Advertisement

Philosophy or Not? The Study of Cultures and Practices of Mathematics

  • Benedikt Löwe
Conference paper
Part of the Trends in the History of Science book series (TRENDSHISTORYSCIENCE)

Abstract

The most commonly accepted name of our research field is Philosophy of Mathematical Practice, giving philosophy a prioritized role among the many disciplines involved in the field. We explore the interplay between philosophy and other disciplines and its effect on the further development of our field.

Keywords

Mathematics Education Philosophical Argument Mathematical Practice Philosophical Theory Philosophical Question 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Baggio, G., van Lambalgen, M., & Hagoort, P. (2008). Computing and recomputing discourse models: An ERP study. Journal of Memory and Language, 59(1), 36–53.CrossRefGoogle Scholar
  2. Buldt, B., Löwe, B., & Müller, T. (2008). Towards a new epistemology of mathematics. Erkenntnis, 68, 309–329.MathSciNetzbMATHCrossRefGoogle Scholar
  3. Corfield, D. (2003). Towards a philosophy of real mathematics. Cambridge: Cambridge University Press.zbMATHCrossRefGoogle Scholar
  4. David, A., Aumann, C., Santos, N., Bewernick, B., Eickhoff, S., Newen, A., et al. (2008). Differential involvement of the posterior temporal cortes in mental versus spatial perspective taking. Social Cognitive and Affective Neuroscience, 3, 279–289.CrossRefGoogle Scholar
  5. David, N., Bewernick, B., Cohen, M., Newen, A., Lux, S., Fink, G., et al. (2006). The self-other distinction in social cognition—Perspective-taking and agency in a virtual ball-tossing game. Journal of Cognitive Neuroscience, 18, 898–910.CrossRefGoogle Scholar
  6. Dutilh Novaes, C. (2012). Towards a practice-based philosophy of logic: Formal languages as a case study. Philosophia Scientiae, 16, 71–102.MathSciNetzbMATHCrossRefGoogle Scholar
  7. Ferreirós, J. (2014). Pragmatism in the philosophy of mathematics. Unpublished talk given at the meeting Pragmatism and the practical Turn in Philosophy of Science of the Académie Internationale de Philosophie des Sciences held in Pont-à-Mousson, September 10–14, 2014.Google Scholar
  8. Ferreirós, J. (2015). Mathematical knowledge and the interplay of practices. Princeton: Princeton University Press.zbMATHGoogle Scholar
  9. Greiffenhagen, C. (2008). Video analysis of mathematical practice? Different attempts to ‘open up’ mathematics for sociological investigation. Forum: Qualitative Social Research, 9(3), 1–20.Google Scholar
  10. Greiffenhagen, C., & Sharrock, W. (2011a). Does mathematics look certain in the front, but fallible in the back? Social Studies of Science, 41(6), 839–866.zbMATHCrossRefGoogle Scholar
  11. Greiffenhagen, C., & Sharrock, W. (2011b). Sources for myths about mathematics. On the significance of the difference between finished mathematics and mathematics-in-the-making. In K. François, B. Löwe, T. Müller, & B. Van Kerkhove (Eds.), Foundations of the formal sciences VII. Bringing together philosophy and sociology of science. Studies in logic (Vol. 32, pp. 91–109). London: College Publications.Google Scholar
  12. Greiffenhagen, C. W. K. (2014). The materiality of mathematics: Presenting mathematics at the blackboard. British Journal of Sociology, 65(3), 502–528.CrossRefGoogle Scholar
  13. Heintz, B. (2000). Die Innenwelt der Mathematik. Zur Kultur und Praxis einer beweisenden Disziplin (pp. 1–22). Wien: Springer.CrossRefGoogle Scholar
  14. Hersh, R. (1997). What is mathematics, really? Oxford: Oxford University Press.zbMATHGoogle Scholar
  15. Inglis, M., & Alcock, L. (2012). Expert and novice approaches to reading mathematical proofs. Journal for Research in Mathematics Education, 43, 358–390.CrossRefGoogle Scholar
  16. Inglis, M., Mejia-Ramos, J. P., Weber, K., & Alcock, L. (2013). On mathematicians’ different standards when evaluating elementary proofs. Topics in Cognitive Science, 5(2), 270–282.CrossRefGoogle Scholar
