Linked bibliography for the SEP article "Intuitionism in the Philosophy of Mathematics" by Rosalie Iemhoff

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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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  • Aczel, P., 1978, ‘The type-theoretic interpretation of constructive set theory,’ in A. Macintyre, L. Pacholski, J. Paris (eds.), Logic Colloquium ’77, special issue of Studies in Logic and the Foundations of Mathematics, 96: 55–66. (Scholar)
  • van Atten, M., 2004, On Brouwer, Belmont: Wadsworth/Thomson Learning. (Scholar)
  • –––, 2007, Brouwer meets Husserl: On the phenomenology of choice sequences, Dordrecht: Springer. (Scholar)
  • –––, 2008, ‘On the hypothetical judgement in the history of intuitionistic logic,’ in C. Glymour and W. Wang and D. Westerståhl (eds.), Proceedings of the 2007 International Congress in Beijing (Logic, Methodology, and Philosophy of Science: Volume XIII), London: King’s College Publications, 122–136. (Scholar)
  • van Atten, M. and D. van Dalen, 2002, ‘Arguments for the continuity principle,’ Bulletin of Symbolic Logic, 8(3): 329–374. (Scholar)
  • Beth, E.W., 1956, ‘Semantic construction of intuitionistic logic,’ Mededeelingen der Koninklijke Nederlandsche Akademie van Wetenschappen, Afdeeling Letterkunde (Nieuwe Serie), 19(11): 357–388. (Scholar)
  • Brouwer, L.E.J., 1975, Collected works I, A. Heyting (ed.), Amsterdam: North-Holland. (Scholar)
  • –––, 1976, Collected works II, H. Freudenthal (ed.), Amsterdam: North-Holland. (Scholar)
  • –––, 1905, Leven, kunst en mystiek, Delft: Waltman. (Scholar)
  • –––, 1907, Over de grondslagen der wiskunde, Ph.D. Thesis, University of Amsterdam, Department of Physics and Mathematics. (Scholar)
  • –––, 1912, ‘Intuïtionisme en formalisme’, Inaugural address at the University of Amsterdam, 1912. Also in Wiskundig tijdschrift, 9, 1913. (Scholar)
  • –––, 1925, ‘Zur Begründung der intuitionistischen Mathematik I,’ Mathematische Annalen, 93: 244–257. (Scholar)
  • –––, 1925, ‘Zur Begründung der intuitionistischen Mathematik II,’ Mathematische Annalen, 95: 453–472. (Scholar)
  • –––, 1948, ‘Essentially negative properties’, Indagationes Mathematicae, 10: 322–323. (Scholar)
  • –––, 1952, ‘Historical background, principles and methods of intuitionism,’ South African Journal of Science, 49 (October-November): 139–146. (Scholar)
  • –––, 1953, ‘Points and Spaces,’ Canadian Journal of Mathematics, 6: 1–17. (Scholar)
  • –––, 1981, Brouwer’s Cambridge lectures on intuitionism, D. van Dalen (ed.), Cambridge: Cambridge University Press, Cambridge. (Scholar)
  • –––, 1992, Intuitionismus, D. van Dalen (ed.), Mannhein: Wissenschaftsverlag. (Scholar)
  • Brouwer, L.E.J. and C.S. Adama van Scheltema, 1984, Droeve snaar, vriend van mij – Brieven, D. van Dalen (ed.), Amsterdam: Uitgeverij de Arbeiderspers. (Scholar)
  • Coquand, T., 1995, ‘A constructive topological proof of van der Waerden’s theorem,’ Journal of Pure and Applied Algebra, 105: 251–259. (Scholar)
  • van Dalen, D., 1978, ‘An interpretation of intuitionistic analysis’, Annals of Mathematical Logic, 13: 1–43. (Scholar)
  • –––, 1997, ‘How connected is the intuitionistic continuum?,’ Journal of Symbolic Logic, 62(4): 1147–1150. (Scholar)
  • –––, 1999/2005, Mystic, geometer and intuitionist, Volumes I (1999) and II (2005), Oxford: Clarendon Press. (Scholar)
