Title

The Interplay between Physics and Mathematics & Nature of Science | HPS

Abstract

Historical epistemology of science is one of the possible approaches to understanding the history and philosophical foundations of science combining historical/epistemological aspects (i.e., primary sources, historical hypothesis, shared knowledge, epistemological interpretations) and using logical and mathematical inquiring. By following this historical–epistemological standpoint, one might ask: what are physics and mathematical objects in a theory? For example in 19th century, one can see scientific theories (particularly, mathematical and physical quantities along the experiments, modeling, properties and structures) which work in a unique discipline: physics mathematics (or mathematics physics). It is not a mathematical physics as mathematical application of physics or vice–versa, but rather it is a new way to work with science. New methodological approach to solve physical (in origin) problems where the quantities may be physical and mathematical at the same time (first novelty), and measurements are not a priority or a prerogative (second novelty) to make a coherent physical science. In addition, it is a structured discipline among mathematical quantities and physical structures (including logic and language) in order to “[...] reducing [experimental electric and magnetic] phenomena into scientific form [...]” (Maxwell 1865, p. 459). By focusing on mathematics, physics and its relationship, an interdisciplinary approach among history, philosophy, epistemology, logic and foundations of physical and mathematical sciences might be adopted. In this talk, some historical-philosophical case-studies on relationship physics-mathematics are presented and educationally discussed, i.e.: lack of relationship physics-logics, space and time in mechanics, mechanics and thermodynamics, ad absurdum proofs, non-Euclidean geometries and the space in physics, planetary model and quantum mechanics, infinite-infinitesimal and measures in laboratory, heat-temperature-friction, and reversibility phenomena, concept of set and field, continuum-discrete models in mechanics and theory of elasticity of the XIX cent., hypothesis ad hoc in the theory, local-global interpretation and differential equations-integral, point-range and physical phenomena, mechanics, kinetic model of gases and thermodynamics.

References

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Contact

raffaele.pisano@univ-lille3.fr