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