  17. Jullien, C., & Soler, L. (2014). Conceptions of mathematical practices: Some remarks. Commentary on “The impact of the philosophy of mathematical practice on the philosophy of mathematics”, by Jean Paul Van Bendegem. In L. Soler, S. Zwart, M. Lynch, & V. Israel-Jost (Eds.), Science after the practice turn in the philosophy, history, and social studies of science. Routledge studies in the philosophy of science (pp. 227–237). New York: Routledge.Google Scholar
  18. Kauppinen, A. (2007). The rise and fall of experimental philosophy. Philosophical Explorations, 10(2), 95–118.CrossRefGoogle Scholar
  19. Kitcher, P., & Aspray, W. (1988). An opinionated introduction. In W. Aspray & P. Kitcher (Eds.), History and philosophy of modern mathematics. Minnesota studies in the philosophy of science (Vol. XI, pp. 3–57). Minneapolis: University of Minnesota Press.Google Scholar
  20. Kockler, H., Scheef, L., Tepest, R., David, N., Bewernick, B. H., Newen, A., et al. (2010). Visuospatial perspective taking in a dynamic environment: Perceiving moving objects from a first-person-perspective induces a disposition to act. Consciousness and Cognition, 19(3), 690–701.CrossRefGoogle Scholar
  21. Larvor, B. P. (2016). What are mathematical cultures? In S. Ju, B. Löwe, T. Müller, & Y. Xie (Eds.), Cultures of Mathematics and Logic, Selected Papers from the Conference in Guangzhou, China, November 9–12, 2012. Trends in the history of science. Berlin: Springer, pp. 1–22.Google Scholar
  22. Larvor, B. P., & Löwe, B. (2016, in preparation). Cultures of mathematical research training. White Paper reporting on a project organised by the International Union for History and Philosophy of Science and Technology.Google Scholar
  23. Lieberson, S., & Lynn, F. B. (2002). Barking up the wrong branch: Scientific alternatives to the current model of sociological science. Annual Review of Sociology, 28, 1–19.CrossRefGoogle Scholar
  24. Löwe, B. (2014). Mathematics and the new technologies. Part I: Philosophical relevance of a changing culture of mathematics. In P. Schroeder-Heister, G. Heinzmann, W. Hodges, & P. E. Bour (Eds.), Logic, Methodology and Philosophy of Science, Proceedings of the 14th International Congress (Nancy), Logic and Science Facing the New Technologies (pp. 399–407). London: College Publications.Google Scholar
  25. Löwe, B., & Müller, T. (Eds.). (2010). PhiMSAMP. Philosophy of mathematics: Sociological aspects and mathematical practice. Texts in philosophy (Vol. 11). London: College Publications.Google Scholar
  26. Löwe, B., Müller, T., & Müller-Hill, E. (2010). Mathematical knowledge: A case study in empirical philosophy of mathematics. In B. Van Kerkhove, J. De Vuyst, & J. P. Van Bendegem (Eds.), Philosophical perspectives on mathematical practice. Texts in philosophy (Vol. 12, pp. 185–203). London: College Publications.Google Scholar
  27. Löwe, B., & Van Kerkhove, B. (in preparation). Methodological triangulation in empirical philosophy of mathematics.Google Scholar
  28. MacKenzie, D. (2006). Computers and the sociology of mathematical proof. In R. Hersh (Ed.), 18 unconventional essays on the nature of mathematics (pp. 128–146). Berlin: Springer.CrossRefGoogle Scholar
  29. Maddirala, N. (2014). Philosophy of logical practice: A case study in formal semantics (Master’s thesis). Universiteit van Amsterdam. ILLC Publications MoL-2014-15.Google Scholar
  30. Maddy, P. (1990). Realism in mathematics. Oxford: Oxford University Press.zbMATHGoogle Scholar
  31. Maddy, P. (1997). Naturalism in mathematics. Oxford: Oxford University Press.zbMATHGoogle Scholar
  32. Maddy, P. (2001). Naturalism: Friends and foes. In J. Tomberlin (Ed.), Philosophical perspectives, Volume 15: Metaphysics (pp. 37–67). Oxford: Blackwell.Google Scholar
  33. Maddy, P. (2003). Second philosophy. Journal of the Indian Council of Philosophical Research, 20, 73–106.Google Scholar
  34. Maddy, P. (2007). Second philosophy. A naturalistic method. Oxford: Oxford University Press.zbMATHCrossRefGoogle Scholar
