hillel et alia, eds.) Jerusalem: The Hebrew University Magness Press: 190–206.

(1962a):

“Dreaming and ‘Depth Grammar’ ”, in Analytical Philosophy, First Series (R. J. Butler, ed.), Oxford: Basil Blackwell: 211–235. Reprinted in (1975b): 304–324.

(1962b):

“On Families of Sets Represented in Theories”, Archiv für Mathematische Logik und Grundlagenforschung 6(1–2): 66–70.

(1962c):

“Review of Hakan Törnebohm ‘On Two Logical Systems Proposed in the Philosophy of Quantum-mechanics’ ”, Journal of Symbolic Logic 27(1): 115.

(1963a):

“A Note on Constructible Sets of Integers”, Notre Dame Journal of Formal Logic 4(4): 270–273.

(1963b):

“An Examination of Grünbaum’s Philosophy of Geometry”, in Philosophy of Science: The Delaware Seminar Volume 2, 1962–1963, (Bernard Baumrin, ed.), New York: John Wiley: 205–255.

(1963c):

“‘Degree of Confirmation’ and Inductive Logic”, in The Philosophy of Rudolph Carnap (Paul A. Schilpp, ed.): 761–783. Reprinted in (1975a): 270–292.

(1963d):

“Diophantine Sets Over Polynomial Rings”, (w/ Martin Davis), Illinios Journal of Mathematics 7(2): 251–256.

(1963e):

“Probability and Confirmation”, The Voice of America Forum Lectures: Philosophy of Science Series Number 10: 1–11. Reprinted in (1975a): 293–304.

(1963f):

“Review of Georg Henrik von Wright, Logical Studies”, Philosophical Review 72(2): 242–249.

(1964a):

Philosophy of Mathematics: Selected Readings (ed., w/ Paul Benacerraf), Englewood Cliffs, New Jersey: Prentice Hall. 2nd Edition 1983, Cambridge UK: Cambridge University Press.

(1964b):

“On Hierarchies and Systems of Notations”, Proceedings of the American Mathematical Society 15(1): 44–50.

(1965a):

“Craig’s Theorem”, Journal of Philosophy 62(10): 251–260. Reprinted in (1975a): 228–236.

(1965b):

“On Minimal and Almost-Minimal Systems of Notation” (w/ David Luckham), Transactions of the American Mathematical Society 119(1): 86–100.

(1965c):

“On the Notational Independence of Various Hierarchies of Degrees of Unsolvability” (w/ Gustav Hensel), Journal of Symbolic Logic 30(1): 69–86.

(1965d):

“Recursively Enumerable Classes and Their Application to Recursive Sequences of Formal Theories”, (w/ Marian Boykan Pour-el), Archiv für Mathematische Logik und Grundlagenforschung 8(3–4): 104–121.

(1965e):

“Trial and Error Predicates and the Solution to a Problem of Mostowski”, Journal of Symbolic Logic 30(1): 49–57.

(1967a):

“The Craig Interpolation Lemma” (w/ Burton Dreben), Notre Dame Journal of Formal Logic 8(3): 229–233.

(1967b):

“Mathematics without Foundations”, Journal of Philosophy 64(1): 5–22. Reprinted in (1975a): 43–59. Reprinted in (1983b): 295–313.

(1967c):

“The Thesis that Mathematics is Logic”, in Bertrand Russell: Philosopher of the Century (Ralph Schoenman ed.), London: Allen & Unwin: 273–303. Reprinted in (1975a): 12–42.

(1967d):

“Time and Physical Geometry”, Journal of Philosophy 64(8): 240–247. Reprinted in (1975a): 198–205.

(1968a):

“Degrees of Unsolvability of Constructible Sets of Integers”, (w/ George Boolos), Journal of Symbolic Logic 33(4): 497–513.

(1968b):

“Is Logic Empirical?”, in Boston Studies in the Philosophy of Science Volume 5 (Robert Cohen & Marx Wartofsky eds.), Dordrecht: D. Reidel: 216–241. Reprinted as “The Logic of Quantum Mechanics” in (1975a): 174–197.

