Mathematical progress: Between reason and society [Book Review]
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Journal for General Philosophy of Science 24 (2):235-256 (1993)
It is shown how the historiographic purport of Lakatosian methodology of mathematics is structured on the theme of analysis and synthesis. This theme is explored and extended to the revolutionary phase around 1800. On the basis of this historical investigation it is argued that major innovations, crucial to the appraisal of mathematical progress, defy reconstruction as irreducibly rational processes and should instead essentially be understood as processes of social-cognitive interaction. A model of conceptual change is developed whose essential ingredients are the variability of rational responses to new intellectual and practical challenges arising in the cultural environment of mathematics, and the shifting selective pressure of society. The resulting view of mathematical development is compared with Kuhn's theory of scientific paradigms in the light of some personal communications
|Keywords||analysis and synthesis the problem of appraisal revisited model of socio-cognitive interplay between Lakatos and Kuhn the rational and the social|
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References found in this work BETA
Eduard Glas (1988). Between Form and Function. Social Issues in Mathematical Change. Philosophica 42 (2):21-41.
Eduard Glas (1986). On the Dynamics of Mathematical Change in the Case of Monge and the French Revolution. Studies in History and Philosophy of Science Part A 17 (3):249-268.
Ts Khn (1970). Reflections on My Critics. In Imre Lakatos & Alan Musgrave (eds.), Criticism and the Growth of Knowledge. Cambridge University Press.
Philip Kitcher (1983). The Nature of Mathematical Knowledge. Oxford University Press.
Thomas S. Kuhn (1983). Rationality and Theory Choice. Journal of Philosophy 80 (10):563-570.
Citations of this work BETA
D. Corfield (1997). Assaying Lakatos's Philosophy of Mathematics. Studies in History and Philosophy of Science Part A 28 (1):99-121.
Eduard Glas (1993). From Form to Function: A Reassessment of Felix Klein's Unified Programme of Mathematical Research, Education and Development. Studies in History and Philosophy of Science Part A 24 (4):611-631.
Eduard Glas (2001). The 'Popperian Programme' and Mathematics. Studies in History and Philosophy of Science Part A 32 (1):119-137.
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