"Cantor and his disciples... think they have knowledge of all sorts of further sets; their fundamental principle... comes to about the same as the axiomaticians. ...[T]his principle is unjustified and... we assert that the several paradoxes of the 'Mengenlehre' [Set theory]... have no right to exist... [I]t would have been the duty of Cantorians, immediately to reject a notion which gives rise to contradictions, because it is... not built... mathematically."
Quote Details
Added by wikiquote-import-bot
Unverified quote
0 likes
Academics from the NetherlandsPhilosophers from the NetherlandsMathematicians from the NetherlandsPeople from RotterdamLogicians from the Netherlands
Original Language: English
Available Languages (1)
Sources
Imported from EN Wikiquote
https://en.wikiquote.org/wiki/L._E._J._Brouwer
Revision History
No revisions have been submitted for this quote.
Categories
L. E. J. Brouwer
Luitzen Egbertus Jan Brouwer ForMemRS (27 February 1881 – 2 December 1966), usually cited as L. E. J. Brouwer but known to his friends as Bertus, was a Dutch mathematician and philosopher, who worked in topology, set theory, measure theory and complex analysis.
17 quotes on TrueQuotesView all quotes by L. E. J. Brouwer →
Related Quotes
"Life is a magic garden. With wondrous softly shining flowers, but between the flowers there are the little gnomes, th…"
"The viewpoint of the formalist must lead to the conviction that if other symbolic formulas should be substituted for …"
"Mathematics is independent of logic. ...Where mathematical objects are given by their relations to the ...parts of a …"
"The words of... mathematical demonstration merely accompany a mathematical construction that is effected without word…"
"Logic depends upon mathematics. ...[I]ntuitive logical reasoning ...remains if ...one restricts oneself to relations …"
"With which mathematical notions a spoken or written symbol will be made to correspond... will... differ according to …"
"[I]t is easily conceivable that, given the same organization of the human intellect and... the same mathematics, a di…"
"Man, inclined to... a mathematical view.., has... applied this bias to mathematical language, and in former centuries…"
"[T]he proposition: A function is either differentiable or not differentiable. says nothing; it expresses the same as.…"
"[T]he idea that by... such linguistic structures we can obtain knowledge of mathematics apart from that... constructe…"