(1969a):

“Normal Models and the Field of \(\Sigma _1\)” (w/ Gustav Hensel) Fundamentae Mathematicae 64(2): 231–240.

(1969b):

“A Recursion-theoretic Characterization of the Ramified Analytic Hierarchy”, (w/ Gustav Hensel & Richard Boyd), Transactions of the American Mathematical Society 141: 37–62.

(1970):

“A Note on the Hyperarithmetical Hierarchy”, (w/ Herbert Enderton), Journal of Symbolic Logic 35(3): 429–430.

(1971a):

Philosophy of Logic, New York: Harper and Row. Reprinted in (1975a), 2nd edition: 323–357.

(1971b):

“An Intrinsic Characterization of the Hierarchy of Constructible Sets of Integers” (w/ Stephen Leeds), in Logic Colloquium ’69 (Robin Grandy & Charles Yates eds.), Amsterdam: North Holland: 311–350.

(1973):

“Recursive Functions and Hierarchies”, American Mathematical Monthly: Supplement: Papers in the Foundations of Mathematics 80(6): 68–86.

(1974a):

“How to Think Quantum-Logically”, Synthese 29(1–4): 55–61.

(1974b):

“Solution to a Problem of Gandy’s” (w/ Stephen Leeds), Fundamentae Mathematica 81(2): 99–106.

(1974c):

“Systems of Notations and the Ramified Analytic Hierarchy” (w/ Joan Lukas), Journal of Symbolic Logic 39(2): 243–253.

(1975a):

Mathematics, Matter, and Method: Philosophical Papers, Volume 1, Cambridge MA: Cambridge University Press. 2nd Edition 1979, Cambridge UK: Cambridge University Press.

(1975a):

Mind, Language, and Reality: Philosophical Papers, Volume 2, Cambridge MA: Cambridge University Press.

(1975c):

“What is Mathematical Truth?”, Historia Mathematica 2(4): 529–533. Reprinted in (1975a): 60–78.

(1978):

“Quantum Logic, Conditional Probability, and Interference”, (w/ Michael Friedman), Dialectica 32(3–4): 305–315.

(1979):

“Philosophy of Mathematics: A Report”, Current Research in Philosophy of Science: Proceedings of the P.S.A. Critical Research Problems Conference (Peter Asquith & Henry Kyburg eds.), East Lansing MI: Philosophy of Science Association: 386–398. Reprinted as “Philosophy of Mathematics: Why Nothing Works” in (1994a): 499–512.

(1980):

“Models and Reality”, Journal of Symbolic Logic 45(3): 464–482. Reprinted in (1983a): 1–25. Reprinted in (1983b): 421–445.

(1982):

“Peirce the Logician”, Historia Mathematica 9(3): 290–301. Reprinted in (1990): 252–260.

(1983):

“Vagueness and Alternative Logic”, Erkenntnis 19(1–3): 297–314. Reprinted in (1983a): 271–285.

(1984):

“Proof and Experience”, Proceedings of the American Philosophical Society 128(1): 31–34.

(1983a):

Realism and Reason: Philosophical Papers, Volume 3, Cambridge MA: Cambridge University Press.

(1983b):

Philosophy of Mathematics: Selected Readings (ed., w/ Paul Benacerraf), 2nd Edition 1983, Cambridge UK: Cambridge University Press.

(1989):

“Model Theory and the ‘Factuality’ of Semantics”, in Reflections on Chomsky (Alex George ed.), Oxford: Basil Blackwell: 213–232. Reprinted in (1994a): 351–375.

(1990):

Realism with a Human Face, James Conant (ed.), Cambridge MA: Cambridge University Press.

(1991):

“Does the Disquotational Theory Really Solve All Philosophical Problems?”, Metaphilosophy 22(1–2): 1–13. Reprinted as “Does the Disquotational Theory of Truth Really Solve All Philosophical Problems?” in (1994a): 264–278.

(1992a):

“Comments on the Lectures”, Reasoning and the Logic of Things, Charles Sanders Peirce (Kenneth Ketner ed.), Cambridge: MA: Harvard University Press: 1–54.

