"The viewpoint of the formalist must lead to the conviction that if other symbolic formulas should be substituted for the ones that now represent the fundamental mathematical relations and the mathematical-logical laws, the absence of the sensation of delight, called "consciousness of legitimacy," which might be the result of such substitution would not in the least invalidate its mathematical exactness. To the philosopher or to the anthropologist, but not to the mathematician, belongs the task of investigating why certain systems of symbolic logic rather than others may be effectively projected upon nature. Not to the mathematician, but to the psychologist, belongs the task of explaining why we believe in certain systems of symbolic logic and not in others, in particular why we are averse to the so-called contradictory systems in which the negative as well as the positive of certain propositions are valid."
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
as translated by Arnold Dresden from: Brouwer, L. E. J. (1913). Intuitionism and formalism. Bulletin of the American Mathematical Society, 20(2), 81–96. (quote on p. 84)
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…"
"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…"
"[W]heresoever in logic the word all or every is used mathematics... tacitly involves the restriction: insofar as belo…"