  • –––, 2001, L.E.J. Brouwer (een biografie), Amsterdam: Uitgeverij Bert Bakker. (Scholar)
  • –––, 2004, ‘Kolmogorov and Brouwer on constructive implication and the Ex Falso rule’ Russian Math Surveys, 59: 247–257. (Scholar)
  • van Dalen, D. (ed.), 2001, L.E.J. Brouwer en de grondslagen van de wiskunde, Utrecht: Epsilon Uitgaven. (Scholar)
  • Diaconescu, R., 1975, ‘Axiom of choice and complementation,’ in Proceedings of the American Mathematical Society, 51: 176–178. (Scholar)
  • Dummett, M., 1975, ‘The Philosophical Basis of Intuitionistic Logic,’ in H.E. Rose and J.C. Shepherdson (eds.), Proceedings of the Logic Colloquium ’73, special issue of Studies in Logic and the Foundations of Mathematics, 80: 5–40. (Scholar)
  • Fourman, M., and R. Grayson, 1982, ‘Formal spaces,’ in A.S. Troelstra and D. van Dalen (eds.), The L.E.J. Brouwer Centenary Symposium, Amsterdam: North-Holland. (Scholar)
  • Gentzen, G., 1934, ‘Untersuchungen über das logische Schließen I, II,’ Mathematische Zeitschrift, 39: 176–210, 405–431. (Scholar)
  • Gödel, K., 1958, ‘Über eine bisher noch nicht benützte Erweiterung des finiten Standpunktes,’ Dialectia, 12: 280–287. (Scholar)
  • Hacker, P. M. S., 1986, Insight & Illusion. Themes in the Philosophy of Wittgenstein, revised edition, Clarendon Press, Oxford. (Scholar)
  • Heyting, A., 1930, ‘Die formalen Regeln der intuitionistischen Logik,’ Sitzungsberichte der Preussischen Akademie von Wissenschaften. Physikalisch-mathematische Klasse, 42–56. (Scholar)
  • –––, 1956, Intuitionism, an introduction, Amsterdam: North-Holland. (Scholar)
  • van der Hoeven, G., and I. Moerdijk, 1984, ‘Sheaf models for choice sequences,’ Annals of Pure and Applied Logic, 27: 63–107. (Scholar)
  • Kleene, S.C., and R.E. Vesley, 1965, The foundations of intuitionistic mathematics, Amsterdam: North-Holland. (Scholar)
  • Kreisel, G., 1959, ‘Interpretation of analysis by means of constructive functionals of finite type,’ in A. Heyting (ed.), Constructivity in Mathematics, Amsterdam: North-Holland. (Scholar)
  • –––, 1962, ‘On weak completeness of intuitionistic predicate logic,’ Journal of Symbolic Logic, 27: 139–158. (Scholar)
  • –––, 1968, ‘Lawless sequences of natural numbers,’ Compositio Mathematica, 20: 222–248. (Scholar)
  • Kripke, S.A., 1965, ‘Semantical analysis of intuitionistic logic’, in J. Crossley and M. Dummett (eds.), Formal systems and recursive functions, Amsterdam: North-Holland. (Scholar)
  • Lubarsky, R., F. Richman, and P. Schuster 2012, ‘The Kripke schema in metric topology’, Mathematical Logic Quarterly, 58(6): 498–501. (Scholar)
  • Maietti, M.E., and G. Sambin, 2007, ‘Toward a minimalist foundation for constructive mathematics,’ in L. Crosilla and P. Schuster (eds.), From sets and types to topology and analysis: toward a minimalist foundation for constructive mathematics, Oxford: Oxford University Press. (Scholar)
  • Marion, M., 2003, ‘Wittgenstein and Brouwer’, Synthese 137: 103–127. (Scholar)
  • Martin-Löf, P., 1970, Notes on constructive mathematics, Stockholm: Almqvist & Wiskell. (Scholar)
  • –––, 1984, Intuitionistic type theory, Napoli: Bibliopolis. (Scholar)
  • Moschovakis, J.R., 1973, ‘A topological interpretation of second-order intuitionistic arithmetic,’ Compositio Mathematica, 26(3): 261–275.
