R: axiomatics
Antonino Drago
drago at unina.it
Thu Apr 23 17:14:42 EDT 2020
For more references one has to focus on Goedel’s incompleteness result. Several scholars considered it as the ultimate evidence of the insufficiency of the axiomatic method:
E.W. Beth: “Fundamental Features of Contemporary Theory of Science”, Brit. J. Phil. Science, 1 (1950) 89-102, p. 102;
J. van Heijenoort: “Goedel Theorem”, in Paul Edwards (ed.): Encyclopedia of Philosophy, MacMillan, London, 1967, p. 356;
G. Kreisel “Logic aspects of axiomatic method”, in H.-D. Ebbinghaus et al. (eds.): Logic Colloquium ’87, North-Holland, Amsterdam, 1989: 183-217.
J. Hintikka:” Is there completeness in Mathematics after Goedel?”, Phil. Topics, 17, 1989 no. 2, 69-90.
Best regards
Antonino Drago
Da: adriano paolo shaul gershom palma [mailto:palmaadriano at gmail.com]
Inviato: giovedì 23 aprile 2020 08:07
A: Joe Shipman
Cc: adriano paolo shaul gershom palma; Antonino Drago; D. Kant; Foundations of Mathematics
Oggetto: Re: axiomatics
Dear Dr Shipman you may find the relevant quotes , not the names fo authors, following, e.g., --108 & ff of Giancarlo Rota.
I include the book as edited by Palombi for Birkhauser.
best regards
may
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הִשְׁתַּדֵּל הִזְדַּקֵּן
palma, a paolo shaul םֹשׁ ְרֵגּ
On Thu, Apr 23, 2020 at 7:56 AM Joe Shipman <joeshipman at aol.com> wrote:
I would appreciate either links or quotes. All people are giving me is names.
— JS
Sent from my iPhone
On Apr 23, 2020, at 1:50 AM, adriano paolo shaul gershom palma <palmaadriano at gmail.com> wrote:
Dear Dr Shipman
you may find a wealth of remarks critical of axiomatic methods
in the works of Giancarlo Rota (MIT.)
While I am unsure whether Rota ought to be categorized as philosopher or mathematician or both.
Best
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Kerem jojjenek maskor es kulonosen masho
הִשְׁתַּדֵּל הִזְדַּקֵּן
palma, a paolo shaul םֹשׁ ְרֵגּ
On Wed, Apr 22, 2020 at 11:23 PM Antonino Drago <drago at unina.it> wrote:
D. Kant: “On the other hand, some philosophers also argue that the axiomatic view on mathematics may be harmful in that it omits fundamental aspects of mathematical practice and idealizes mathematical reasoning in an unfaithful way.”
Which philosophers? I’m interested in any references you have on this topic.
Joe Shipman
Take for example Jean Le Rond D’Alembert “Elémens” in Encyclopédie Française : a « rational » theory leaves always some « holes »(trous)
Lazare Carnot Essai sur les machines en général ; pp. 105-106
A century ago Lorentz, Poincaré and Einstein contrasted two kinds of theories, as Flores illustrated: Flores, F. (1999). Einstein’s Theory of Theories and Types of Theoretical Explanation. International Studies in Philosophy of Science, 13, 123-134.https://doi.org/10.1080/02698599908573613.
In my opinion, axiomatic theories cannot represent theories based on the search of a new method for solving a basic problem (as e.g. is Kolmogorov’s paper of 1924-25, or Markov’s paper on constructive mathematics 1971).
Best regards
Antonino Drago
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