  35. Mancosu, P. (2008a). Introduction. In P. Mancosu (Ed.), The philosophy of mathematical practice (pp. 1–21). Oxford: Oxford University Press.CrossRefGoogle Scholar
  36. Mancosu, P. (Ed.). (2008b). The philosophy of mathematical practice. Oxford: Oxford University Press.zbMATHGoogle Scholar
  37. Marrou, H.-I. (1934). “Doctrina” et “Disciplina” dans la langue des pères de l’église. Bulletin du Cange, Archivum Latinitatis Medii Aevi, 9, 5–25.Google Scholar
  38. Müller-Hill, E. (2009). Formalizability and knowledge ascriptions in mathematical practice. Philosophia Scientiae, 13(2), 21–43.zbMATHCrossRefGoogle Scholar
  39. Müller-Hill, E. (2011). Die epistemische Rolle formalisierbarer mathematischer Beweise—Formalisierbarkeitsorientierte Konzeptionen mathematischen Wissens und mathematischer Rechtfertigung innerhalb einer sozio-empirisch informierten Erkenntnistheorie der Mathematik (PhD thesis). Rheinische Friedrich-Wilhelms-Universität Bonn.Google Scholar
  40. Papineau, D. (2015). Naturalism. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy (Fall 2015 Edn.). CSLI, Stanford.Google Scholar
  41. Pijnacker, J., Geurts, B., van Lambalgen, M., Buitelaar, J., & Hagoort, P. (2011). Reasoning with exceptions: An event-related brain potentials study. Journal of Cognitive Neuroscience, 23(2), 471–480.CrossRefGoogle Scholar
  42. Prinz, J. J. (2008). Empirical philosophy and experimental philosophy. In J. Knobe & S. Nichols (Eds.), Experimental philosophy (pp. 198–208). Oxford: Oxford University Press.Google Scholar
  43. Rosental, C. (2008). Weaving self-evidence. A sociology of logic. Princeton: Princeton University Press.zbMATHGoogle Scholar
  44. Stokhof, M., & van Lambalgen, M. (2011). Abstractions and idealisations: The construction of modern linguistics. Theoretical Linguistics, 37(1–2), 1–26.CrossRefGoogle Scholar
  45. Sutherland, W. J., Fleishman, E., Mascia, M. B., Pretty, J., & Rudd, M. A. (2011). Methods for collaboratively identifying research priorities and emerging issues in science and policy. Methods in Ecology and Evolution, 2(3), 238–247.CrossRefGoogle Scholar
  46. Van Bendegem, J. P. (2014). The impact of the philosophy of mathematical practice on the philosophy of mathematics. In L. Soler, S. Zwart, M. Lynch, & V. Israel-Jost (Eds.), Science after the practice turn in the philosophy, history, and social studies of science. Routledge studies in the philosophy of science (pp. 215–226). London: Routledge.Google Scholar
  47. Van Kerkhove, B. (Ed.). (2008). New Perspectives on Mathematical Practices. Essays in Philosophy and History of Mathematics, Brussels, Belgium, March 26–28, 2007. Singapore: World Scientific.Google Scholar
  48. Van Kerkhove, B., De Vuyst, J., & Van Bendegem, J. P. (Eds.). (2010). Philosophical perspectives on mathematical practice. Texts in philosophy (Vol. 12). London: College Publications.Google Scholar
  49. Van Kerkhove, B., & Van Bendegem, J. P. (Eds.). (2007). Perspectives on mathematical practices. Bringing together philosophy of mathematics, sociology of mathematics, and mathematics education. Logic, epistemology, and the unity of science (Vol. 5). Berlin: Springer.Google Scholar
  50. Weber, K., Inglis, M., & Mejia-Ramos, J. P. (2014). How mathematicians obtain conviction: Implications for mathematics instruction and research on epistemic cognition. Educational Psychologist, 49, 36–58.CrossRefGoogle Scholar
  51. Weber, K., & Mejia-Ramos, J. P. (2011). Why and how mathematicians read proofs: An exploratory study. Educational Studies in Mathematics, 76(3), 329–344.CrossRefGoogle Scholar
  52. Weinberg, J. M., Nichols, S., & Stich, S. (2001). Normativity and epistemic intuitions. Philosophical Topics, 29, 429–460.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Institute for Logic, Language and ComputationUniversiteit van AmsterdamAmsterdamThe Netherlands
  2. 2.Fachbereich MathematikUniversität HamburgHamburgGermany
  3. 3.Corpus Christi CollegeUniversity of CambridgeCambridgeEngland
  4. 4.Isaac Newton Institute for Mathematical SciencesCambridgeEngland

Personalised recommendations