# Mathematical practice and naturalist epistemology : structures with potential for interaction

Bart Van Kerkhove; Jean Paul Van Bendegem

Philosophia Scientiae (2005)

- Volume: 9, Issue: 2, page 61-78
- ISSN: 1281-2463

## Access Full Article

top## Abstract

top## How to cite

topVan Kerkhove, Bart, and Van Bendegem, Jean Paul. "Mathematical practice and naturalist epistemology : structures with potential for interaction." Philosophia Scientiae 9.2 (2005): 61-78. <http://eudml.org/doc/103761>.

@article{VanKerkhove2005,

abstract = {In current philosophical research, there is a rather one-sided focus on the foundations of proof. A full picture of mathematical practice should however additionally involve considerations about various methodological aspects. A number of these is identified, from large-scale to small-scale ones. After that, naturalism, a philosophical school concerned with scientific practice, is looked at, as far as the translations of its epistemic principles to mathematics is concerned. Finally, we call for intensifying the interaction between both dimensions of practice and epistemology.},

author = {Van Kerkhove, Bart, Van Bendegem, Jean Paul},

journal = {Philosophia Scientiae},

language = {eng},

number = {2},

pages = {61-78},

publisher = {Éditions Kimé},

title = {Mathematical practice and naturalist epistemology : structures with potential for interaction},

url = {http://eudml.org/doc/103761},

volume = {9},

year = {2005},

}

TY - JOUR

AU - Van Kerkhove, Bart

AU - Van Bendegem, Jean Paul

TI - Mathematical practice and naturalist epistemology : structures with potential for interaction

JO - Philosophia Scientiae

PY - 2005

PB - Éditions Kimé

VL - 9

IS - 2

SP - 61

EP - 78

AB - In current philosophical research, there is a rather one-sided focus on the foundations of proof. A full picture of mathematical practice should however additionally involve considerations about various methodological aspects. A number of these is identified, from large-scale to small-scale ones. After that, naturalism, a philosophical school concerned with scientific practice, is looked at, as far as the translations of its epistemic principles to mathematics is concerned. Finally, we call for intensifying the interaction between both dimensions of practice and epistemology.

