Is a mathematical theorem proved because provable, or provable because proved? If Brouwer’s intuitionism is accepted, we’re committed, it seems, to the latter, which is highly problematic. Or so I will argue. This and other consequences of Brouwer’s attempt to found mathematics on the intuition of a move of time have heretofore been insufficiently appreciated. Whereas the mathematical anomalies of intuitionism have received enormous attention, too little time, I’ll try to show, has been devoted to some of the temporal anomalies that Brouwer has invited us to introduce into mathematics.
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Chapter
von Plato, Jan;
(2009)
Proof Theory of Classical and Intuitionistic Logic
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Article
Mumford, David;
(2011)
Intuition and Rigor and Enriques's Quest
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Book
Atten, Mark Sebastiaan Paul Rogier van;
(2004)
On Brouwer
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Article
Niekusa, Joop;
(2010)
Brouwer's Incomplete Objects
(/isis/citation/CBB001210970/)
Chapter
Aberdein, Andrew;
Read, Stephen;
(2009)
The Philosophy of Alternative Logics
(/isis/citation/CBB001210355/)
Book
Dalen, Dirk van;
(2013)
L. E. J. Brouwer: Topologist, Intuitionist, Philosopher---How Mathematics is Rooted in Life
(/isis/citation/CBB001500395/)
Book
John P. Burgess;
(2015)
Rigor and Structure
(/isis/citation/CBB621282384/)
Book
Gabriele Lolli;
(2022)
The Meaning of Proofs: Mathematics as Storytelling
(/isis/citation/CBB293361801/)
Chapter
Harari, Orna;
(2012)
John Philoponus and the Conformity of Mathematical Proofs to Aristotelian Demonstrations
(/isis/citation/CBB001320142/)
Article
Miriam Franchella;
(2019)
Shaping the Enemy: Foundational Labelling by L.E.J. Brouwer and A. Heyting
(/isis/citation/CBB604456688/)
Article
Ageron, Pierre;
(2002)
L'autre axiome du choix
(/isis/citation/CBB000500323/)
Article
Alessandro Antonello;
(2022)
Antarctic Krill and the Temporalities of Oceanic Abundance, 1930s–1960s
(/isis/citation/CBB132455694/)
Book
Franchella, Miriam;
(1994)
L.E.J. Brouwer pensatore eterodosso: L'intuizionismo tra matematica e filosofia
(/isis/citation/CBB000033779/)
Article
Posy, Carl J.;
(1980)
On Brouwer's definition of inextendable order
(/isis/citation/CBB000002678/)
Book
Dalen, Dirk van;
(2005)
Mystic, Geometer, and Intuitionist: The Life of L. E. J. Brouwer 1881--1966
(/isis/citation/CBB000640795/)
Chapter
Johnson, Dale M.;
(1987)
L.E.J. Brouwer's coming of age as a topologist
(/isis/citation/CBB000042993/)
Book
Dalen, Dirk van;
(2001)
L.E.J. Brouwer, 1881--1966: Een biografie: Het heldere licht van de wiskunde
(/isis/citation/CBB000740446/)
Thesis
Eggenberger, Peter B.;
(1976)
The philosophical background of L.E.J. Brouwer's intuitionistic mathematics
(/isis/citation/CBB001564114/)
Book
Brouwer, Luitzen E. J.;
(1981)
Brouwer's Cambridge lectures on intuitionism. Edited by Dalen, D. van
(/isis/citation/CBB000016571/)
Essay Review
Gillies, D. A.;
(1980)
Brouwer's philosophy of mathematics
(/isis/citation/CBB000001003/)
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