He {{Poincaré}} is reported to have said in a talk at the international congress of mathematicians at Rome in 1908 that in future set theory would be considered as a disease from which one has recovered. [...] It seems indeed that Hilbert wants to maintain Cantor's opinions in their old absolutistic sense. I find that rather strange. It is indicative that he never felt the necessity to consider the relativism that I have proven for every finitely formulated set axiomatics. [...] Firstly I have given a more precise grounds for the general set theoretic relativism, which has the particular consequence that the absolutely uncountable has no justification on an axiomatic basis. [T. Skolem: "Über die Grundlagendiskussionen in der Mathematik", Den Syvende Skandinav. Matematikerkongr. Oslo (1929). "Selected Works in Logic", J.E. Fenstak (ed.), Scand. Univ. Books, Universitetsforlaget, Oslo (1970)]

Presumably, the reason for this division of the contents of "Einleitung in die Mengenlehre" into two different books is that the subject matter has grown too large. The reviewer, however, is not enthusiastic about this division since such a textbook as the present one will be read primarily by students and they might form the impression that classical set theory is securely founded just as other parts of mathematics, e.g. arithmetic. Such an impression would, however, be misleading. [...] On the other hand, it must be conceded that the lack of knowledge of the results of foundational research will not mean much to mathematicians who are not especially interested in the logical development of mathematics. [T. Skolem: "Review of A.A. Fraenkel: 'Abstract set theory'", Mathematica Skandinavica 1 (1953) p. 313]

I never met a mathematician who to a higher degree than Hermite has been a realist in the sense of Plato, and yet I can claim that I never met a more decided opponent of the Cantorian ideas. This is the more a seeming contradiction, as he himself stated frankly: I am an opponent of Cantor because I am a realist. [H. Poincaré: "Letzte Gedanken: Die Mathematik und die Logik", Akademische Verlagsgesellschaft, Leipzig (1913) p. 162f]

fredag 17 december 2021 kl. 10:28:57 UTC+1 skrev WM:
> He {{Poincaré}} is reported to have said in a talk at the international congress of mathematicians at Rome in 1908 that in future set theory would be considered as a disease from which one has recovered. [...] It seems indeed that Hilbert wants to maintain Cantor's opinions in their old absolutistic sense. I find that rather strange. It is indicative that he never felt the necessity to consider the relativism that I have proven for every finitely formulated set axiomatics. [...] Firstly I have given a more precise grounds for the general set theoretic relativism, which has the particular consequence that the absolutely uncountable has no justification on an axiomatic basis. [T. Skolem: "Über die Grundlagendiskussionen in der Mathematik", Den Syvende Skandinav. Matematikerkongr. Oslo (1929). "Selected Works in Logic", J.E. Fenstak (ed.), Scand. Univ. Books, Universitetsforlaget, Oslo (1970)]
>
> Presumably, the reason for this division of the contents of "Einleitung in die Mengenlehre" into two different books is that the subject matter has grown too large. The reviewer, however, is not enthusiastic about this division since such a textbook as the present one will be read primarily by students and they might form the impression that classical set theory is securely founded just as other parts of mathematics, e.g. arithmetic. Such an impression would, however, be misleading. [...] On the other hand, it must be conceded that the lack of knowledge of the results of foundational research will not mean much to mathematicians who are not especially interested in the logical development of mathematics. [T. Skolem: "Review of A.A. Fraenkel: 'Abstract set theory'", Mathematica Skandinavica 1 (1953) p. 313]
>
> I never met a mathematician who to a higher degree than Hermite has been a realist in the sense of Plato, and yet I can claim that I never met a more decided opponent of the Cantorian ideas. This is the more a seeming contradiction, as he himself stated frankly: I am an opponent of Cantor because I am a realist. [H. Poincaré: "Letzte Gedanken: Die Mathematik und die Logik", Akademische Verlagsgesellschaft, Leipzig (1913) p. 162f]
you still provide no actual mathematics.

On 12/17/2021 3:28 AM, WM wrote:
> He {{Poincaré}} is reported to have said in a talk at the international congress of mathematicians at Rome in *1908*
>
> Presumably, the reason for this division of the contents of "Einleitung in die Mengenlehre" *1919*,
>
> (*1913*) p. 162f]

1908, 1919, 1913, the graveyard of OLD math