Philosophical Investigation 2023 KCI Impact Factor : 0.41
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pISSN : 1598-7213 / eISSN : 2671-7565
- https://journal.kci.go.kr/philinst
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Brouwer’s Intuitionism and Construction
- Philosophical Investigation
- 2016, 44(), pp.69~102
- DOI : 10.33156/philos.2016.44..003
- Publisher : Institute of philosophy in Chung-Ang Univ.
- Research Area : Humanities > Philosophy
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ABSTRACT
This paper purposes to show that Brouwer’s intuitionism can be regarded as a philosophical account of the early constructivism, a trend exemplified by the works of Kronecker and Poincaré, and then to consider its implications on classical mathematics. For these, I first reconstruct Brouwer’s claim that mathematics is a mental activity. Next, I argue that the claim plays an important role in the development of constructivism. Thirdly, after showing that choice sequences define real numbers, I examine the argument that the choice sequence method leads to undermining of the classical notion of truth and may be regarded as an alternative way to the classical definition of real numbers. Finally, I argue that Wittgenstein’s objection to Brouwerian real number construction is not successful.
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[journal]
van Atten, M
/ 2002
/ The Irreflexivity of Brouwer's Philosophy
/ Axiomathes
13
: 65~77
[book]
van Atten, M
/ 2004
/ On Brouwer, Wadsworth Philosophers Series
/ Thomson Learning
[journal]
Brouwer, L.E.J
/ 1905
/ Life, Art and Mysticism
/ Notre Dame Journal of Formal Logic
37(3)
: 391~429
[other]
Brouwer, L.E.J
/ 1907
/ On The Foundations of Mathematics
/ BCW
: 11~101
[other]
Brouwer, L.E.J
/ 1908
/ Die Mögliche Mächtigkeiten
/ BCW
: 102~104
[other]
Brouwer, L.E.J
/ 1908
/ The Unreliability of The Logical Principles
/ BCW
: 107~111
[other]
Brouwer, L.E.J
/ 1912
/ Intuitionism and Formalism
/ BCW
: 123~138
[other]
Brouwer, L.E.J
/ 1918
/ Begründung der Mengenlehre unabhänig vom logischen Satz vom ausgeschlossen Dritten, Erst Teil
/ BCW
: 151~190
[other]
Brouwer, L. E. J
/ 1923
/ On the Significance of the Principle of Excluded Middle in Mathematics, especially in Function Theory
/ van Heijenoort
: 334~341
[other]
Brouwer, L. E. J
/ 1925
/ Zur Begründung der Intuitionistischen Mathematik I
/ BCW
: 301~314
[other]
Brouwer, L. E. J
/ 1927
/ On the Domains of Definition of Functions
/ van Heijenoort
: 457~463
[other]
Brouwer, L.E.J
/ 1929
/ Mathematics, Science, and Language
/ Mancosu
: 45~53
[other]
Brouwer, L.E.J
/ 1930
/ The Structure of the Continuum
/ Manscou
: 54~63
[other]
Brouwer, L.E.J
/ 1933
/ Will, Knowledge and Speech
/ van Stigt
: 418~431
[other]
Brouwer, L.E.J
/ 1947
/ Guidelines of Intuitionistics
/ BCW
: 477~
[other]
Brouwer, L.E.J
/ 1948
/ Consciousness, Philosophy, and Mathematics
/ BCW
: 480~494
[other]
Brouwer, L.E.J
/ 1952
/ Historical Background, Principles and Method of Intuitionism
/ BCW
: 508~515
[other]
Brouwer, L.E.J
/ 1954
/ Points and Spaces
/ BCW
: 522~538
[other]
Brouwer, L.E.J
/ (BMS15), Notes for a course on set theory. 50-page Dutch manuscript of a course on set theory in Amsterdam between 1914 and 1916
[other]
Brouwer, L.E.J
/ 1990
/ (BMS37), Real Functions
/ van Stigt
: 469~480
[other]
Brouwer, L.E.J
/ 1990
/ (BMS59), Changes in the Relation between Clasical Logic and Mathematics
/ van Stigt
: 453~458
[book]
van Dalen. D
/ 1981
/ Brouwer's Cambridge Lectures on Intuitionism
/ Cambridge university Press
[book]
Dedekind, R
/ 1996
/ Continuity and Irrational Numbers
: 765~779
[book]
Dedekind, R
/ 1877
/ Theory of Algebraic Integer
/ Cambridge University Press
[book]
Dedekind, R
/ 1996
/ Was Sind und Was Sollen die Zahlen?
/ Ewald
: 787~833
[book]
Ewald, W
/ 1996
/ From Kant to Hilbert: A Source Book in the Foundations of Mathematics, vol. I, II
/ Clarendon Press
[book]
Goldfarb, W
/ 1988
/ History and Philosophy of Modern Mathematics
/ University of Minnesota Press
[book]
van Heijenoort, J
/ 1977
/ From Frege to Gödel: A Source Book in Manthematical Logic, 1879-1931
/ Harvard University Press
[book]
Heyting, A
/ 1983
/ The Intuitionist Foundation of Mathematics
: 52~61
[book]
Heyting, A
/ 1966
/ Intuitionism, An Introduction
/ north Holland
[book]
Kant, I
/ 1970
/ Immanuel Kant's Critique of Pure Reason
/ Macmillan
[book]
Mancosu, P
/ 1998
/ From Brouwer to Hilbert: The Debate on the Foundations of Mathematics in the 1920s
/ Oxford uiversity Press
[book]
Marion, M
/ 1998
/ Wittgenstein, Finitism, and the Foundations of Mathematics
/ Clarendon Press
[journal]
Marion, M
/ 2003
/ Wittgenstein And Brouwer
/ Synthese
137
: 103~127
[book]
McCarty. D.C
/ 2007
/ Intuitionism in Mathematics
: 356~386
[book]
Parsons, C
/ 1977
/ An Introductory Note to Brouwer
: 446~457
[book]
Shapiro, S
/ 2007
/ The Oxford Handbook of Philosophy of Mathematics and Logic
/ Oxford Univesrity Press
[book]
van Stigt, W.P
/ 1990
/ Brouwer's Intuitionism
/ North-Holland
[book]
Troelstra, A. S
/ 1969
/ Principles of Intuitionism, Lecture notes in mathematics, vol. 95
/ Springer
[book]
van Stigt, W.P
/ 1982
/ The Origin and Development of Brouwer's Concept of Choice
: 465~486
[book]
Troelstra, A.S
/ 1982
/ The L.E.J. Brouwer's Centenary Symposium
/ North Holland
[other]
Weyl, H
/ 1998
/ On the New Foundational Crisis of Mathematics
[book]
Wittgenstein, L
/ 1974
/ Philosophical Grammar
/ Blackwell
[book]
Wittgenstein, L
/ 1975
/ Philosophical Remarks
/ Blackwell
[book]
Wittgenstein, L
/ 1979
/ Wittgenstein's Lectures, Cambridge 1932-1935
/ Blackwell
[book]
Wittgenstein, L
/ 1979
/ Ludwig Wittgenstein and the Vienna Circle
/ Blackwell
[journal]
Yap, A
/ 2009
/ Predicativity and Structualism in Dedekind's Construction of the Reals
/ Erkenntnis
71
: 157~173