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Reading the Use of Analogies in Newton's Philosophiae Naturalis Principia

Mathematica

Ra f aele Pisano

CIREL, Lille 3 University, France

e-mail: ra f aele.pisano@univ-lille3.fr

Paolo Bussotti

Department of Humanities and the Cultural Heritage, Udine University, Italy e-mail: paolobussotti66@gmail.com Abstract. In Philosophiae Naturalis Principia Mathema tica an d in other m athematical works, Isaac Newton ( 1643-1727) resorts to magnitudes which, in modern language, should be called infinitesimal quantities. It is well known that Newton did not recognize the existence of actually infinitesimal quantities and numbers. His conception considers the infinity and infinitesimal as potential quantities. Nonetheless, on several occasions - (i.e., Principia, Book I: Proposition XXXIX, sect. VII and Proposition XLI, sect. VIII), where he deals with the so called inverse problem of the c entral forces, Newton argues of given infinitesimal quantities. The fact that these quantities are given, might induce to think of actually infinitesimal mag nitudes. This is not the case. Howeve r, they cannot be considered ordinary potentially in finitesimal quantities. Rather, in our talk, it will be shown they represent a fiction, an analogy, which gets a particularly significant role as to the development of Newton's physical and logi cal argumentative structure. The use of analogy in science is a wide argument. The one made by Ne wton is exactly a n exemplification of a corre ct use of analogy: the magnitud e to which Ne wton reso rts resembles, is analogous to an actually infinite quantity, but, in fact, it is not. Many other uses of analogy in science are not correct. In the second part of our talk, we will point out the di f erences between a correct and an incorrect use of analogy within science. We will refer to our researches developed on the subject on history of science, history of science & science education and epistemology of science.

Selected References

Bussotti P, Pisano R ( 2014) New ton's Philosophiae Na turalis Principia Mathematica "Jesuit" Edition: The Tenor of a Huge Work. Accademia Nazionale Lincei-Rendiconti Lincei

Matematica e Applicazioni 25/4:413-444.

Bussotti P, Pisano R (2014) On the Jesuit Edition of Newton's Principia. Science and Advanced Researches in the Western Civilization. Advances in Historical Studies 3/1:33-55 Gillispie CC, R Pisano (2014) Lazare and Sadi Carnot. A Scientific and Filial Relationship, 2 nd edition. Dordrecht, Springer Newton I, (1687, 1 726, 1739 -1742, 1822) Philoso phiae naturalis pr incipia mathematica, auctore Isaaco Newtono, Eq. Aurato. Perpetuis commentariis illustrate, c ommuni studio pp. Thomae le Seur et F rancisci Jacquier ex Gallicana Minimorum Fam ilia, matheseos professorum. Editio nova, summa cura recensita, Glasgow, J. Duncan Pisano R (2011) Phys ics-Math ematics Relationship. Historical and Epistemological notes. In: Barbin E, Kronfellner M, Tzanakis C, (eds.) European Summer University History And Epistemology In Mathematics, Vienna, Verlag H olzhausen GmbH-Holzhausen

Publishing Ltd: 457-472.

Arguments par parallélisme et ressemblance. Exemplification, symétrie et analogie : Approches conceptuelles et didactiques |

8h30-18h30

ADA 2017

12 mai, 2017, MESHS, Lille, France

Keynote Speaker

Comité scientifique et organisation

Raffaele Pisano, CIREL-Théodile, Université de Lille 3, France Shahid Rahman, STL, Université de Lille 3, France Pisano R (2017) A Development of the Principle of Virtual Laws and its Framework in Lazare Carnot's Mechanics as Ma nifest Relationship between Phy sics and Mathematics. Transversal-International Journal for Historiography of Science, in press Pisano R, Bussotti P (2 017) (ed s) Homage to Galileo Galilei 1564-2014. Reading Iuvenilia Galilean Works within History and Historical Epistemology of Science. Philosophiae

Scientiae 21(1)

Pisano R, Bussotti P (2016a) A Newtonian tale details on notes and proofs in Geneva edition of Newton's Principia. BS HM Bulletin-Journal of the British Society for the History of

Mathematics 31/3:160-178

Pisano R, Bussotti P (2016b) The Fiction of the Infinitesimals in Newton's Works: A note on the Metaphoric use of Infinitesimals in Newton. Special Issue Isonomia, in press Pisano R, Bussotti P (2 015) Gal ileo in Padua: archi tecture, fortifications, mathematics and "practical" science. Lettera Matematica Springer 2:209-222 Pisano R, Capecchi D (2015) Tartaglia's Science of Weights. The Mechanics in XVI century.

Dordrecht, Springer

Pisano R, Bussotti P (2 014) Note s on mechanics and mathematics in Torricelli as physics- mathematics relationship in the history of science. Problems of Education in the 21 st

Century 61: 88-97

Wright JMF (1833) A commentary on Newton's Principia with a supplement volume designed for the use of students at the university. 2 Vols. TT & J Tegg, London Arguments par parallélisme et ressemblance. Exemplification, symétrie et analogie : Approches conceptuelles et didactiques |

8h30-18h30

ADA 2017

12 mai, 2017, MESHS, Lille, France

Keynote Speaker

Comité scientifique et organisation

Raffaele Pisano, CIREL-Théodile, Université de Lille 3, France Shahid Rahman, STL, Université de Lille 3, Francequotesdbs_dbs44.pdfusesText_44

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