Wittgenstein’s Writings

Notes on Wittgenstein’s Lectures and Recorded Conversations

Secondary Sources and Relevant Primary Literature

• Ambrose, Alice, 1935a, “Finitism in Mathematics (I)”, Mind, 44(174): 186–203. doi:10.1093/mind/xliv.174.186 (Scholar)
• –––, 1935b, “Finitism in Mathematics (II)”, Mind, 44(175): 317–340. doi:10.1093/mind/xliv.175.317 (Scholar)
• –––, 1972, “Mathematical Generality”, in Ambrose and Lazerowitz 1972: 287–318. (Scholar)
• –––, 1982, “Wittgenstein on Mathematical Proof”, Mind, 91(362): 264–372. doi:10.1093/mind/xci.362.264 (Scholar)
• Ambrose, Alice and Morris Lazerowitz (eds.), 1972, Ludwig Wittgenstein: Philosophy and Language, London: George Allen and Unwin Ltd. (Scholar)
• Anderson, Alan Ross, 1958, “Mathematics and the ‘Language Game’”, The Review of Metaphysics, 11(3): 446–458; reprinted in Benacerraf & Putnam 1964b: 481–490. (Scholar)
• Baker, Gordon and P.M.S. Hacker, 1985, Wittgenstein: Rules, Grammar and Necessity, Volume 2 of an Analytical Commentary on the Philosophical Investigations, Oxford: Blackwell. (Scholar)
• Bays, Timothy, 2004, “On Floyd and Putnam on Wittgenstein on Gödel”, Journal of Philosophy, 101(4): 197–210. doi:10.5840/jphil2004101422 (Scholar)
• Benacerraf, Paul and Hilary Putnam, 1964a, “Introduction”, in Benacerraf & Putnam 1964b: 1–27. (Scholar)
• Benacerraf, Paul and Hilary Putnam (eds.), 1964b, Philosophy of Mathematics, Englewood Cliffs, NJ: Prentice-Hall. (Scholar)
• ––– (eds.), 1983, Philosophy of Mathematics, second edition, Cambridge: Cambridge University Press. Note there are considerable differences between the first and second editions. (Scholar)
• Bernays, Paul, 1959, “Comments on Ludwig Wittgenstein’s Remarks on the Foundations of Mathematics”, Ratio, 2(1): 1–22. (Scholar)
• Berto, Fransesco, 2009a, “The Gödel Paradox and Wittgenstein’s Reasons”, Philosophia Mathematica, 17(2): 208–219. doi:10.1093/philmat/nkp001 (Scholar)
• –––, 2009b, “Gödel versus Wittgenstein and the Paraconsistent Interpretation”, in his There’s Something About Gödel: The Complete Guide to the Incompleteness Theorem, West Sussex, UK: Wiley-Blackwell, Chapter 12, 189–213. doi:10.1002/9781444315028.ch12 (Scholar)
• Black, Max, 1964, A Companion to Wittgenstein’s Tractatus, Ithaca, NY: Cornell University Press. (Scholar)
• Black, Max, 1969, “Verificationism and Wittgenstein’s Reflections on Mathematics”, Revue Internationale de Philosophie, 23(88/89): 284–95; reprinted in Shanker 1986: 68–76. (Scholar)
• Brouwer, L.E.J., 1907 [1975], Over de Grondslagen der Wiskunde (On the Foundations of Mathematics), Ph.D. thesis, Universiteit van Amsterdam. English translation in Brouwer 1975: 11–101. (Scholar)
• –––, 1908 [1975], “De onbetrouwbaarheid der logische principes” (The Unreliability of the Logical Principles), Tijdschrift voor Wijsbegeerte, 2: 152–158. English translation in Brouwer 1975: 107–111. doi:10.1016/B978-0-7204-2076-0.50009-X (Scholar)
• –––, 1929 [1998], “Mathematik, Wissenschaft und Sprache” (Mathematics, Science, and Language), Monatshefte für Mathematik und Physik, 36: 153–164. English translation in Mancosu 1998: 45–53. doi:10.1007/BF02307611 (Scholar)
• –––, 1948 [1983], “Consciousness, Philosophy and Mathematics”, Proceedings of the 10th International Congress of Philosophy, Amsterdam 1948, Amsterdam: North-Holland, 3: 1235–1249. Reprinted in Benacerraf & Putnam 1983: 90–96. doi:10.1017/CBO9781139171519.005 (Scholar)
• –––, 1955, “The Effect of Intuitionism on Classical Algebra of Logic”, Proceedings of the Royal Irish Academy, 57: 113–116. (Scholar)
• –––, 1981, Brouwer’s Cambridge Lectures on Intuitionism, Cambridge: Cambridge University Press. (Scholar)
