Bertus

  "Once and for all there is a great deal I do not want to know - Wisdom sets bounds even to knowledge"

(F. Nietzsche - Twilight of the idols)

" (...) Mathematics rigorously treated from [the] point of view [of] deducing theorems exclusively by means of introspective construction, is called intuitionistic mathematics..."

" (...) I hope I have made clear that intuitionism on the one hand subtilizes logic, on the other hand denounces logic as a source of truth. Further that intuitionistic mathematics is inner architecture, and that research in foundations of mathematics is inner inquiry with revealing and liberating consequences, also in non-mathematical domains of thought."

( Brouwer, L. E. J., Consciousness, Philosophy and Mathematics, (1948) in

Benacerraf, Paul and Putnam, Hilary (ed.), Philosophy of mathematics, second edition (1983), CUP )

" (...) In fact, mathematics, from the intuitionistic point of view, is a study of certain functions of the human mind"

( Heyting, Arend, Intuitionism, an Introduction, (1956), Amsterdam-North Holland )

1. " (...) Mathematicians have a loathing for ambiguity and indefiniteness, so that often a manifold is defined by one of two polite fictions: an equivalence class of G-atlases, or a maximal G-atlas. Either object is so huge and complicated as to be unimaginable ... "

( Thurston, W. P., Three-Dimensional Geometry and Topology, Vol.1 (1997), Princeton University Press, pp.111 )

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