The Jesuits and the Method of Indivisibles

David Sherry

摘要：亚历山大（Alexander）的无穷小量认为耶稣会对意大利数学产生了令人不寒而栗的影响，但我对他对耶稣会压制不可分割性动机的描述提出了质疑。亚历山大宣称，耶稣会士对亚里士多德（Aristotle）和欧几里德（Euclid）的不妥协承诺，解释了他们反对不可分割方法的立场。另一个不同的假设是不可分割的方法和天主教圣餐教义之间的冲突，而亚历山大并不追求这一假设。这很遗憾，因为与圣餐的冲突比耶稣会对亚里士多德和欧几里得的承诺更有优势。不可分割法是17世纪发展起来的一种方法，那些依赖于亚里士多德和欧几里德的理想在“阿尔卑斯山之外”发展起来的人。亚历山大未能认识到亚里士多德和欧几里德的重要性，因为不可分割的方法的发展产生于不可分割和无穷小的毫无根据的合并(第一节)。一旦不可分割和无穷小被区别开来，我们观察到不可分割方法的发展明白无误地展示了对亚里士多德和欧几里得同情(第二节)。因此,考虑对耶稣会厌恶不可分量的另一种解释是有意义的。事实上，不可分割但并非无限小的东西与圣餐的教义相冲突，圣餐是教会的中心教义(第三节)。

关键词：不可分割，无穷小，耶稣会科学，圣餐，欧几里得，伽利略，卡瓦列里，托里切利，帕斯卡，巴罗

Abstract：Alexander’s Infinitesimal is right to argue that the Jesuits had a chilling effect on Italian mathematics, but I question his account of the Jesuit motivations for suppressing indivisibles. Alexander alleges that the Jesuits’ intransigent commitment to Aristotle and Euclid explains their opposition to the method of indivisibles. A different hypothesis, which Alexander doesn’t pursue, is a conflict between the method of indivisibles and the Catholic doctrine of the Eucharist. This is a pity, for the conflict with the Eucharist has advantages over the Jesuit commitment to Aristotle and Euclid. The method of indivisibles was a method that developed in the course of the seventeenth century, and those who developed ‘beyond the Alps’ relied upon Aristotelian and Euclidean ideals. Alexander’s failure to recognize the importance of Aristotle and Euclid for the development of the method of indivisibles arises from an unwarranted conflation of indivisibles and infinitesimals (Sect. 1). Once indivisibles and infinitesimals are distinguished, we observe that the development of the method of indivisibles exhibits an unmistakable sympathy for Aristotle and Euclid (Sect. 2). Thus, it makes sense to consider an alternative explanation for the Jesuit abhorrence of indivisibles. And indeed, indivisibles but not infinitesimals conflict with the doctrine of the Eucharist, the central dogma of the Church (Sect. 3).

Keywords：Indivisibles，Infinitesimals，Jesuit science，Eucharist，Euclid，Galileo ， Cavalieri ，Toricelli ，Pascal，Barrow

The Jesuits and the Method of Indivisibles​dx.doi.orgMatches for: MR=3803897​mathscinet.ams.org