• –––, 1975, Collected Works. I: Philosophy and Foundations of Mathematics, Arend Heyting (ed.), Amsterdam: North-Holland. (Scholar)
• Coliva, Annalisa and Eva Picardi (eds.), 2004, Wittgenstein Today, Padova: Il Poligrafo. (Scholar)
• Conant, James, 1997, “On Wittgenstein’s Philosophy of Mathematics”, Proceedings of the Aristotelian Society, 97(1): 195–222. doi:10.1111/1467-9264.00013 (Scholar)
• Crary, Alice and Rupert Read (eds.), 2000, The New Wittgenstein, London and New York: Routledge. (Scholar)
• Da Silva, Jairo Jose, 1993, “Wittgenstein on Irrational Numbers”, in Puhl 1993: 93–99. (Scholar)
• Dawson, Ryan, 2016a, “Wittgenstein on Set Theory and the Enormously Big”, Philosophical Investigations, 39(4): 313–334. doi:10.1111/phin.12107 (Scholar)
• –––, 2016b, “Was Wittgenstein Really a Constructivist About Mathematics?”, Wittgenstein Studien, 7(1): 81–104. doi: 10.1515/witt-2016-0107 (Scholar)
• Dreben, Burton and Juliet Floyd, 1991, “Tautology: How Not To Use A Word”, Synthese, 87(1): 23–49. doi:10.1007/bf00485329 (Scholar)
• Dummett, Michael, 1959, “Wittgenstein’s Philosophy of Mathematics”, The Philosophical Review, 68: 324–348. (Scholar)
• –––, 1978, “Reckonings: Wittgenstein on Mathematics”, Encounter, 50(3): 63–68; reprinted in Shanker 1986: 111–120. (Scholar)
• –––, 1994, “Wittgenstein on Necessity: Some Reflections”, in Peter Clark and Bob Hale (eds.), Reading Putnam, Cambridge, MA: Blackwell Publishers: 49–65. (Scholar)
• Finch, Henry Le Roy, 1977, Wittgenstein: The Later Philosophy, Atlantic Highlands, NJ: Humanities Press. (Scholar)
• Floyd, Juliet, 1991, “Wittgenstein on 2, 2, 2…: The Opening of Remarks on the Foundations of Mathematics”, Synthese, 87(1): 143–180. doi:10.1007/bf00485332 (Scholar)
• –––, 1995, “On Saying What You Really Want to Say: Wittgenstein, Gödel, and the Trisection of the Angle”, in Hintikka 1995: 373–425. (Scholar)
• –––, 2000, “Wittgenstein, Mathematics and Philosophy”, in Crary and Read 2000: 232–261. (Scholar)
• –––, 2001, “Prose versus Proof: Wittgenstein on Gödel, Tarski, and Truth”, Philosophia Mathematica, 9(3): 280–307. doi:10.1093/philmat/9.3.280 (Scholar)
• –––, 2002, “Number and Ascriptions of Number in Wittgenstein’s Tractatus”, in Reck 2002: 308–352. (Scholar)
• –––, 2005, “Wittgenstein on Philosophy of Logic and Mathematics”, in Stewart Shapiro (ed.), The Oxford Handbook of Philosophy of Logic and Mathematics, Oxford: Oxford University Press: 75–128. (Scholar)
• –––, 2012, “Wittgenstein’s Diagonal Argument: A Variation on Cantor and Turing”, in P. Dybjer, S. Lindström, E. Palmgren, and B.G. Sundholm (eds.), Epistemology versus Ontology: Essays on the Philosophy and Foundations of Mathematics in Honour of Per Martin-Löf, Dordrecht: Springer, 25–44. (Scholar)
• –––, 2015, “Review of Felix Mühlhölzer’s Does Mathematics Need a Foundation?”, Philosophia Mathematica, 23(2): 255–276. doi:10.1093/philmat/nku037 (Scholar)
• Floyd, Juliet and Hilary Putnam, 2000, “A Note on Wittgenstein’s ‘Notorious Paragraph’ about the Gödel Theorem”, The Journal of Philosophy, 97(11): 624–632. doi:10.2307/2678455">10.2307/2678455 (Scholar)
• –––, 2006, “Bays, Steiner, and Wittgenstein’s ‘Notorious’ Paragraph about the Gödel Theorem”, The Journal of Philosophy, 103(2): 101–110. doi:10.5840/jphil2006103228 (Scholar)
• Fogelin, Robert J., 1968, “Wittgenstein and Intuitionism”, American Philosophical Quarterly, 5(4): 267–274. (Scholar)
• –––, 1987 [1976], Wittgenstein, Second Edition, New York: Routledge & Kegan Paul. (Scholar)
• Frascolla, Pasquale, 1980, “The Constructivist Model in Wittgenstein’s Philosophy of Mathematics”, Revista Filosofia, 71: 297–306; reprinted in Shanker 1986: 242–249. (Scholar)
