axiomatics

[Joe Shipman]

The Rota book is very helpful (not just on the page referenced but in many other places), and clarifies that the problem is one of philosophy rather than mathematics. Rota explains that philosophers misapprehend the role of axiomatics and as a result have done damage to philosophy. As for mathematicians, axiomatics is important for presentation, verification, pedagogy, and clarification, but mathematicians themselves are not, or need not be, straitjacketed by axiomatics in a way that hinders discovery, if I am interpreting Rota correctly.

I’m interested in criticisms of axiomatics by mathematicians, and Rota’s book is uniquely helpful because he was eminent in both philosophy and mathematics.

— JS

Sent from my iPhone

> On Apr 23, 2020, at 2:07 AM, adriano paolo shaul gershom palma <palmaadriano at gmail.com> wrote:
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> 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.
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> best regards 
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> may
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> הִשְׁתַּדֵּל‎   הִזְדַּקֵּן‎ 
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> palma,  a paolo shaul םֹשׁ ְרֵגּ‎ 
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>> 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.
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>> — JS
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>> Sent from my iPhone
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>>>> On Apr 23, 2020, at 1:50 AM, adriano paolo shaul gershom palma <palmaadriano at gmail.com> wrote:
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>>> 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.
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>>> Best
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>>> Quatsch wird gelöscht, ohne gelesen zu werden
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>>> Kerem jojjenek maskor es kulonosen masho 
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>>> הִשְׁתַּדֵּל‎   הִזְדַּקֵּן‎ 
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>>> palma,  a paolo shaul םֹשׁ ְרֵגּ‎ 
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>>>> 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.”
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>>>> Which philosophers? I’m interested in any references you have on this topic.
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>>>> Joe Shipman
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>>>> Take for example Jean Le Rond D’Alembert “Elémens” in Encyclopédie Française :  a « rational » theory leaves always some « holes »(trous)
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>>>> Lazare Carnot  Essai sur les machines en général ; pp. 105-106
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>>>> 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.
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>>>> 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).
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>>>> Best regards
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>>>> Antonino Drago
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> <Indiscrete Thoughts by Gian-Carlo Rota (auth.), Fabrizio Palombi (eds.) (z-lib.org).pdf>
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