Articles (refereed)

19. The correspondence between Moritz Pasch and Felix Klein. Historia Mathematica, 40(2):183-202, May 2013. (online)
18. Mathematical practice and conceptual metaphors. Topics in Cognitive Science, 2013. Accepted for publication. (prefinal draft)
17. Axioms in mathematical practice. Philosophia Mathematica, 21(1):37-92, February 2013. (online)
16. Mathematical concepts and investigative practice. In: U. Feest and F. Steinle (eds.), Scientific Concepts and Investigative Practice, pp. 127-147. De Gruyter, Berlin, 2012. (prefinal draft)
15. Methodological reflections on typologies for numerical notations (with Theodore R. Widom). Science in Context, 25(2): 155-195, June 2012. (online)
14. On the creative role of axiomatics. The discovery of lattices by Schröder, Dedekind, Birkhoff, and others. Synthese, 183(1): 47-68, November 2011. (online)
13. Learning and understanding numeral systems: Semantic aspects of number representations from an educational perspective (with Katja Lengnink). In: B. Löwe and T. Müller (eds.), Philosophy of Mathematics: Sociological Aspects and Mathematical Practice, pp. 235-264. College Publications, London, 2010. (online)
12. Loss of vision: How mathematics turned blind while it learned to see more clearly (with Bernd Buldt). In: B. Löwe and T. Müller (eds.), Philosophy of Mathematics: Sociological Aspects and Mathematical Practice, pp. 87-106. College Publications, London, 2010. (online)
11. The cognitive basis of arithmetic (with Helen de Cruz and Hansjörg Neth). In: B. Löwe and T. Müller (eds.), Philosophy of Mathematics: Sociological Aspects and Mathematical Practice, pp. 39-86. College Publications, London, 2010. (online)
10. Pasch's philosophy of mathematics. Review of Symbolic Logic, 3(1): 93-118, March 2010. (online)
9. Learning the structure of abstract groups (with Thomas R. Shultz). In: N.A. Taatgen & H. van Rijn (eds.), Proceedings of the 31th Annual Conference of the Cognitive Science Society, pp. 2950-2955. Cognitive Science Society, Austin, TX, 2009. (online)
8. Learning from the existence of models. On psychic machines, tortoises, and computer simulations. Synthese, 169(3):521-538, August 2009. (online).
7. Bridging theories with axioms: Boole, Stone, and Tarski. In: B. van Kerkhove (ed.), New Perspectives on Mathematical Practices, pp. 222-235. World Scientific, 2009. (info, preprint)
6. Two ways of analogy: Extending the study of analogies to mathematical domains. Philosophy of Science, 75(2):178-200. April 2008. (online)
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 (eds.), Proceedings of the 30th Annual Meeting of the Cognitive Science Society, pp. 2007-2012. Cognitive Science Society, Austin, TX, 2008. (online)
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)
3. Axiomatics and progress in the light of 20th century philosophy of science and mathematics. In: B. Löwe, V. Peckhaus, and T. Rasch (eds.), 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)

Reviews

  6. A new look at analogical reasoning. (Book review of Paul F. A. Bartha, "By Parallel Reasoning. The construction and evaluation of analogical arguments"), Metascience, 21(1):197-201, 2012. (online)
  5. Book review of Torkel Franzén, "Gödel's Theorem," Review of Modern Logic, 10(3/4):257-261, March 2005-May 2007.
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. (online)
1. Book review of Kevin Possin, "Critical Thinking," Teaching Philosophy, 26(3):305-307, September 2003.

Articles in conference proceedings or technical reports

  • Symbols for nothing: Different symbolic roles of zero and their gradual emergence in Mesopotamia (with Katherine Skosnik). In: A. Cupillari (ed.), Proceedings of the 2010 Meeting of the Canadian Society for History and Philosophy of Mathematics, Montreal, 29–31 May 2010, vol. 23, pp. 257-266, 2011.
  • Dedekind's analysis of number (Part I) - systems and axioms (with Wilfried Sieg). Technical Report CMU-PHIL-139, March 18 2003.
  • Towards axiomatic foundations of mathematics: The evolution of Richard Dedekind's treatment of numbers. In: D. Curtin, D. Kullmann, D. Otero (eds.), Proceedings of the Eighth Midwest History of Mathematics Conference, Northern Kentucky University, October 13-14, 2000.

Other

  • Introduction, Ampersand, Journal of the Bachelor in Arts and Science, McGill University. Vol. 2: viii-ix, December 2009. (online)
  • Two metaphors for teaching, Graduate Times, Carnegie Mellon Graduate Student Newsletter. Vol. V, No. 4, p. 2, Summer 2003. (online)

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).