Abstract
I.—May 3.—The Logic of the Infinite.-Some years ago, M. Poincare said, he had published a certain number of articles upon the subject, which had involved him in a veritable polemic. He would not attempt to renew the arguments that had been used on either side, or to bring forward any fresh arguments, as he believed that the divergence of the two schools was irreducible. It arose from an essential difference of mentality; he would therefore accept it as an experimental fact, and would endeavour to account for this divergence. For the first school, whom, for the sake of convenience, he would call Pragmatists, the infinite was derived from the finite; for the second, the Cantorians, the infinite preexisted, and the finite was only a small piece of the infinite. From another point of view, to use the language of the scholastics, the Pragmatists were extensionists, while the Cantorians were comprehensionists. This appeared in the nature of the definitions used by the two schools. For the first a definition consisted in the addition of one new object, expressed in terms of the aggregate of known objects; for the second a definition was a fresh subdivision of the aggregate of all objects known and unknown. The Pragmatists were idealists, and for them an object did not exist until it had been thought. The Cantorians were realists for whom the existence of objects was independent of a thinking subject. For them the infinite was independent of man or any thinking being; it was pre-existent and was discovered by man.
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M. Poincaré's Lectures at the University of London . Nature 89, 279 (1912). https://doi.org/10.1038/089279a0
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DOI: https://doi.org/10.1038/089279a0