From Kronecker to Brouwer
There is no need to recall the polemics between Kronecker and Cantor, simply because it did not exist. H. Edwards (1987) has recently shown that if there has been any quarrel between the two, it has not been the virulent one some had evoked. The intransigent Kronecker, a <Verbotsdiktator> in Hilbert’s words, is supposed to have been a fiend of Cantor, whom he would have called a youth perverter <Verderber der Jugend>. Cantor is said to have returned the compliment by calling Kronecker <der kleine Despot>. I would like to draw the attention to facts of a more mathematical import.
KeywordsDeductive System Double Negation Internal Logic General Arithmetic Pure Logic
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- Weyl even thanks Brouwer for such an internal logic: « Ich glaube, für diese Erkenntnis der Grenzen des inhaltlichen Denkens sind wir ihm (Brouwer) alle zu Danke verplichtet » (Weyl, 1968, III, p. 147).Google Scholar
- C. Chevalley and A. Weil characteristically declare: «il s’abandonna un moment à l’intuitionnisme brouwerien » in their obituary of L’enseignement mathématique, tome III, fasc. 3 (1957) reprinted in (Weyl, 1968, IV, p. 659 ).Google Scholar
- The topological interpretation (see Scott, 1969) is not without interest, nor is the “toposical” interpretationGoogle Scholar