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

Résumé

(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.