• –––, 1994, Wittgenstein’s Philosophy of Mathematics, London and New York: Routledge. (Scholar)
• –––, 1997, “The Tractatus System of Arithmetic”, Synthese, 112(3): 353–378. doi:10.1023/a:1004952810156 (Scholar)
• –––, 1998, “The Early Wittgenstein’s Logicism”, Acta Analytica, 13(21): 133–137. (Scholar)
• –––, 2004, “Wittgenstein on Mathematical Proof”, in Coliva & Picardi 2004: 167–184. (Scholar)
• Frege, Gottlob, 1959 [1884], The Foundations of Arithmetic, translated by J.L. Austin, Oxford: Basil Blackwell. (Scholar)
• Garavaso, Pieranna, 1988, “Wittgenstein’s Philosophy of Mathematics: A Reply to Two Objections”, Southern Journal of Philosophy, 26(2): 179–191. doi:10.1111/j.2041-6962.1988.tb00450.x (Scholar)
• Gerrard, Steve, 1991, “Wittgenstein’s Philosophies of Mathematics”, Synthese, 87(1) 125–142. doi:10.1007/bf00485331 (Scholar)
• –––, 1996, “A Philosophy of Mathematics Between Two Camps”, in Sluga & Stern 1996: 171–197. (Scholar)
• –––, 2002, “One Wittgenstein?”, in Reck 2002: 52–71. (Scholar)
• Glock, Hans-Johann, 1996, “Necessity and Normativity”, in Sluga & Stern 1996: 198–225. (Scholar)
• Gödel, Kurt, 1931, “On Formally Undecidable Propositions of Principia Mathematica and Related Systems I”, in van Heijenoort 1967: 596–616. (Scholar)
• –––, 1953–1957, “Is Mathematics Syntax of Language?”, Version III, in Gödel 1995: 334–356. (Scholar)
• –––, 1995, Collected Works, Vol. III, S. Feferman, J. Dawson, Jr., W. Goldfarb, C. Parsons, and R. Solovay (eds.), Oxford: Oxford University Press. (Scholar)
• Goldstein, Laurence, 1986, “The Development of Wittgenstein’s Views on Contradiction”, History and Philosophy of Logic, 7(1): 43–56. doi:10.1080/01445348608837090 (Scholar)
• –––, 1989, “Wittgenstein and Paraconsistency”, in Graham Priest, Richard Routley, and Jean Norman (eds.), Paraconsistent Logic: Essays on the Inconsistent, Munich: Philosophia Verlag: 540–562. (Scholar)
• Goodstein, R.L., 1957, “Critical Notice of Remarks on the Foundations of Mathematics”, Mind, 66(264): 549–553. doi:10.1093/mind/lxvi.264.549 (Scholar)
• –––, 1972, “Wittgenstein’s Philosophy of Mathematics”, in Ambrose and Lazerowitz 1972: 271–86. (Scholar)
• Hacker, P.M.S., 1986, Insight & Illusion. Themes in the Philosophy of Wittgenstein, revised edition, Oxford: Clarendon Press. (Scholar)
• Han, Daesuk, 2010, “Wittgenstein and the Real Numbers”, History and Philosophy of Logic, 31(3): 219–245. doi:10.1080/01445340.2010.485350 (Scholar)
• van Heijenoort, Jean, (ed.), 1967, From Frege to Gödel: A Sourcebook in Mathematical Logic, Cambridge, MA: Harvard University Press. (Scholar)
• Hilbert, David, 1925, “On the Infinite”, in van Heijenoort 1967: 369–392. (Scholar)
• Hintikka, Jaakko, 1993, “The Original Sinn of Wittgenstein’s Philosophy of Mathematics”, in Puhl 1993: 24–51. (Scholar)
• –––, (ed.), 1995, From Dedekind to Gödel: Essays on the Development of Mathematics, Dordrecht: Kluwer Academic Publishers. (Scholar)
• Hintikka, Jaakko and K. Puhl (eds.), 1994, The British Tradition in 20^th Century Philosophy: Papers of the 17^th International Wittgenstein Symposium 1994, Kirchberg-am-Wechsel: Austrian Ludwig Wittgenstein Society. (Scholar)
• Kielkopf, Charles F., 1970, Strict Finitism, The Hague: Mouton. (Scholar)
• Klenk, V.H., 1976, Wittgenstein’s Philosophy of Mathematics, The Hague: Martinus Nijhoff. (Scholar)
• Kreisel, Georg, 1958, “Wittgenstein’s Remarks on the Foundations of Mathematics”, British Journal for the Philosophy of Science, 9(34): 135–57. doi:10.1093/bjps/ix.34.135 (Scholar)
