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.
Bibliographical noteFunding Information:
M. Katz was partially funded by the Israel Science Foundation Grant Number 1517/12.
© 2016, Springer Science+Business Media Dordrecht.
- Abraham Robinson
- First order logic
- Infinitesimal calculus