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| Articles (in journals or books): |
| [ | 9 | ] |
On the creative role of
axiomatics. The discovery of lattices by Schröder,
Dedekind, Birkhoff, and others. Synthese,
forthcoming.
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| [ | 8 | ] |
Bridging theories with
axioms: Boole, Stone, and Tarski. In: J.-P. van Bendegem and
B. van
Kerkhove (editors), Perspectives on
Mathematical Practices, Vol. II
forthcoming.
(preprint) |
| [ | 7 | ] |
Learning from the existence of models. On psychic machines,
tortoises, and computer simulations. Synthese. (online).
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| [ | 6 | ] |
Two ways of analogy: Extending the study of analogies to
mathematical domains. Philosophy of Science,
75(2):178-200. April 2008.
(online)
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| [ | 5 | ] |
Modeling ancient and modern
arithmetic practices: Addition and multiplication with Arabic and
Roman numerals (with Hansjörg
Neth).
In: V. Sloutsky, B. Love, and K. McRae (editors),
Proceedings of the 30th Annual Meeting of
the Cognitive Science Society, pp. 2007-2012.
Cognitive Science Society, Austin, TX, 2008.
(preprint)
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| [ | 4 | ] |
On abstraction and the importance of asking the right research
questions: Could Jordan have proved the Jordan-Hölder
Theorem? Erkenntnis, 68(3):409-420, May 2008.
(online)
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| [ | 3 | ] |
Axiomatics and progress in the light of 20th century
philosophy of science and mathematics. In:
B. Loewe, V. Peckhaus, and T. Rasch (editors), Foundations
of the Formal Sciences IV,
pp. 233-253. Studies in Logic Series, College Publications, London, 2006.
(preprint) |
| [ | 2 | ] |
Against against Intuitionism. Synthese
147(1):171-188, October 2005.
(online) |
| [ | 1 | ] |
Dedekind's analysis of number: systems and axioms (with
Wilfried Sieg). Synthese 147(1):121-170, October 2005. (online) |
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| Reviews: |
| [ | 5 | ] |
Book review of Torkel Franzén, "Gödel's Theorem,"
Review of Modern Logic, 10(3/4):257-261, March 2005-May 2007.
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| [ | 4 | ] |
Book review of Volker Peckhaus (ed.), "Oskar Becker und die
Philosophie der Mathematik,"
History and Philosophy of Logic, 27(2):198-200, May 2006.
(online) |
| [ | 3 | ] |
Review of Richard Zach, "Hilbert's 'Verunglückter Beweis'
the first epsilon theorem, and consistency proofs,"
Bulletin of Symbolic Logic, 11(2):247-248, June 2005.
(online) |
| [ | 2 | ] |
Book review of Marcus Giaquinto, "The Search for
Certainty,"
Review of Modern Logic, 10(1/2):187-190, September 2004-February 2005. |
| [ | 1 | ] |
Book review of Kevin Possin, "Critical Thinking,"
Teaching Philosophy, 26(3):305-307, September 2003. |
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| Article in conference proceedings: |
- Towards axiomatic foundations of mathematics: The evolution of
Richard Dedekind's treatment of numbers, Proceedings of
the Eighth Midwest History of Mathematics Conference, Northern
Kentucky University, October 13-14, 2000. D. Curtin,
D. Kullmann, D. Otero (editors).
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| Technical reports: |
- Dedekind's analysis of number (Part I) - systems and axioms (with
Wilfried Sieg). Technical Report CMU-PHIL-139, March 18 2003.
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| Theses: |
- Axiomatics as Engine for Driving Discovery in Mathematics and
Science,
Ph.D. thesis in Logic, Computation, and Methodology, Department of
Philosophy, Carnegie Mellon University, Pittsburgh, May
2005.
Thesis committee:
Clark Glymour (chair),
Jeremy Avigad,
John Earman (U Pittsburgh),
Richard Scheines.
- Richard Dedekind: Axiomatic Foundations of Mathematics,
Master's thesis in Logic and Computation, Department of
Philosophy, Carnegie Mellon University, Pittsburgh, May
2000.
Thesis committee:
Wilfried Sieg (chair),
Steve Awodey,
Erick Reck (UC Riverside).
- Intuitionism and Computer Science - A historical and
philosophical investigation of the logical
foundations of computer science with special attention to
L.E.J. Brouwer's Intuitionism,
Diploma thesis,
Department of Computer Science, Technical University
Darmstadt, January 1997 (in German).
Thesis committee:
Christoph Kreitz (Computer Science, TU Darmstadt),
Barbara Brüning (Philosophy, Frankfurt).
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| Other: |
- Two metaphors for teaching,
Graduate Times, Carnegie Mellon
Graduate Student Newsletter. Vol. V, No. 4, p. 2,
Summer 2003. (online)
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| Manuscripts: |
- Aspects of theory construction: Clark Hull's philosophy of
science (with Uljana Feest). Presented at CSHPS
2003. Selected as runner-up for the Hadden Prize for best student paper.
- Extending the study of analogies to abstract domains:
Difficulties and solutions.
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