Let two Poincaré's quotation for an abstract:
„It has, for instance, been observed that a weight A of 10 grammes and a weight B of 11 grammes produced identical sensations, that the weight B could no longer be distinguished from a weight C of 12 grammes, but that the weight A was readily distinguished from the weight C.
Thus the rough results of the experiments may be expressed by the following relations:
A=B,
B=C,
A < C,
which may be regarded as the formula of the physical continuum.
But here is an intolerable disagreement with the law of contradiction, and the necessity of banishing this disagreement has compelled us to invent the mathematical continuum.”1
"There is no actual infinite; the Cantorians have forgotten this, and that is why they have fallen into contradiction."2
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1 Poincaré, Science and Hypothesis, http://strangebeautiful.com/other-texts/poincare-science-hypothesis.pdf
2 See for example: http://books.google.hu/books?id=v4tBTBlU05sC&pg=PA190&hl=hu#v=onepage&q&f=false
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