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.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1016/S0039-3681(00)00010-8
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
Download options
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 21,428
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
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

Add more references

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.

Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

24 ( #165,650 of 1,911,593 )

Recent downloads (6 months)

2 ( #321,691 of 1,911,593 )

How can I increase my downloads?

My notes
Sign in to use this feature

Start a new thread
There  are no threads in this forum
Nothing in this forum yet.