  • –––, 1986, ‘Relative lawlessness in intuitionistic analysis,’ Journal of Symbolic Logic, 52(1): 68–87. (Scholar)
  • Myhill, J., 1975, ‘Constructive set theory,’ Journal of Symbolic Logic, 40: 347–382. (Scholar)
  • Niekus, J., 2010, ‘Brouwer’s incomplete objects’ History and Philosophy of Logic, 31: 31–46. (Scholar)
  • van Oosten, J., 2008, Realizability: An introduction to its categorical side, (Studies in Logic and the Foundations of Mathematics: Volume 152), Amsterdam: Elsevier. (Scholar)
  • Prawitz, D., 1977, ‘Meaning and proofs: On the conflict between classical and intuitionistic logic,’ Theoria, 43(1): 2–40. (Scholar)
  • Parsons, C., 1986, ‘Intuition in Constructive Mathematics,’ in Language, Mind and Logic, J. Butter (ed.), Cambridge: Cambridge University Press. (Scholar)
  • Sambin, G., 1987, ‘Intuitionistic formal spaces,’ in Mathematical Logic and its Applications, D. Skordev (ed.), New York: Plenum. (Scholar)
  • Scott, D., 1968, ‘Extending the topological interpretation to intuitionistic analysis,’ Compositio Mathematica, 20: 194–210. (Scholar)
  • –––, 1970, ‘Extending the topological interpretation to intuitionistic analysis II’, in Intuitionism and proof theory, J. Myhill, A. Kino, and R. Vesley (eds.), Amsterdam: North-Holland. (Scholar)
  • Sundholm, B.G., ‘Constructive Recursive Functions, Church’s Thesis, and Brouwer's Theory of the Creating Subject: Afterthoughts on a Paris Joint Session’, in Jacque Dubucs & Michel Bordeau (eds.), Constructivity and Computability in Historical and Philosophical Perspective (Logic, Epistemology, and the Unity of Science: Volume 34), Dordrecht: Springer: 1–35. (Scholar)
  • Tarski, A., 1938, ‘Der Aussagenkalkül und die Topologie,’ Fundamenta Mathematicae, 31: 103–134. (Scholar)
  • Tieszen, R., 1994, ‘What is the philosophical basis of intuitionistic mathematics?,‘ in D. Prawitz, B. Skyrms and D. Westerstahl (eds.), Logic, Methodology and Philosophy of Science, IX: 579–594. (Scholar)
  • –––, 2000, ‘Intuitionism, Meaning Theory and Cognition,‘ History and Philosophy of Logic, 21: 179–194. (Scholar)
  • Troelstra, A.S., 1973, Metamathematical investigations of intuitionistic arithmetic and analysis, (Lecture Notes in Mathematics: Volume 344), Berlin: Springer. (Scholar)
  • –––, 1977, Choice sequences (Oxford Logic Guides), Oxford: Clarendon Press. (Scholar)
  • Troelstra, A.S., and D. van Dalen, 1988, Constructivism I and II, Amsterdam: North-Holland. (Scholar)
  • Veldman, W., 1976, ‘An intuitionistic completeness theorem for intuitionistic predicate logic,’ Journal of Symbolic Logic, 41(1): 159–166. (Scholar)
  • –––, 1999, ‘The Borel hierarchy and the projective hierarchy in intuitionistic mathematics,’ Report Number 0103, Department of Mathematics, University of Nijmegen. [available online] (Scholar)
  • –––, 2004, ‘An intuitionistic proof of Kruskal’s theorem,’ Archive for Mathematical Logic, 43(2): 215–264. (Scholar)
  • –––, 2009, ‘Brouwer’s Approximate Fixed-Point Theorem is Equivalent to Brouwer’s Fan Theorem,’ in S. Lindström, E. Palmgren, K. Segerberg, V. Stoltenberg-Hansen (eds.), Logicism, Intuitionism, and Formalism (Synthese Library: Volume 341), Dordrecht: Springer, 277–299. (Scholar)
  • –––, 2014, ‘Brouwer’s Fan Theorem as an axiom and as a contrast to Kleene’s Alternative,’ in Archive for Mathematical Logic, 53(5–6): 621–693. (Scholar)
  • –––, forthcoming, ‘Intuitionism is all bosh, entirely. Unless it is an inspiration,’ in G. Alberts, L. Bergmans, and F. Muller, (eds.), Significs and the Vienna Circle: Intersections, Dordrecht: Springer. [preprint available online] (Scholar)
  • Weyl, H., 1921, ‘Über die neue Grundlagenkrise der Mathematik,’ Mathematische Zeitschrift, 10: 39–70. (Scholar)
  • Wittgenstein, L., 1994, Wiener Ausgabe, Band 1, Philosophische Bemerkungen, Vienna, New York: Springer Verlag. (Scholar)
  • Wright, C., 1982, ‘Strict Finitism’, Synthese 51(2): 203–282. (Scholar)
  • Yessenin-Volpin, A.S., 1970, ‘The ultra–intuitionistic criticism and the antitraditional program for foundations of mathematics’, in A. Kino, J. Myhill, and R. Vesley (eds.), Intuitionism and Proof Theory, Amsterdam: North-Holland Publishing Company, 3–45. (Scholar)

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