Is Leibnizian calculus embeddable in first order logic?
arXiv:1605.03501 · doi:10.1007/s10699-016-9495-6
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
arXiv comment22 pages, to appear in Foundations of Science
References in corpus (13)
- Leibniz's Infinitesimals: Their Fictionality, Their Modern Implementations, And Their Foes From Berkeley To Russell And Beyond
- Who Gave you the Cauchy-Weierstrass Tale? The Dual History of Rigorous Calculus
- Tools, objects, and chimeras: Connes on the role of hyperreals in mathematics
- Leibniz's Laws of Continuity and Homogeneity
- A Burgessian critique of nominalistic tendencies in contemporary mathematics and its historiography
- Cauchy's continuum
- Interpreting the infinitesimal mathematics of Leibniz and Euler
- Infinitesimals, Imaginaries, Ideals, and Fictions
- Leibniz vs Ishiguro: Closing a quarter-century of syncategoremania
- Differential geometry via infinitesimal displacements
- Euler's lute and Edwards' oud
- A Purely Algebraic Proof of the Fundamental Theorem of Algebra
- Edward Nelson (1932-2014)