Везде
Revolutions in mathematics: an old debate revisited. Part 2
Table of contents
Annotation Estimate Publication content
References Comments
Share
QR
Metrics
Revolutions in mathematics: an old debate revisited. Part 2
Annotation
PII
S2413-90840000616-5-1
Publication type
Article
Status
Published
Authors
Vladislav Shaposhnikov 
Edition
Volume 25 Issue 1
Pages
5-17
Abstract
This paper is the second (and final) part of a study of the debate concerning the existence and meaning of revolutions in the history of mathematics. The discussion in question has emerged in the 1970s and was inspired by T.S. Kuhn’s hugely influential theory of science. In the previous part of this study, an initial Crowe - Dauben controversy is considered. M.J. Crowe put forward ten “laws” concerning the evolution of mathematics with the final one stating that revolutions never occur in mathematics. At the same time, J.W. Dauben tried to support the occurrence of revolutions in mathematics. The story of the debate - which was famously summed up in D. Gillies’s 1992 edited collection “Revolutions in Mathematics” - apparently suggested that Dauben’s position entirely predominates over Crowe’s among the scholars; even Crowe was finally forced to acknowledge the occurrence of revolutions in mathematics. In 2000 B. Pourciau disputed such a view of the debate’s outcome, stressing that the overwhelming majority of the scholars who took part in the 1992 collection, happily married the recognition of revolutions in the history of mathematics with the strictly cumulative character of mathematics as far as mathematical results are concerned. In other words, they were talking about “revolutions” that cannot be called “Kuhnian”. It means that only the nominal victory is Dauben’s while the real one is Crowe’s. In this part of the study, a lot of additional material belonging to the debate is analyzed. This analysis corroborates Pourciau’s thesis and takes a closer look at the varieties of the “compromise” position accepting revolutions in mathematics on one level while rejecting them on the other. Some reviewers consider the debate on the revolutions in mathematics futile. Still, this study shows it to be highly instructive in bringing to light some ambivalent trends in the philosophy of mathematical practice.
Keywords
philosophy of mathematics, philosophy of mathematical practice, revolutions in mathematics, cumulativity of the development of mathematics, T.S. Kuhn
Date of publication
01.06.2020
Number of purchasers
22
Views
466
Readers community rating
0.0 (0 votes)
Cite Download pdf

References



Additional sources and materials

    

  1. Barany, MacKenzie, 2014 – Barany M.J., MacKenzie D. Chalk: Materials and Concepts in Mathematics Research // Representation in Scientific Practice Revisited / Ed. by C. Coopmans, J. Vertesi, M. Lynch and S. Woolgar. Cambridge, MA: The MIT Press, 2014. P. 107−129.
    2. 

  2. Bloor, 1991 – Bloor D. Knowledge and Social Imagery. 2nd ed. Chicago: University of Chicago Press, 1991. 203 p.
    3. 

  3. Bueno, 2007 – Bueno O. Incommensurability in Mathematics // Perspectives on Mathematical Practices / Ed. by B. Van Kerkhove and J.P. Van Bendegem. Dordrecht: Springer, 2007. P. 83−105.
    4. 

  4. Bueno, 2012 – Bueno O. Styles of Reasoning: A Pluralist View // Studies in History and Philosophy of Science. Part A. 2012. Vol. 43. No. 4. P. 657−665.
    5. 

  5. Bunge, 1983a – Bunge M. Treatise on Basic Philosophy, Vol. 5. Epistemology and Methodology I: Exploring the World. Dordrecht: D. Reidel Publishing Company, 1983. 404 p.
    6. 

  6. Bunge, 1983b – Bunge M. Treatise on Basic Philosophy, Vol. 6. Epistemology and Methodology II: Understanding the World. Dordrecht: D. Reidel Publishing Company, 1983. 296 p.
    7. 

  7. Corry, 1989 – Corry L. Linearity and Reflexivity in the Growth of Mathematical Knowledge // Science in Context. 1989. Vol. 3. No. 2. P. 409−440.
    8. 

  8. Corry, 1993 – Corry L. Kuhnian Issues, Scientific Revolutions and the History of Mathematics // Studies in History and Philosophy of Science. Part A. 1993. Vol. 24. No. 1. P. 95−117.
    9. 

  9. Corry, 1996 – Corry L. Paradigms and Paradigmatic Change in the History of Mathematics // Paradigms and Mathematics / Ed. by E. Ausejo and M. Hormigón. Madrid: Siglo XXI de España Editores, 1996. P. 169−191.
    10. 

  10. Corry, 2004/1996 – Corry L. Modern Algebra and the Rise of Mathematical Structures. 2nd rev. ed. Basel: Birkhäuser, 2004. 451 p. (First edition was published in 1996.)
    11. 

  11. Crowe, 1975 – Crowe M.J. Ten “Laws” Concerning Patterns of Change in the History of Mathematics // Historia Mathematica. 1975. Vol. 2. No. 2. P. 161−166.
    12. 

