Evolution of Leibniz’s Thought in the Matter of Fictions and Infinitesimals

In Bharath Sriraman (ed.), Handbook of the History and Philosophy of Mathematical Practice. Cham: Springer. pp. 341-384 (2024)
  Copy   BIBTEX

Abstract

In this chapter, we offer a reconstruction of the evolution of Leibniz’s thought concerning the problem of the infinite divisibility of bodies, the tension between actuality, unassignability, and syncategorematicity, and the closely related question of the possibility of infinitesimal quantities, both in physics and in mathematics.Some scholars have argued that syncategorematicity is a mature acquisition, to which Leibniz resorts to solve the question of his infinitesimals – namely the idea that infinitesimals are just signs for Archimedean exhaustions, and their unassignability is a nominalist maneuver. On the contrary, we show that syncategorematicity, as a traditional idea of classical scholasticism, is a feature of young Leibniz’s thinking, from which he moves away in order to solve the same problem, as he gains mathematical knowledge.We have divided Leibniz’s path toward his mature view of infinitesimals into five phases, which are especially significant for reconstructing the entire evolution. In our reconstruction, an important role is played by Leibniz’s text De Quadratura Arithmetica. Based on this and other texts, we dispute the thesis that fictionality coincides with syncategorematicity, and that unassignability can be bypassed. (In this chapter, we employ “syncategorematic” as a shorthand for “eventually identifiable with a procedure of exhaustion” and, as a consequence, “involving only assignable quantities.” We also identify syncategorematicity with potentiality, as suggested by some part of the scholastics, and in Sect. 2.2, we show that the two characterizations are equivalent, provided that “potentiality” is intended in the correct way: namely as in the unending iterative procedures of Greek mathematics.) On the contrary, we maintain that unassignability, as incompatible with the principle of harmony, is the ultimate reason for the fictionality of infinitesimals.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 92,953

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Leibniz versus Ishiguro: Closing a Quarter Century of Syncategoremania.Tiziana Bascelli, Piotr Błaszczyk, Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz, David M. Schaps & David Sherry - 2016 - Hopos: The Journal of the International Society for the History of Philosophy of Science 6 (1):117-147.
Leibniz’s syncategorematic infinitesimals.Richard T. W. Arthur - 2013 - Archive for History of Exact Sciences 67 (5):553-593.
Infinitesimals as an issue of neo-Kantian philosophy of science.Thomas Mormann & Mikhail Katz - 2013 - Hopos: The Journal of the International Society for the History of Philosophy of Science (2):236-280.

Analytics

Added to PP
2024-04-27

Downloads
8 (#1,342,200)

6 months
8 (#415,941)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Monica Ugaglia
Università degli Studi di Firenze

Citations of this work

No citations found.

Add more citations

References found in this work

No references found.

Add more references