by Corry Shores
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[Walter P. van Stigt, entry directory]
[Stigt, “Brouwer’s Intuitionist Programme,” entry directory]
[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”
1.2
“Intuitionism and Brouwer’s Intuitionist Philosophy of Mathematics”
1.2.0
[Introductory Material]
Brief summary:
(1.2.0.1) Brouwer’s intuitionism is primarily a philosophy of mathematics. (1.2.0.2) “Most of Brouwer’s philosophical views on life in general and on the nature of mathematics were formed during the years of undergraduate and doctoral studies, and they remained virtually the same throughout his life” (4). (1.2.0.3) “This section is a brief introduction to Philosophical Intuitionism and the main aspects of Brouwer’s philosophy as are relevant to his Intuitionist practice” (4).
[Intuitionism as Mathematics]
[Brouwer’s Early Philosophical Development]
[Announcing the Content of This Section]
Summary
[Intuitionism as Mathematics]
[Brouwer’s intuitionism is primarily a philosophy of mathematics.]
[ditto]
Brouwer’s Intuitionist reform of mathematics and his revolutionary views on the use of logic can only be fully understood in the context of his particular philosophy of mathematics. Indeed, his Intuitionism is first and foremost a philosophy of mathematics from which these new ideas emerge quite naturally.
(4)
[Brouwer’s Early Philosophical Development]
[“Most of Brouwer’s philosophical views on life in general and on the nature of mathematics were formed during the years of undergraduate and doctoral studies, and they remained virtually the same throughout his life” (4).]
[ditto]
Most of Brouwer’s philosophical views on life in general and on the nature of mathematics were formed during the years of undergraduate and doctoral studies, and they remained virtually the same throughout his life. They are expressed most clearly in his early publications: his doctoral thesis On the Foundations of Mathematics (B1907) and Life, Art and Mysticism (B1905), in some of his post-1928 papers such as “Mathematics, Science and Language” (B1929), “Will, Knowledge and Speech” (B1933), and “Consciousness, Philosophy and Mathematics” (B1948C), and in unpublished papers.
(4)
[Announcing the Content of This Section]
[“This section is a brief introduction to Philosophical Intuitionism and the main aspects of Brouwer’s philosophy as are relevant to his Intuitionist practice” (4).]
[ditto]
This section is a brief introduction to Philosophical Intuitionism and the main aspects of Brouwer’s philosophy as are relevant to his Intuitionist practice. A more detailed analysis is given in van Stigt 1990.
(4)
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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