by Corry Shores
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[The following is summary. I am not a mathematician, so please consult the original text instead of trusting my summarizations. Bracketed comments are my own. Proofreading is incomplete, so please forgive my mistakes.]
Summary of
Walter P. van Stigt
“Brouwer’s Intuitionist Programme”
in
From Brouwer to Hilbert:
The Debate on the Foundations of Mathematics in the 1920’s
Part I.
L.E.J. Brouwer
Ch1.:
“Brouwer’s Intuitionist Programme”
[1.0]
[Introductory material]
Brief summary:
(1.0.1) Luitzen Egbertus Jan Brouwer (1881-1966) “main contributions are in the field of topology and the foundations of mathematics,” but “It is Brouwer’s contribution to the foundations of mathematics, the intuitionist programme, that has made him known to the wider scientific and philosophical community” (1). His influence is still great today. van Stigt will give an overview of Brouwer’s intuitionistic program.
[General Introduction to Brouwer and His Intuitionistic Program]
Summary
[General Introduction to Brouwer and His Intuitionistic Program]
[Luitzen Egbertus Jan Brouwer (1881-1966) “main contributions are in the field of topology and the foundations of mathematics,” but “It is Brouwer’s contribution to the foundations of mathematics, the intuitionist programme, that has made him known to the wider scientific and philosophical community” (1). His influence is still great today. van Stigt will give an overview of Brouwer’s intuitionistic program.]
[ditto]
Luitzen Egbertus Jan Brouwer (1881-1966) is a central figure in the history of contemporary mathematics and philosophy.1 His main contributions are in the field of topology and the foundations of mathematics. It is Brouwer’s contribution to the foundations of mathematics, the intuitionist programme, that has made him known to the wider scientific and philosophical community. His influence is very much alive today, as is witnessed by the ongoing mathematical research in intuitionist and constructive mathematics (see Bridges, Richman 1987, and Troelstra, van Dalen, 1988) and by the variety of philosophical contributions that have their roots in Brouwer’s intuitionism (see, for instance, Detlefsen 1990, Dummett 1973, 1977, McCarthy 1983). However, although many of these contributions take their start from Brouwer’s intuitionist approach, it is also true that they have departed to a great extent from Brouwer’s original formulation of the programme. In van Stigt 1990 I have endeavored to present Brouwer and his intuitionist programme in their historical setting. The following introduction is conceived in the same spirit. I shall begin with a section on the intuitionist-formalist controversy. Section 1.2 is about Brouwer's intuitionist philosophy of mathematics. Sections 1.3 and 1.4 present Brouwer’s views on the nature of mathematics and on the relationship between mathematics, language, and logic. Section 1.5 gives an account of Brouwer’s new set theory and his conception of the continuum. Finally, Section 1.6 gives a short introduction to the selected contributions.
(1)
1. Brouwer was professor of mathematics at the University of Amsterdam from 1912 until his retirement in 1951 . For further details of his life and career, see van Stigt 1990. A Brouwer biography by D . van Dalen is in preparation. Franchella 1994 contains an extended bibliography on B rouwer and intuitionism.
(20)
van Stigt, W. P., 1990, Brouwer’s Intuitionism, North-Holland, Amsterdam.
(22)
From:
Stigt, Walter P. van. (1989). “Brouwer’s Intuitionist Programme” In: From Brouwer to Hilbert: The Debate on the Foundations of Mathematics in the 1920’s, edited by Paolo Mancosu. Oxford: Oxford University.
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