Intuitionism as a (failed) Kuhnian revolution in mathematics

In this paper it is argued, firstly, that Kuhnian revolutions in mathematics are logically possible, in the sense of not being inconsistent with the nature of mathematics; and, secondly, that Kuhnian revolutions are actually possible, in the sense that a Kuhnian paradigm for mathematics can be exhibited which would, if accepted by the mathematical community, produce a full Kuhnian revolution. These two arguments depend on first proving that a shift from a classical conception of mathematics to an intuitionist conception would be incommensurable, that is, that some classical statements, possessing meanings which cannot be preserved in the intuitionist language, would become unintelligible. The vague but intriguing thesis is then tentatively advanced that Kuhnian revolutions are even historically possible, in the sense that only what we might call 'accidental' historical factors may have prevented mathematics from undergoing just such a Kuhnian revolution in the early years of the twentieth century.
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DOI 10.1016/S0039-3681(00)00010-8
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References found in this work BETA
Errett Bishop & Douglas Bridges (1987). Constructive Analysis. Journal of Symbolic Logic 52 (4):1047-1048.
Ts Khn (1970). Reflections on My Critics. In Imre Lakatos & Alan Musgrave (eds.), Criticism and the Growth of Knowledge. Cambridge University Press

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Citations of this work BETA
Alexander Paseau (2005). What the Foundationalist Filter Kept Out. Studies in History and Philosophy of Science Part A 36 (1):191-201.
E. Glas (2002). Socially Conditioned Mathematical Change: The Case of the French Revolution. Studies in History and Philosophy of Science Part A 33 (4):709-728.

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