Linked bibliography for the SEP article "Formalism in the Philosophy of Mathematics" by Alan Weir
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If everything goes well, this page should display the bibliography of the aforementioned article as it appears in the Stanford Encyclopedia of Philosophy, but with links added to PhilPapers records and Google Scholar for your convenience. Some bibliographies are not going to be represented correctly or fully up to date. In general, bibliographies of recent works are going to be much better linked than bibliographies of primary literature and older works. Entries with PhilPapers records have links on their titles. A green link indicates that the item is available online at least partially.
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- Awodey, Steve, 2014, ‘Structuralism, Invariance, and Univalence’, Philosophia Mathematica (III), 22: 135–159. (Scholar)
- Azzouni, Jody, 2004, ‘The Derivation-Indicator View of Mathematical Practice’, Philosophia Mathematica, (III) 12: 81–105. (Scholar)
- –––, 2005, ‘How to Nominalize Formalism’, Philosophia Mathematica (III), 13: 135–159. (Scholar)
- –––, 2006, Tracking Reason: Proof, Consequence and Truth, Oxford: Oxford University Press (especially Chapter 7). (Scholar)
- –––, 2009, ‘Why do Informal Proofs Conform to Formal Norms’, Foundations of Science, 14: 9–26. (Scholar)
- Barendregt, H.P., 1984, The Lambda Calculus, Amsterdam: North Holland. (Scholar)
- Boolos, George, 1987, ‘A Curious Inference’, Journal of Philosophical Logic, 16: 1–12; reprinted in George Boolos, Logic, Logic and Logic Cambridge, MA: Harvard University Press, 1998, 376–82. (Scholar)
- Carnap, Rudolf, 1934 [1937], Logische Syntax der Sprache, Vienna: Springer; translated by A. Smeaton as The Logical Syntax of Language, London: Kegan, Paul, Trench, Trubner & Co. 1937. (Scholar)
- –––, 1950 [1956], ‘Empiricism, Semantics and Ontology’, Revue Internationale de Philosophie, 4: 20–40; reprinted in Meaning and Necessity, Chicago: University of Chicago Press, 2nd edition, 1956: 205–221. (Scholar)
- Church, Alonzo, 1932, ‘A Set of Postulates for the Foundation of Logic’, Annals of Mathematics, 33(2): 346–366. (Scholar)
- –––,1940, ‘A Formulation of the Simple Theory of Types’, Journal of Symbolic Logic, 5(2): 56–68. (Scholar)
- Cohen, Paul, 1971, ‘Comments on the foundations of set theory’, in Dana Scott (ed.), Axiomatic Set Theory: Proceedings of Symposia in Pure Mathematics (Volume 13), Providence: American Mathematical Society: 9–15. (Scholar)
- Curry, Haskell, 1951, Outlines of Formalist Philosophy of Mathematics, Amsterdam: North Holland. (Scholar)
- Curry, Haskell and Feys, Robert, 1958, Combinatory Logic, Amsterdam: North Holland. (Scholar)
- Detlefsen, Michael, 1993, ‘Hilbert’s Formalism’, Revue Internationale de Philosophie, 47(186): 285–304. (Scholar)
- –––, 2005, ‘Formalism’, in Stewart Shapiro (ed.), The Oxford Handbook of Philosophy of Mathematics and Logic, Oxford: Oxford University Press, 236–317. (Scholar)
- Dummett, Michael, 1975, ‘Wang’s Paradox,” Synthese, 30(3/4): 301–324 reprinted in Truth and Other Enigmaas London: Duckworth, 248–268. (Scholar)
- –––, 1991, Frege, Philosophy of Mathematics, London: Duckworth. (Scholar)
- Field, Hartry, 1989, Realism, Mathematics and Modality, Oxford: Blackwell. (Scholar)
- Floyd, Juliet, 2002, ‘Number and Ascriptions of Number in Wittgenstein’s Tractatus’, in From Frege to Wittgenstein: Perspectives on Early Analytic Philosophy, Erich H. Reck (ed.), Oxford: Oxford University Press, 308–352. (Scholar)
- Floyd, Juliet and Putnam, Hilary, 2000, “A Note on Wittgenstein’s ‘Notorious Paragraph’ about the Gödel Theorem”, Journal of Philosophy, 97: 624–632. (Scholar)
- Frege, Gottlob, 1903, Grundgesetze der Arithmetik, Begriffsschriftlich Abgeleitet (Volume II), Jena: Pohle; reprinted 1962, Hildesheim: George Olms. (Scholar)
- –––, 1903 [1980], ‘Frege Against the Formalists: Vol II of Frege 1903, §§86–137) in Black and Geach (1980): 162–213. (Scholar)
- Gabbay, Michael, 2010, ‘A Formalist Philosophy of Mathematics, Part I: Arithmetic’, Studia Logica, 96: 219–238. (Scholar)
- Giaquinto, Marcus, 2002, The Search for Certainty, Oxford: Clarendon. (See especially 210ff). (Scholar)
- Gödel, Kurt, 1953–9, ‘Is Mathematics Syntax of Language’, in S. Feferman et al. (eds.), Kurt Gödel: Collected Works (Volume III), New York: Oxford University Press, 1995: 334–362, (Scholar)
- Goldfarb, Warren, 1995, “Introduction to Gödel’s ‘Is Mathematics Syntax of Language’” in S. Feferman et al. (eds.), Kurt Gödel: Collected Works (Volume III), New York: Oxford University Press, 1995: 324–34. (Scholar)