LA - eng

UR - http://eudml.org/doc/103761

ER -

## References

top- [1] Ascher, Marcia1998.— Ethnomathematics. A Multicultural View of Mathematical Ideas, Boca Raton: Chapman & Hall / CRC. Zbl1089.01501MR1343249
- [2] Ascher, Marcia2002.— Mathematics Elsewhere. An Exploration of Ideas Across Cultures, Princeton - Oxford: Princeton University Press. Zbl1115.01003MR1918532
- [3] Bell, E.T.1992.— The Development of Mathematics, New York: Dover Publications. (unaltered from the 1945 second edition published by McGraw-Hill.) 1991 Knowledge and Social Imagery, Chicago - London: The University of Chicago Press. (second edition) Zbl0061.00101MR16318
- [4] Browder, Felix E.2002.— Reflections on the Future of Mathematics, Notices of the AMS, 49(6), 658–62. Zbl1126.01302MR1908329
- [5] Butterworth, Brian2000.— The Mathematical Brain, London: Papermac. (reprint of the 1999 original published by Macmillan)
- [6] Cheng Don, Pan & Cheng Biao, Pan 1992.— Goldbach Conjecture, Beijing: Science Press. MR1287852
- [7] Code, Lorraine1996.— What is Natural about Epistemology Naturalized?, American Philosophical Quarterly, 33(1), 1–22.
- [8] Corry, Leo1992.— Nicolas Bourbaki and the Concept of Mathematical Structure, Synthese, 92, 315–48. Zbl0752.00004MR1186173
- [9] Cox, David A.1994.— Introduction to Fermat’s Last Theorem, American Mathematical Monthly, 101(1), 3–14. Zbl0849.11002MR1252700
- [10] Courant, Richard & Robbins, Herbert1996.— What Is Mathematics? An Elementary Approach to Ideas and Methods, Oxford - New York: Oxford University Press. (second, revised edition by Ian Stewart of the 1941 original) Zbl0865.00001MR5358
- [11] Davis, Philip J.1972.— Fidelity in Mathematical Discourse: Is One and One Really Two?, American Mathematical Monthly, 79(3), 252–63. Zbl0229.02006MR300839
- [12] Dehaene, Stanislas1998.— The Number Sense. How the Mind Creates Mathematics, London - New York: Allen Lane - The Penguin Press. (first published in 1997 by Oxford University Press, New York) Zbl1041.00504
- [13] Devlin, Keith1992.— The Death of Proof?, Notices of the AMS, 40, 1352.
- [14] Duda, Roman1997.— Mathematics: Essential Tensions, Foundations of Science 2(1), 11–9. Zbl1031.00505
- [15] Ernest, Paul1998.— Social Constructivism as a Philosophy of Mathematics, Albany: State University of New York Press. MR1483070
- [16] Fritsch, Rudolf & Fritsch, Gerda1998.— The Four-Color Theorem. History, Topological Foundations and Idea of Proof, New York: Springer-Verlag. (translated from the German original text by Julie Peschke) Zbl0908.05041MR1633950
- [17] Gelbart, Stephen1984.— An Elementary Introduction to the Langlands Programme, Bulletin (New Series) of the AMS, 10(2), 177–219. Zbl0539.12008MR733692
- [18] Gillies, Donald (ed.) 1992.— Revolutions in Mathematics, Oxford: Oxford University Press. Zbl0758.01019MR1192351
- [19] Goodman, Nicolas D.1990.— Mathematics as Natural Science, Journal of Symbolic Logic, 55(1), 182–93. Zbl0713.00001MR1043551
- [20] Heintz, Bettina2000.— Die Innenwelt der Mathematik. Zur Kultur und Praxis einer beweisenden Disziplin, Vienna - New York: Springer. Zbl0949.01033MR1831554
- [21] Hilbert, David2002.— Mathematical Problems, Bulletin (New Series) of the AMS, 8, 437–79.
- [22] Jaffe, Arthur & Quinn, Frank1993.— Theoretical Mathematics: Toward a Cultural Synthesis of Mathematics and Theoretical Physics, Bulletin (New Series) of the AMS, 29(1), 1–13. Zbl0780.00001MR1202292
- [23] Kline, Morris1990.— Mathematical Thought from Ancient to Modern Times, New York: Oxford University Press. (three volumes, second print of the 1972 original edition) Zbl0784.01048MR472307
- [24] Koetsier, Teun1991.— Lakatos’ Philosophy of Mathematics. A Historical Approach, Amsterdam: North-Holland. Zbl0743.00017MR1138463
- [25] Kornblith, Hilary1997.— Naturalizing Epistemology, Cambridge, MA – London: The MIT Press.
- [26] Kuhn, Thomas S.1962.— The Structure of Scientific Revolutions, Chicago – London: The University of Chicago Press.
- [27] Lakatos, Imre1976.— Proofs and Refutations. The Logic of Mathematical Discovery, Cambridge, MA: Cambridge University Press. (edited by J. Worrall and E. Zahar) Zbl0334.00022MR479916
- [28] Livingston, Eric1986.— The Ethnomethodological Foundations of Mathematics, London: Routledge & Kegan Paul. 1997 Naturalism in Mathematics, Oxford: Clarendon Press. MR835209
- [29] Maddy, Penelope1998.— How to Be a Naturalist about Mathematics, H.G. Dales and G. Oliveri (eds.), Truth in Mathematics, Oxford: Clarendon Press, 161–80. Zbl0927.03010MR1688341
- [30] Otte, Michael1999.— Mathematical Creativity and the Character of Mathematical Objects, Logique et Analyse, 167-168, 387–410. Zbl1035.00004MR1947596
- [31] Parshall, Karen Hunger & Rice, Adrian C. (eds.) 2002.— Mathematics Unbound: The Evolution of an International Mathematical Research Community, 1800-1945. History of Mathematics Vol.23, Providence (RI) - London: American Mathematical Society. Zbl1004.01016MR1907166
- [32] Peressini, Anthony1999.— Confirming Mathematical Theories: An Ontologically Agnostic Stance, Synthese, 118(2), 257–77. Zbl0942.03006MR1718715
- [33] Polya, George1973.— Mathematics and Plausible Reasoning. Two Vols, Princeton (NJ): Princeton University Press. (eight print of the 1954 original) Zbl0931.00012
- [34] Putnam, Hilary2002.— The Collapse of the Fact/Value Dichotomy and Other Essays, Cambridge (MA) - London: Harvard University Press.
- [35] Resnik, Michael1998.— Holistic Mathematics, Matthias Schirn (ed.), The Philosophy of Mathematics Today, Oxford: Clarendon Press, 227–46. Zbl0915.03007MR1701942
- [36] Restivo, Sal1992.— Mathematics in Society and History. Episteme Vol.20, Dordrecht - Boston - London: Kluwer Academic Publishers. Zbl0869.01001MR1247703
- [37] Rotman, Brian2000.— Mathematics as Sign: Writing, Imagining, Counting, Stanford: Stanford University Press. Zbl1001.00003MR1820834
- [38] Solomon, Ronald2001.— A Brief History of the Classification of the Finite Simple Groups, Bulletin (New Series) of the AMS, 38(3), 315–52. Zbl0983.20001MR1824893
- [39] Van Bendegem, Jean Paul 1998.— What, If Anything, Is an Experiment in Mathematics?, Dionysios Anapolitanos (ed.), Philosophy and the Many Faces of Science, Lanham: Rowman & Littlefield, Lanham, 172–82.
- [40] Van Bendegem, Jean Paul 1999.— The Creative Growth of Mathematics, Philosophica, 63, 119–52. Zbl1195.00022
- [41] Van Bendegem, Jean Paul 2000.— Analogy and Metaphor as Essentials Tools for the Working Mathematician, Fernand Hallyn, ed., Metaphor and Analogy in the Sciences, Dordrecht - Boston: Kluwer Academic Publishers, 105–23.
- [42] Van Kerkhove, Bart2002.— Guises of Naturalism in the Foundations of Mathematics Debate, Proceedings of the Canadian Society for the History and Philosophy of Mathematics, 15, 169–82.
- [43] Van Kerkhove, Bart2004.— Review of [Heintz 2000], Philosophia Mathematica (III), 12(1), 69–74.
- [44] Wang, Hao1974.— From Mathematics to Philosophy, London: Routledge & Kegan Paul. Zbl0554.03002
- [45] Weinberg, Steven1993.— Dreams of a Final Theory. The Search for the Fundamental Laws of Nature, London: Vintage. (First published by Hutchinson Radius.)

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.