(1992b):

“Introduction: The Consequence of Mathematics”, Reasoning and the Logic of Things, Charles Sanders Peirce (Kenneth Ketner ed.), Cambridge: MA: Harvard University Press: 1–54.

(1994a):

Words and Life, James Conant (ed.), Cambridge MA: Harvard University Press.

(1994b):

“Afterthoughts on ‘Models and Reality”’, Diálogos 29(63): 7–39.

(1994c):

“Logic and Psychology”, in The Logical Foundations of Cognition: Vancouver Studies in Cognitive Science Volume 4 (John Macnamara & Gonzalo Reyes eds.), Oxford: Oxford University Press: 35–42.

(1994d):

“Mathematical Necessity Reconsidered”, in On Quine: New Essays (Paulo Leonardi & Marco Santambrogio eds.), Cambridge UK: Cambridge University Press: 267–282. Reprinted as “Rethinking Mathematical Necessity” in (1994a): 245–263.

(1995):

“Peirce’s Continuum”, in Peirce and Contemporary Thought: Philosophical Inquiries (Kenneth Ketner ed.), New York: Fordham Press: 1–22.

(1996):

“On Wittgenstein’s Philosophy of Mathematics”, Proceedings of the Aristotelian Society 70 Supplement: 243–264.

(1997a):

“James’ Theory of Truth”, in The Cambridge Companion to William James (Ruth Putnam, ed.), Cambridge UK: Cambridge University Press: 166–185.

(2000a):

“A Note on Wittgenstein’s ‘Notorious Paragraph’ About the Gödel Theorem” (w/ Juliet Floyd) Journal of Philosophy 97(11): 624–632.

(2000b):

“Nonstandard Models and Kripke’s Proof of the Gödel Theorem”, Notre Dame Journal of Formal Logic 41(1): 53–58. Reprinted in (2012a): 263–269.

(2000c):

“Paradox Revisited I: Truth”, in Between Logic and Intuition: Essays in Honor of Charles Parsons (Gila Sher & Richard Tieszen eds.), Cambridge UK: Cambridge University Press: 3–15. Reprinted as “Revisiting the Liar Paradox” in (2012a): 202–215.

(2000c):

“Paradox Revisited II: Sets”, in Between Logic and Intuition: Essays in Honor of Charles Parsons (Gila Sher & Richard Tieszen eds.), Cambridge UK: Cambridge University Press: 16–26.

(2001):

“Was Wittgenstein Really an Anti-Realist about Mathematics?”, Philosophical Explorations 4(1): 2–16. An Expanded version of (1996). Reprinted in (2012a): 495–513.

(2005):

“James on Truth (Again)”, in William James and the Varieties of Religious Experience: A Centenary Celebration (Jeremy Carrette ed.), London & New York: Routledge: 172–182.

(2006a):

“After Gödel”, Logic Journal of the IGPL 14(5): 745–759. Reprinted in (2012a): 256–262.

(2006b):

“Bays, Steiner, and Wittgenstein’s ‘Notorious’ Paragraph about the Gödel Theorem” (w/ Juliet Floyd), Journal of Philosophy 103(2): 101–110.

(2007):

“Wittgenstein and the Real Numbers”, in Wittgenstein and the Moral Life (Alice Crary ed.), Cambridge MA: MIT Press: 235–250. Reprinted in (2012a): 442–457.

(2008):

“A Note on Steiner on Wittgenstein, Gödel, and Tarski”, Proceedings and Addresses of the American Philosophical Association 82(2): 101–115.

(2010):

“Between Dolev and Dummett: Some Comments on Antirealism, Presentism, and Bivalence”, International Journal of Philosophical Studies 18(1): 91–96.

(2011):

“The Gödel Theorem and Human Nature”, in Kurt Gödel and the Foundations of Mathematics: Horizons of Truth (Matthias Baaz, ed.) Cambridge UK: Cambridge University Press. Reprinted in (2012a): 239–255.

(2012a):

Philosophy in an Age of Science: Physics, Mathematics, and Skepticism, (Mario De Caro & David MacArthur eds.), Cambridge MA: Cambridge University Press.

(2012b):

“On Mathematics, Realism, and Ethics”, Harvard Review of Philosophy 18(1): 143–160.