David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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History and Philosophy of Logic 21 (3):179-194 (2000)
Michael Dummett has interpreted and expounded upon intuitionism under the influence of Wittgensteinian views on language, meaning and cognition. I argue against the application of some of these views to intuitionism and point to shortcomings in Dummett's approach. The alternative I propose makes use of recent, post-Wittgensteinian views in the philosophy of mind, meaning and language. These views are associated with the claim that human cognition exhibits intentionality and with related ideas in philosophical psychology. Intuitionism holds that mathematical constructions are mental processes or objects. Constructions are, in the first instance, forms of consciousness or possible experience of a particular type. As such, they must be understood in terms of the concept of intentionality. This view has a historical basis in the literature on intuitionism. In a famous 1931 lecture Heyting in fact identifies constructions with fulfilled or fulfillable mathematical intentions. I consider some of the consequences of this identification and contrast them with Dummett's views on intuitionism
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References found in this work BETA
Paul Benacerraf & Hilary Putnam (eds.) (1983). Philosophy of Mathematics: Selected Readings. Cambridge University Press.
Michael A. E. Dummett (2000). Elements of Intuitionism. Oxford University Press.
Michael A. E. Dummett (1978). Truth and Other Enigmas. Harvard University Press.
Michael A. E. Dummett (1991). The Logical Basis of Metaphysics. Harvard University Press.
Michael A. E. Dummett (1993). The Seas of Language. Oxford University Press.
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