From the History of Physics to the Discovery of the Foundations of Science
BY TRANSCEND MEMBERS, 4 Jun 2018
Among the many formulation of a physical theory, e.g. Mechanics, also Mach(1) recognized technical differences only, instead my suggestion is to consider their differences as revealing the characteristic features of their foundations. No more radical differences may exist than those concerning both their kinds of Mathematics and their kinds of Logic. As a fact, after the 20th Century within each of these sciences there exist two antagonist foundations, i.e. within Mathematics either the classical one or the constructive one(2) , and within Mathematical Logic either the classical lofi or the intuitionist one(3).
Let us take Mechanics as an instance. Being the choices of the Newton’s formulation respectively the actual infinity of the differential equations relying on the infinitesimals and the classical logic, a formulation based on the alternative choices is Lazare Carnot’s, whose mathematics is no more than an algebraic-trigonometric one and the logic is the intuitionist one, because this formulation makes use of doubly negated propositions, whose corresponding affirmative propositions are idealistic or false; i.e. in these cases the law of double negation fails, a characteristic intuitionist law.(4)
By considering these two dichotomies as the foundations of the physical theories, the choices upon them fashion four models of scientific theory, called through their most representative theories: Newtonian, Carnotian, Lagrangian, Descartesian. In correspondence foru versions of the principle of inertia are recognized, as suggested by respectively: Descartes. Lazare Vcarnot, Enriques and Cavalieri.(5) The birth of modern physics is characterized by the two theories, special relativity and Einstein’s first paper on quanta, whose choices are alternative to those of the previously dominant physical theory, Newtonian mechanics: in the latter paper Einstein i) declares the dichotomy on the kinds of mathematics and then he chooses the discrete ; ii) by using doubly negated propositions he organizes his theory in an alternative way to the deductive-axiomatic one.(6)
By taking these dichotomies as interpretative categories, a first interpretive history of Physics including both classical and modern physics results according to a quadrilinear development. All that suggests that the four models of scientific theory may be graphically represented as a compass orientating our minds among the so many physical theories.
Moreover, a new history of Philosophy of knowledge results. Kant’s first two a priori categories represent only Newton’s two choices out of the four pairs of choices on the two dichotomies. Hegel’s dialectic was misleading w.r.t. the subsequent intuitionist logic. Rather, Leibniz’s suggestion of the two labyrinths of human minds may be seen as an anticipation of the two above dichotomies.(7)
- Mach E. (1883), Die Mechanik, Leipzig: Brockhaus, Chap. IV, Sect. III-
- Bishop E. (1967), Constructive Analysis, New York: Mc Graw-Hill.
- Heyting A. (1962), Intuitionism. An Introduction, Amsterdam: North-Holland.
- Drago A. (2004), “A new appraisal of old formulations of mechanics”, Am. J. Phys., 72(3), pp. 407-9.
- Vella M.R. (2007), “Le quattro versioni del principio di inerzi”, in M. Leone et al. (eds.), L’eredità di Fermi, Majorana e altri Temi. Napoli: ESI.
- Drago A. (2014), “The emergence of two options from Einstein°s first paper on Quanta”, in Pisano R., Capecchi D., Lukesova A. (eds.), Physics, Astronomy and Engineering. Critical Problems in the History of Science and Society, Scientia Socialis P., Siauliai, 2013, pp. 227-234.
- This and all in the above points are illustrated by the book Drago A. (2017), Dalla Storia della Fisica ai Fondamenti della Scienza, Roma: Aracne.
This article originally appeared on Transcend Media Service (TMS) on 4 Jun 2018.
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