Abstract
Poincaré wrote very ironically about logicism, so that it can be hard to sort out his views on it. But he declared his faith in logic itself so many times that I think we have to believe him. Some commentators neglect this side of Poincaré, largely viewing him as Russell’s opponent and Brouwer’s predecessor. To a pedagogical audience in 1899 he said:
If we read a book written fifty years ago, the greater part of the reasoning we find will strike us as devoid of rigor.... One admitted many claims which were sometimes false. So we see that we have advanced towards rigor; and I would add that we have attained it and our reasonings will not appear ridiculous to our descendents....But how have we attained rigor? It is by restraining the part of intuition in science, and increasing the part of formal logic... Today only one [intuition] remains, that of whole number; all the others are only combinations, and at this price we have attained perfect rigor (Poincaré 1899, 157).
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McLarty, C. (2000). Voir-Dire in the Case of Mathematical Progress. In: Grosholz, E., Breger, H. (eds) The Growth of Mathematical Knowledge. Synthese Library, vol 289. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9558-2_18
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