R: 31st Novembertagung 2020

[Antonino Drago]

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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