FROM THE HISTORY OF PHYSICS TO THE DISCOVERY OF THE FOUNDATIONS OF
By Antonino Drago, formerly at Naples University “Federico II”, Italy – [email protected]
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The book summarizes a half a century author’s work on the foundations of physics. For the
forst time is established a level of discourse on theoretical physics which at the same time is
philosophical in nature (kinds of infinity, kinds of organization) and formal (kinds of mathematics,
kinds of logic). This double side of the two dichotomies assures a deep comprehension of
theoretical physics by avoiding both a purely philosophical analysis and a purely formal analysis,
each manifestly insufficient for representing all the aspects of theoretical physics.
Among the many formulations 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, within Mathematics
either the classical one or the constructive one(2); within Mathematical Logic either the classical
logic 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,(4) whose mathematics is no more than algebraic-trigonometric 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, as in intuitionist logic occurs.
By considering these two dichotomies as the foundations of the physical theories, each
couple of choices upon them fashions one out four models of scientific theory, which are baptized
through the authors of their most representative theories: Newtonian, Carnotian, Lagrangian,
Descartesian. In correspondence four versions of the principle of inertia are recognized, as
suggested by respectively: Descartes. Lazare Carnot, Enriques and Cavalieri.(5)
All that suggests that the four models of scientific theory may be graphically represented as
a compass orientating our minds amid the so numerous physical theories.
By taking these dichotomies as interpretative categories, a new interpretative history of
Physics including both classical and modern physics results according to a quadrilinear
The birth of modern physics is characterized by the two theories - Einstein’s paper on
special relativity and Einstein’s first paper on quanta - whose choices are the alternative ones to
those of the previously dominant physical theory, Newtonian mechanics: in the latter paper Einstein
i) declares the dichotomy on the kinds of mathematics (“Introduction”) and then he chooses
the discrete mathematics;
ii) by using doubly negated propositions he organizes his theory in an alternative way to the
Moreover, a new history of Philosophy of knowledge results. Kant’s first two a priori
transcendental categories represent the physical interpretation of the two choices out of the four
pairs of choices on the two dichotomies, i.e. the choices of the dominant theory of mechanics,
Newton’s. Hegel’s dialectic was a misleading attempt of anticipating the subsequent intuitionist
The book starts by a comparison of different formulations of thermodynamics in order to
recognize the first dichotomy on the kind of organization. In chapter 2 the dichotomy on the kind of
infinity is recognized through a comparison of Newrton’s mechanics and Lazare Carnot’s. A
quickly history of the other classical physical theories is illustrated in chapter 3; it results a
foundational conflict between the last two theories, and hence a conflict between their opposite
couples of choices. The two main theories of modern physics, special realtivity and quantum
mechanics confirm the foundational role played by the two dichotomies which gives reason for the
radical change in the history of theoretical physics. Indeed, the opposition of the two main pairs of
choices gives reason of the crisis in theoretical physics in the early 1900s.
As a global result, the book represents the first interpretation of the entire history of Physics,
both classical and modern; This fact proves that the four models of scientific theories can works as
a compass (that of the front cover) suggesting a direction among the many physical theories.
This new history of physics leads to re-visit both Koyré’s and Kuhn’s historiographies.
Their interpretative categories are interpreted and explained through the two dichotomies so that it
is possible to suggest à la Koyré categories based on the alternative choices theories to Newton’s as
the suitable categories for interpreting the alternative theories to Newton’s mechanics.
All that suggests a new interpretation of the crucial step in the history of Western philosophy
of knowledge, i.e. the passage from Leibniz to Kant: Leibniz’s suggestion of the two labyrinths of
human minds may be seen as a close anticipation of the two above dichotomies. Kant applied them
in order to construct the well-known four cosmological proofs, which however he misinterpreted as
leading to contradictions, instead to tow different methods of investigation corresponding to the two
different kinds of logic.(7)
1. Mach E. (1883), Die Mechanik, Leipzig: Brockhaus, Chap. IV, Sect. III.
2. Bishop E. (1967), Constructive Analysis, New York: Mc Graw-Hill.
3. Heyting A. (1962), Intuitionism. An Introduction, Amsterdam: North-Holland.
4. L. Carnot (1783), Essai on the Machines en général, Defay, Dijion (Enlish translation:
Springer, Berlin, 2020). Drago A. (2004), “A new appraisal of old formulations of mechanics”, Am.
J. Phys., 72(3), pp. 407-9.
5. Vella M.R. (2007), “Le quattro versioni del principio di inerzia”, in M. Leone et al. (eds.),
L’eredità di Fermi, Majorana e altri Temi. Napoli: ESI, pp. 147-151.
6. 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.
7. 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.