Problems of infinitesimals1/13/2024 It just seems that the history of both mathematical and philosophical understanding of the continuum is totally neglected. So, is there a mathematically rigorous statement of a problem in this thread, or not?įirst, I agree with what Wes Raikowski already remarked above: the questions as they are raised here are too vague. If this thread is not about mathematics, and is about, say, philosophy, okay, but the risk is lack of precision arising from how different individuals may not use the same words to mean the same thing, and there is no authority to whom the philosophers might appeal, except other philosophers. ![]() The easily available sources (Wiki,etc.) about the condemnation of indivisibles of Galileo and Cavalieri (dated August 10, 1632), led the Revisors General of the Jesuits Jacob Bidermann all ref to Amir Alexander's book.Geng Ouyang, Sir: There exists an article by Solomon Feferman "Conceptions of the Continuum" that discusses at least a dozen conceptions, including "The continuum in infinitesimal analysis." My view is that there are numerous alternative (and very interesting) mental models of "the continuum," some of which explicitly include mathematical microlects with a notion of "infinitesimal." To me there is no useful question about which one is "right." Just as one cannot appreciate a sculpture without viewing it from enough angles and positions to have seen its entire surface, one cannot comprehend the continuum - including its infinitesimal parts - without some mastery of several alternative (preferably mathematical) microlects. ![]() I think that the modern source is Egidio Festa, La querelle de l'atomisme: Galilee, Cavalieri et les jesuites (1990). See also Mordechai Feingold (editor), Jesuit Science and the Republic of Letters (MIT Press, 2002), page 28-29, for details about jesuit Rodrogo de Arriaga's Cursus philosophicus (Anversa, 1632) condemnation of 1632, concerning "mathematical atomism" and "the opinion on quantity made up of indivisibles". The jesuit mathematician Paul Guldin was an harsh critic of Cavalieri's method of indivisibles into his De centro gravitatis (or Centrobaryca, three volumes, 1635-41), on mathematical grounds. Unlike The Assayer, which had recourse to the lethal polemical weapons of satire and the new philosophy, the Ratio used those no-less-lethal weapons of doctrinal and dialectical retort based on religious and philosophical orthodoxy. Grassi's second response to Il Saggiatore, the Ratio ponderum librae et simbellae (1626), focused mainly on doctrinal issues. The beginning of the demonstration of the law of falling bodies.Īnd see : Galileo's Saggiatore (1623) and the reply by the jesuit Orazio Grassi ( Libra, published under the name : Lotario Grassi)Īsserting that Galileo's book advanced an atomic theory of matter, and that this conflicted with the Catholic doctrine of the Eucharist, because atomism would make transubstantiation impossible. ![]() Indivisibles are implicitly mentioned in part of the second day of the Dialogo (1632), at In February and March 1626, Cavalieri reminded him of the project: “do you remember the work on indivisibles that you had decided to write?” On, Galileo wrote, in a letter to the secretary of the Grand Duke of Tuscany, that he was planning a piece of work on the De Compositione continui. See : Vincent Jullien (editor), Seventeenth-Century Indivisibles Revisited (2015, Birkhauser) for details about the works of Kepler (1609), Cavalieri (1635) and Guldin (1640).Ĭavalieri developed his theory of geometry during the years 1620–1622.Īccording to Vincent Jullien's chapter dedicated to Indivisibles in the Work of Galileo : The issue regards more indivisibles than infinitesimals and must be located in the context of the Early Modern European debate about the "revamping" of atomism.
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