Linked bibliography for the SEP article "Formalism in the Philosophy of Mathematics" by Alan Weir
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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)