  12. Dauben, 1984 – Dauben J.W. Conceptual Revolutions and the History of Mathematics: Two Studies in the Growth of Knowledge // Transformation and Tradition in the Sciences: Essays in Honor of I. Bernard Cohen / Ed. by E. Mendelsohn. N.Y.: Cambridge University Press, 1984. P. 81−103.
    13. 

  13. Dauben, 1996 – Dauben J.W. Paradigms and Proofs: How Revolutions Transform Mathematics // Paradigms and Mathematics / Ed. by E. Ausejo and M. Hormigón. Madrid: Siglo XXI de España Editores, 1996. P. 117−148.
    14. 

  14. Elkana, 1981 – Elkana Y. A Programmatic Attempt at an Anthropology of Knowledge // Sciences and Cultures: Anthropological and Historical Studies of Sciences / Ed. by E. Mendelsohn and Y. Elkana. Dordrecht: D. Reidel, 1981. P. 1−76.
    15. 

  15. François, Van Bendegem, 2010 – François K., Van Bendegem J.P. Revolutions in Mathematics. More Than Thirty Years after Crowe’s “Ten Laws”. A New Interpretation // PhiMSAMP. Philosophy of Mathematics: Sociological Aspects and Mathematical Practice / Ed. by B. Löwe and T. Müller. L.: College Publications, 2010. P. 107‒120.
    16. 

  16. Gillies (ed.), 1992 – Revolutions in Mathematics / Ed. by D. Gillies. N.Y.: Oxford University Press, 1992. 353 p.
    17. 

  17. Grabiner, 1974 – Grabiner J.V. Is Mathematical Truth Time-Dependent? // The American Mathematical Monthly. 1974. Vol. 81. No. 4. P. 354−365.
    18. 

  18. Greiffenhagen, 2014 – Greiffenhagen C. The Materiality of Mathematics: Presenting Mathematics at the Blackboard // The British Journal of Sociology. 2014. Vol. 65. No. 3. P. 502−528.
    19. 

  19. Kitcher, 1983 – Kitcher P. The Nature of Mathematical Knowledge. N.Y.: Oxford University Press, 1983. 296 p.
    20. 

  20. Kuznetsova, I.S. Gnoseologicheskiye problemy matematicheskogo znaniya [Epistemological Problems of Mathematical Knowledge]. Leningrad: Leningrad University Press, 1984. 136 pp. (In Russian)
    21. 

  21. McCleary, McKinney, 1986 – McCleary J., McKinney A. What Mathematics Isn’t // Mathematical Intelligencer. 1986. Vol. 8. No. 3. P. 51−53, 77.
    22. 

  22. Porter, 1995 – Porter T.M. Trust in Numbers: The Pursuit of Objectivity in Science and Public Life. Princeton, NJ: Princeton University Press, 1995. 310 p.
    23. 

  23. Pourciau, 2000 – Pourciau B. Intuitionism as a (Failed) Kuhnian Revolution in Mathematics // Studies in the History and Philosophy of Science. Part A. 2000. Vol. 31. No. 2. P. 297−329.
    24. 

  24. Rodin, A.V. “Kontseptsiya permanentnoy nauchnoy revolyutsii i osnovaniya matematiki (vozvrashchayas’ k sporu mezhdu Krou i Daubenom)” [The Concept of Permanent Scientific Revolution and the Foundations of Mathematics: the Crowe−Dauben Debate Revisited], in: Revolyutsiya i evolyutsiya: modeli razvitiya v nauke, kul’ture, sotsiume [Revolution and Evolution: Models of Development in Science, Culture and Society], ed. by I.T. Kasavin and A.M. Feigelman. Nizhny Novgorod: Lobachevsky University Press, 2017, pp. 34−36. (In Russian)
    25. 

  25. Ruzavin, G.I. “Ob osobennostyakh nauchnykh revolyutsiy v matematike” [On the Special Characteristics of Scientific Revolutions in Mathematics], in: Metodologicheskiy analiz zakonomernostey razvitiya matematiki [Methodological Analysis of the Patterns of Change in Mathematics], ed. by A.G. Barabashev, S.S. Demidov and M.I. Panov. Moscow: VINITI, 1989, pp. 180−193. (In Russian)
    26. 

  26. Sialaros (ed.), 2018 – Revolutions and Continuity in Greek Mathematics / Ed. by M. Sialaros. Berlin: De Gruyter, 2018. 391 p.
    27. 

  27. Sokuler, Z.A. Zarubezhnyye issledovaniya po filosofskim problemam matematiki 90-kh godov: Nauchno-analiticheskiy obzor [Foreign Studies in the Philosophy of Mathematics of the 1990s: A Review]. Moscow: INION, 1995. 75 pp. (In Russian)
    28. 

  28. Tymoczko (ed.), 1986 – New Directions in the Philosophy of Mathematics: An Anthology / Ed. by T. Tymoczko. Boston, MA: Birkhäuser, 1986. 341 p.
    29. 

  29. Wilder, 1981 – Wilder R.L. Mathematics as a Cultural System. Oxford: Pergamon Press, 1981. 190 p.
    30.

Comments

No posts found

Write a review
Translate