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5. Abstract on: History of Science, Epistemology | nature of Science [Prof. Pisano, France]

Start Date:
11. October 2017, 14:45
Finish date:
11. October 2017, 15:45
École Dotorale Lille 3 University



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



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.



  • Bussotti P, Pisano R (2014) Newton’s Philosophiae Naturalis Principia Mathematica “Jesuit” Edition: The Tenor of a Huge Work. Accademia Nazionale Lincei-Rendiconti Matematica e Applicazioni 25:413-444
  • Gillispie CC, Pisano R (2014) Lazare and Sadi Carnot. A Scientific and Filial Relationship. 2nd edition. Dordrecht. Springer
  • Maxwell JC (1865) A dynamical theory of the Electromagnetic field. Philosophical Transactions of The Royal Society of London CLV:459-512
  • Mellone M, Pisano R (2012) Learning Mathematics In Physics Phenomenology And Historical Conceptual Streams. Problems of Education in the 21st Century 46:93-100
  • Newton I ([1671] 1736) The method of fluxions and infinite series. Henry Woodfall. London
  • Newton I ([1713] 1729) The Mathematical principles of natural philosophy. Translated by Motte Andrew. Motte B. London
  • Newton I ([1726] [1739-1742] 1822) Philosophiae Naturalis Principia Mathematica, auctore Isaaco Newtono, Eq. Aurato. Perpetuis commentariis illustrate, communi studio Thomae le Seur et Francisci Jacquier ex Gallicana Minimorum Familia, matheseos professorum. Editio nova, summa cura recensita. A. et J. Duncan. Glasgow
  • Newton I (1746) Methodus fluxionum et serierum infinitarum, in Opuscula mathematica. Marcum Michaelem Bousque Lausanne et Genevae, I, 29-200
  • Pisano R (2010) On Principles In Sadi Carnot’s Theory (1824). Epistemological reflections. Almagest 2/1:128–179
  • Pisano R (2011) Physics–Mathematics Relationship. Historical and Epistemological notes. In: Barbin E, Kronfellner M, Tzanakis C (Eds). Proceedings of the ESU 6 European Summer University History and Epistemology in Mathematics. Vienna. Verlag Holzhausen GmbH–Holzhausen Publishing Ltd., pp 457–472
  • Pisano R (2011) Textbooks, Foundations, History of Science and Science education. Problems of education in the 21st century 35:5-10
  • Pisano R (2012) Historical Reflections on Physics Mathematics Relationship in Electromagnetic Theory. In: Barbin E, Pisano R (Eds). The Dialectic Relation between Physics and Mathematics in the XIXth Century. Dordrecht. Springer, pp 31-57
  • Pisano R (2013) On Lagrangian in Maxwell's electromagnetic theory. Scientiatum VI. História das Ciências e das Técnicas e Epistemologia. The Federate University of Rio de Janeiro. Rio de Janeiro University Press, pp 44-59
  • Pisano R (2017) A Development of the Principle of Virtual Laws and its Conceptual Framework in Mechanics as Fundamental Relationship between Physics and Mathematics. Transversal: International Journal for the Historiography of Science 2:166-203
  • Pisano R (ed.) (2015) A Bridge between Conceptual Frameworks, Science, Society and Technology Studies. Dordrecht. Springer NL
  • Pisano R, Agassi J, Drozdova D (Eds) (2017) Hypotheses and Perspectives in the History and Philosophy of Science. Homage to Alexandre Koyré 1964-2014. Springer. Dordrecht.
  • Pisano R, Bussotti P (2013) Open problems in mathematical modelling and physical experiments: exploring exponential function. Problems of education 21st century 50:56-69
  • Pisano R, Bussotti P (2014a) Notes on mechanics and mathematics in Torricelli as physics mathematics relationships in the history of science. Problems of Education in the 21st Century 61/61:88–97
  • Pisano R, Bussotti P (2014b) Historical and Philosophical Reflections on the Culture of Machines around the Renaissance. How Science and Technique Work? Acta Baltica Historiae et Philosophiae Scientiarum 2/2:20-42
  • Pisano R, Bussotti P (2016a) A Newtonian Tale Details on Notes and Proofs in Geneva Edition of Newton’s Principia. BSHM-Journal of the British Society for the History of Mathematics 31/3:160-178
  • Pisano R, Bussotti P (2017) The Emergencies of Mechanics and Thermodynamics in the Western Society during 18th–19th Century. In: Pisano 2015 (ed), pp 399-436
  • Pisano R, Bussotti P (2017) The Fiction of the Infinitesimals in Newton’s Works: On the Metaphoric use of Infinitesimals in Newton. Special Issue Isonomia 9:139-158
  • Pisano R, Capecchi D (2013) Conceptual and Mathematical Structures of Mechanical Science in the Western Civilization around 18th Century. Almagest 4/2:86-121
  • Pisano R, Capecchi D (2015) Tartaglia’s science weights and Mechanics in XVI century. Selections from Quesiti et invention diverse: Books VII–VIII. Dordrecht. Springer
  • Pisano R, Fichant M, Bussotti P, Oliveira ARE (Eds) (2017). The Dialogue between Sciences, Philosophy and Engineering. New Historical and Epistemological Insights. Homage to Gottfried W. Leibniz 1646-1716. The College Publications. London
  • Pisano R, Gaudiello I (2009) Continuity and discontinuity. An epistemological inquiry based on the use of categories in history of science. Organon 41:245-265