Seminar "Philosophie der Mathematik"

Sommersemester 2002

Literatur:

Bei einigen Texten haben wir Links auf Online-Versionen der Artikel angegeben.

Für die meisten der angegebenen Links muß man von einem Rechner der Universität Bonn oder einer anderen Institution mit einem Abonnement der entsprechenden Zeitschriften aus arbeiten.

Vielen Dank an Herrn Peter N.Posch für die Idee und einige Hinweise.

• [Bag89/90] F. Bagemihl, Throwing a dart at Freiling's argument against the continuum hypothesis, Real Analysis Exchange 15 (1989/90), p. 342-345.
• [Bal94] Mark Balaguer, Against (Maddian) Naturalized Platonism, Philosophia Mathematica 3 (1994), p. 97-108
• [Bal99] Mark Balaguer, Review of Maddy, Philosophy of Science 66 (1999), p. 502-504
• [Cal94] Cristian S. Calude, Information and randomness. An algorithmic perspective. With forewords by Gregory J. Chaitin and Arto Salomaa, Berlin 1994 [Monographs in Theoretical Computer Science. An EATCS Series]
• [Cha74] Gregory J. Chaitin, Information-Theoretic Computational Complexity, IEEE Transactions on Information Theory IT-20 (1974), p. 10-15 (auch in [Tym98])
• [Cha82] Gregory J. Chaitin, Gödel's Theorem and Information, International Journal of Theoretical Physics 21 (1982), p. 941-954 (auch in [Tym98]).
• [Cha87] Gregory J. Chaitin, Algorithmic information theory, With a foreword by J. T. Schwartz, Cambridge 1987 [Cambridge Tracts in Theoretical Computer Science 1]
• [Cha95/96] Gregory J. Chaitin, A new version of algorithmic information theory, Complexity 1 (1995/96), p. 55-59
• [Cha98] Gregory J. Chaitin, The Limits of Mathematics, A course on information theory and the limits of formal reasoning, With a foreword by Cristian Calude, Singapore 1998 [Springer Series in Discrete Mathematics and Theoretical Computer Science]
• [Cha02] Gregory J. Chaitin, Foundations of Mathematics, Meta-Mathematics, Contribution to the updating volume From the 20th to the 21st century: problems and perspectives of the Enciclopedia del Novecento
• [Chi82] Charles S. Chihara A Gödelian Thesis Regarding Mathematical Objects: Do They Exist? And Can We Perceive Them?, Philosophical Review 91 (1982), p. 211-227
• [Chi91] Charles S. Chihara, Constructibility and Mathematical Existence, Oxford 1991
• [Chi93] Charles S. Chihara, Modality without worlds, in: Johannes Czernak (ed.), Philosophie der Mathematik, Akten des 15. Internationalen Wittgenstein-Symposiums I, 16. bis 23. August 1992, Kirchberg am Wechsel (Österreich), Wien 1993, S.253-268
• [Chi98] Charles S. Chihara, The worlds of possibility, Modal realism and the semantics of modal logic, Oxford 1998
• [Col99] Mark Colynan, Review of Maddy, Mind 108 (1999), p. 586-590
• [Dec99] L. Decock, Review of Maddy, Tijdschrift voor Filosofie 61 (1999), p. 139-155
• [Die99] J. M. Dieterle, Mathematical, Astrological, and Theological Naturalism, Philosophia Mathematica 7 (1999), p. 129-135
• [Fal96] Don Fallis, The Source of Chaitin's Incorrectness, Philosophia Mathematica 4 (1996), p.261-269
• [FOM98] Excerpts of a discussion in the mailing list Foundations of Mathematics on "Freiling's Darts" 1998 (PostScript-File; PDF-File)
• [FOM01] Excerpts of a discussion in the mailing list Foundations of Mathematics on Chaitin 2001 (PostScript-File; PDF-File)
• [Fr86] Chris Freiling, Axioms of symmetry: throwing darts at the real number line. Journal of Symbolic Logic 51 (1986), p. 190-200.
• [FrSi89/90] Chris Freiling, John C. Simms, A three-dart response to an argument of Bagemihl. A comment on: ``Throwing a dart at Freiling's argument against the continuum hypothesis'' by F. Bagemihl. Real Analysis Exchange 15 (1989/90), p. 772-776
• [Gac89] Peter Gacs, Review of Chaitin, Journal for Symbolic Logic 54 (1989), p. 624
• [Hal99] Bob Hale, Review of Maddy, Journal of Symbolic Logic 64 (1999), p. 394-396
• [Hau?] Kai Hauser, What new axioms could not be, to appear in Dialectica
• [Heth99] Eric D. Hetherington, Review of Maddy, Review of Metaphysics 52 (1999), p. 704-706
• [Kie91] Charles F. Kielkopf, Review of [Chi91], Mathematical Reviews 91i:03007
• [Kit98] Philip Kitcher, What, if anything, is it all about? Fresh attempts by `structuralists' and `naturalists' to identify the foundations of mathematics, TLS [Times Literary Supplement] (September 11, 1998), 4980:7-9.
• [Mad97] Penelope Maddy, Naturalism in Mathematics, Oxford 1997
• [Man01] Paolo Mancosu, Mathematical Explanation: Problems and Prospects, Topoi 20 (2001), p. 97-117
• [Mar98] Donald A. Martin, Mathematical Evidence, in: H. Garth Dales, Gianluigi Oliveri (eds.), Truth in mathematics, Papers from the conference held in Mussomeli, September 13-20, 1995, Oxford 1998
• [Par79/80] Charles Parsons, Mathematical Intuition, Proceedings of the Aristotelian Society 80 (1979/80), p.145-168
• [Par95] Charles Parsons, Platonism and mathematical intuition in Kurt Gödel's thought, Bulletin of Symbolic Logic 1 (1995), p. 44-74
• [Par98] Charles Parsons, Intuition and the Abstract, in: Marcelo Stamm (ed.) Philosophie in synthetischer Absicht, Stuttgart 1998
• [Par00] Charles Parsons, Reason and Intuition, Synthese 125 (2000), p. 299-315
• [Raa97] Panu Raatikainen, The Problem of the Simplest Diophantine Representation, Nordic Journal of Philosophical Logic 2 (1997), p.47-54
• [Raa98] Panu Raatikainen, On interpreting Chaitin's incompleteness theorem, Journal of Philosophical Logic 27 (1998), p. 569-586
• [Raa00] Panu Raatikainen, Algorithmic information theory and undecidability, Synthese 123 (2000), p. 217-225
• [Res92] Michael D. Resnik, Proof as a source of truth, in: Michael Detlefsen (ed.), Proof and knowledge in mathematics, London 1992, p. 6-32 (auch in [Tym98]).
• [Ros99] Gidoen Rosen, Review of Maddy, British Journal for the Philosophy of Science 50 (1999), p. 467
• [RozSal94] Grzegorz Rozenberg, Arto Salomaa, Cornerstones of Undecidability, New York 1994
• [Sh00] Stewart Shapiro, Thinking about Mathematics, The philosophy of mathematics, Oxford 2000
• [Tym98] Thomas Tymoczko (ed.), New directions in the philosophy of mathematics, Princeton 1998
• [vL89] Michiel van Lambalgen, Algorithmic Information Theory, Journal of Symbolic Logic 54 (1989), p. 1389-1400