Is Leibnizian Calculus Embeddable in First Order Logic?

摘要 为了探讨莱布尼兹无穷小微积分在一阶逻辑(FOL)和现代框架中可嵌入性，我们提出将本体论问题放在一边，关注过程问题。这将使Leibiniz的程序能够在一个只加上少量其他因素——例如无限接近的关系——的FOL的框架内得到解释。正如我们在这里所讨论的，如果一阶逻辑确实适用于为莱布尼兹无穷小微积分中发现的推理动作（inferential moves）做出现代表述，那么现代无穷小框架比现代魏尔斯特拉斯方程更合适解释莱布尼兹无穷小微积分。

关键词 一阶逻辑；无穷小微积分；本体；程序；莱布尼兹，魏尔斯特拉斯，鲁滨逊

【Abstract】To explore the extent of embeddability of Leibnizian infinitesimal calculus in first-order logic (FOL) and modern frameworks, we propose to set aside ontological issues and focus on procedural questions. This would enable an account of Leibnizian procedures in a framework limited to FOL with a small number of additional ingredients such as the relation of infinite proximity. If, as we argue here, first order logic is indeed suitable for developing modern proxies for the inferential moves found in Leibnizian infinitesimal calculus, then modern infinitesimal frameworks are more appropriate to interpreting Leibnizian infinitesimal calculus than modern Weierstrassian ones.

Keywords First order logic Infinitesimal calculus Ontology Procedures Leibniz Weierstrass Abraham Robinson

http://dx.doi.org/10.1007/s10699-016-9495-6​dx.doi.org

Is Leibnizian calculus embeddable in first order logic?​arxiv.org

Matches for: MR=3720412​mathscinet.ams.org