- Goodman, Nelson and Quine, W. V., 1947, ‘Steps towards a Constructive Nominalism’, Journal of Symbolic Logic, 12: 97–122. (Scholar)
- Griffin, Timothy, 1990, ‘A Formulae–as–Types Notion of Control’, in Principles of Programming Languages, Association of Computing Machinery, 47‐58. (Scholar)
- Hintikka, Jaakko, 1956, ‘Identity, variables, and impredicative definitions,’ Journal of Symbolic Logic, 21: 225–45. (Scholar)
- Howard, W.A., 1969, ‘The Formula-as-Types Notion of Construction’, in Seldin, J.P. and Hindley, J.R. (eds.) To H.B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, London: Academic Press, 1980: 479–490. (Scholar)
- Hylton, Peter, 1997 ‘Functions, Operations and Sense in Wittgenstein’s Tractatus’, in W.W. Tait (ed.), Early analytic philosophy: Frege, Russell, Wittgenstein: essays in honor of Leonard Linsky, Chicago: Open Court: 91–106. (Scholar)
- Kaplan, David, 1989, ‘Demonstratives’, in J. Almog, J. Perry, and H. Wettstein (eds.), Themes from Kaplan, New York: Oxford University Press, 481‐563. (Scholar)
- Kleene, Stephen, and Rosser, J.B., 1935, ‘The Inconsistency of Certain Formal Logics’, Annals of Mathematics, 36: 630–636. (Scholar)
- Landini, Gregory, 2007, Wittgenstein’s Apprenticeship with Russell, Cambridge: Cambridge University Press. (Scholar)
- Leng, Mary, 2010, Mathematics and Reality, Oxford: Oxford University Press. (Scholar)
- Lewy, Casimir, 1967, ‘A note on the text of the Tractatus’ Mind, 76: 416–423. (Scholar)
- Martin-Löf, Per, 1975, ‘An intuitionistic theory of types: Predicative part’, in Logic colloquium ’73, H.E. Rose and J. Shepherdson (eds.), Amsterdam: North-Holland: 73‐118. (Scholar)
- Potter, Michael, 2000, Reason’s Nearest Kin, Oxford: Oxford University Press; see especially 10–17 and Chapter 6. (Scholar)
- Resnik, Michael, 1980, Frege and the Philosophy of Mathematics, Ithaca: Cornell University Press, 1980. (Scholar)
- Robinson, Abraham, 1965, ‘Formalism’ in Bar-Hillel et al. (eds.) Logic, Methodology and Philosophy of Science, Amsterdam: North Holland. (Scholar)
- –––, 1969, ‘From a Formalist’s point of view’, Dialectica, 23: 45–9. (Scholar)
- Scott, Dana, 1970, ‘Constructive Validity’, in Symposium on Automatics Demonstration (Versailles, December 1968), M. Laudet, D. Lacombe, L. Nolin, and M. Schützenberg (eds), Lecture Notes in Mathematics (Volume 125), Berlin: Springer, 237‐275. (Scholar)
- Shapiro, Stewart, 2000, Thinking about Mathematics, Oxford: Oxford University Press. (Scholar)
- Simons, Peter, 2009, ‘Formalism’ in Andrew D. Irvine (ed.), Philosophy of Mathematics, Amsterdam: North Holland: 291–310. (Scholar)
- Tennant, Neil, 1997, The Taming of the True, Oxford: Clarendon Press. (Scholar)
- –––, 2008, ‘Carnap, Gödel, and the Analyticity of Arithmetic’, Philosophia Mathematica, 16: 110–12. (Scholar)
- Wadler, Philip, 2015, ‘Propositions as Types’, Communications of the Association for Computing Machinery, 58: 75–84. (Scholar)
- Wehmeier, Kai, 2004, ‘Wittgensteinian Predicate Logic’, Notre Dame Journal of Formal Logic, 45: 1–11. (Scholar)
- Weir, Alan, 1991, ‘An Instructive Nominalism’: Critical Review of H. Field: Realism, Mathematics and Modality, Philosophical Books, 32: 17–26. (Scholar)
- –––, 1993, ‘Putnam, Gödel and Mathematical Realism’, International Journal of Philosophical Studies, 1: 255–285. (Scholar)
- –––, 2010, Truth through Proof: A Formalist Foundation for Mathematics, Oxford: Oxford University Press. (Scholar)
- –––, 2016, ‘Informal Proof, Formal Proof and Formalism’, The Review of Symbolic Logic, 9: 23–43. (Scholar)
- Wittgenstein, Ludwig, 1921/1960, Tractatus Logico-Philosophicus, D. Pears and B. McGuinness (trans.), London: Routledge and Kegan Paul. (Scholar)
- –––, 1956/1978, Remarks on the Foundations of Mathematics, revised edition, G. E. M. Anscombe (trans.), G. E. M. Anscombe, R. Rhees, and G. H. von Wright, (eds.), Oxford: Blackwell. (Scholar)
- –––, 1975, Philosophical Grammar, A. Kenny (trans.), Rush Rees (ed.), Oxford: Blackwell. (Scholar)
- Yessenin-Volpin, A., 1961, ‘Le Programme Ultra-Intuitionniste Des Fondements Des Mathématiques.’ in Infinitistic Methods, Proceedings of the Symposium on the Foundations of Mathematics, Oxford: Pergamon Press, 201‐223. (Scholar)
- –––, 1970, ‘The Ultra-Intuitionistic Criticism and the Antitraditional Program for the Foundations of Mathematics’, in A. Kino, J. Myhill, & R. Vesley (eds.),Intuitionism and Proof Theory, Amsterdam: North-Holland,3–45. (Scholar)