• –––, 1998, “Second Thoughts Around Some of Gödel’s Writings: A Non-Academic Option”, Synthese, 114(1): 99–160. doi:10.1023/a:1005006610269 (Scholar)
• Kremer, Michael, 2002, “Mathematics and Meaning in the Tractatus”, Philosophical Investigations, 25(3): 272–303. doi:10.1111/1467-9205.00175 (Scholar)
• Kripke, Saul A., 1982, Wittgenstein on Rules and Private Language, Cambridge, MA: Harvard University Press. (Scholar)
• Lampert, Timm, 2008, “Wittgenstein on the Infinity of Primes”, History and Philosophy of Logic, 29(3): 272–303. (Scholar)
• –––, 2009, “Wittgenstein on Pseudo-Irrationals, Diagonal-Numbers and Decidability”, in Logica Yearbook 2008, Michal Peliš, (ed.), London: College Publications: 95–110. (Scholar)
• –––, forthcoming, “Wittgenstein and Gödel: An Attempt to Make ‘Wittgenstein’s Objection’ Reasonable”, Philosophia Mathematica, first online 03 August 2017. doi:org/10.1093/philmat/nkx017 (Scholar)
• Maddy, Penelope, 1986, “Mathematical Alchemy”, British Journal for the Philosophy of Science, 37(3): 279–312. doi:10.1093/bjps/37.3.279 (Scholar)
• –––, 1993, “Wittgenstein’s Anti-Philosophy of Mathematics”, in Puhl 1993: 52–72. (Scholar)
• Mancosu, Paolo, 1998, From Brouwer to Hilbert: The Debate on the Foundations of Mathematics in the 1920s, Oxford: Oxford University Press. (Scholar)
• Mancosu, Paolo & Mathieu Marion, 2002, “Wittgenstein’s Constructivization of Euler’s Proof of the Infinity of Primes”, in Friedrich Stadler (ed.), The Vienna Circle and Logical Empiricism: Re-Evaluation and Future Perspectives, (Vienna Circle Institute Yearbook, 10), Dordrecht: Kluwer: 171–188. doi:10.1007/0-306-48214-2_15 (Scholar)
• Marconi, Diego, 1984, “Wittgenstein on Contradiction and the Philosophy of Paraconsistent Logic”, History of Philosophy Quarterly, 1(3): 333–352. (Scholar)
• Marion, Mathieu, 1993, “Wittgenstein and the Dark Cellar of Platonism”, in Puhl 1993: 110–118. (Scholar)
• –––, 1995a, “Wittgenstein and Finitism”, Synthese, 105(2): 143–65. doi:10.1007/bf01064216 (Scholar)
• –––, 1995b, “Wittgenstein and Ramsey on Identity”, in Hintikka 1995: 343–371. (Scholar)
• –––, 1995c, “Kronecker’s ‘Safe Haven of Real Mathematics’,” in Marion & Cohen Quebec Studies in the Philosophy of Science, Part I, Dordrecht: Kluwer: 135–87. (Scholar)
• –––, 1998, Wittgenstein, Finitism, and the Foundations of Mathematics, Oxford: Clarendon Press. doi:10.1093/acprof:oso/9780199550470.001.0001 (Scholar)
• –––, 2003, “Wittgenstein and Brouwer”, Synthese, 137(1–2): 103–127. doi:10.1023/a:1026230917748 (Scholar)
• –––, 2004, “Wittgenstein on Mathematics: Constructivism or Constructivity?”, in Coliva & Picardi 2004: 201–222. (Scholar)
• –––, 2008, “Brouwer on ‘Hypotheses’ and the Middle Wittgenstein”, in One Hundred Years of Intuitionism, Mark van Atten, Pascal Boldini, Michel Bourdreau, and Gerhard Heinzmann (eds.), Basel: Birkhauser: 96–114. doi:10.1007/978-3-7643-8653-5_7 (Scholar)
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• Morton, Adam and Stephen P. Stich, 1996, Benacerraf and His Critics, Oxford: Blackwell. (Scholar)
• Mühlhölzer, Felix, 2010, Braucht die Mathematik eine Grundlegung? Eine Kommentar des Teils III von Wittgensteins Bemerkungen über die Grundlagen der Mathematik [Does Mathematics Need a Foundation? A Commentary on Part III of Wittgenstein’s Remarks on the Foundations of Mathematics], Frankfurt: Vittorio Klostermann. (Scholar)
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• –––, 2007, “Wittgenstein and the Real Numbers”, in Wittgenstein and the Moral Life: Essays in Honor of Cora Diamond, Alice Crary (ed.), Cambridge, MA: The MIT Press: 235–250. (Scholar)
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