On Axiomatic Foundations Common to Classical Physics and Special Relativity

Bressan, Aldo

Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 16 (2005) no. 3, pp. 143-157.

Abstract (VO)

(i) The class of the axiomatic foundations mentioned in the title is called Ax Found; and its structure is treated in the introduction. (ii) This consists of Parts A to G followed by the References. (iii) In [17] Bressan's modal logic is treated in a consciously non-rigorous way. Instead here, as well as Ax Found, it has a rigorous treatment. Such a treatment had been appreciated by the mathematical physicist C. Truesdell in [62]. (iv) In 1953 Truesdell had a remarkable intuition, whose correctness appeared only in 1962, from Bressan's monograph [3]. (v) As a foreign member of the Lincei Academy, Truesdell supported some logical features, absent in his school, and he gave M. Pitteri a "confidential copy" involving this fact. (vi) Since thus the present rigorous treatment of Bressan's modal logic appears strongly supported by Truesdell, it was natural to dedicate the present work to his memory. (vii) In the introduction one says to have proved certain results (whose proof does not appear there) concerning rational mechanics or Bressan's modal logic treated rigorously.

Riassunto

(i) La classe dei fondamenti assiomatici menzionati nel titolo è detta brevemente Ax Found; ed è trattata nell'introduzione. (ii) Questa consiste nelle Parts A,...,G seguite dalle References. (iii) In [17] la logica modale di Bressan è trattata in modo consciamente non rigoroso. Invece qui essa, al pari di Ax Found, ha una trattazione rigorosa. Una tale trattazione era stata apprezzata dal fisico matematico Truesdell in [62]. (iv) Nel 1953 Truesdell ebbe una notevole intuizione, la cui correttezza risultò solo nel 1962, dalla monografia [3] di Bressan. (v) Come Socio straniero dei Lincei, Truesdell sostenne degli aspetti logici, assenti nella sua scuola. Inoltre diede a M. Pitteri una "confidential copy" involgente tale fatto. (vi) La presente trattazione rigorosa della logica modale di Bressan appare perciò fortemente sostenuta da Truesdell. Era quindi naturale dedicare alla sua memoria il lavoro inviato. (vii) Nell'introduzione si dice di aver ottenuto certi risultati (la cui dimostrazione non appare ivi) concernenti la Meccanica razionale o la logica modale di Bressan trattata rigorosamente.

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