Leibniz’s well-founded fictions and their interpetations
Journal Title: Математичні Студії - Year 2018, Vol 49, Issue 2
Abstract
Leibniz used the term fiction in conjunction with infinitesimals. What kind of fictions they were exactly is a subject of scholarly dispute. The position of Bos and Mancosu contrasts with that of Ishiguro and Arthur. Leibniz's own views, expressed in his published articles and correspondence, led Bos to distinguish between two methods in Leibniz's work: (A) one exploiting classical `exhaustion' arguments, and (B) one exploiting inassignable infinitesimals together with a law of continuity. Of particular interest is evidence stemming from Leibniz's work Nouveaux Essais sur l'En- tendement Humain as well as from his correspondence with Arnauld, Bignon, Dagincourt, Des Bosses, and Varignon. A careful examination of the evidence leads us to the opposite conclusion from Arthur's. We analyze a hitherto unnoticed objection of Rolle's concerning the lack of justification for extending axioms and operations in geometry and analysis from the ordinary domain to that of infinitesimal calculus, and reactions to it by Saurin and Leibniz. A newly released 1705 manuscript by Leibniz (Puisque des personnes. . . ) currently in the process of digitalisation, sheds light on the nature of Leibnizian inassignable infinitesimals. In a pair of 1695 texts Leibniz made it clear that his incomparable magnitudes violate Euclid's Definition V.4, a.k.a. the Archimedean property, corroborating the non-Archimedean construal of the Leibnizian calculus.
Authors and Affiliations
J. Bair, P. Blaszczyk, R. Ely, M. G. Katz
Keywords
Related Articles
- EP ID EP411804
- DOI 10.15330/ms.49.2.186-224
- Views 40
- Downloads 0
Asymptotic properties of the impulse perturbation process under Levy approximation conditions with the point of equilibrium of the quality criterion
For the system of stochastic differential equations with Markov switchings and impulse disturbance in the conditions of Levy approximation in the conditions of a single point of equilibrium of the quality criterion, limi...
On a Banach space of Laplace-Stieltjes integrals
Let Ω be class of positive unbounded functions Φ on (−∞,+∞) such that the derivative Φ′ is positive, continuously differentiable and increasing to +∞ on (−∞,+∞), φ be the inverse function to Φ′, and Ψ(x)=x−Φ(x)Φ′(x) be t...
Composition, product and sum of analytic functions of bounded L-index in direction in the unit ball
In this paper, we investigate a composition of entire function of one variable and analytic function in the unit ball. There are obtained conditions which provide equivalence of bounded\-ness of L-index in a direction fo...
On belonging of entire Dirichlet series to a modified generalized convergence class
For entire Dirichlet series F(s)=∑+∞n=0anesλn we found conditions on an, λn and on positive functions α and β continuous increasing to +∞ on [0,+∞) are found, under which the condition ∫+∞σ01β(σ)α(1σlnM(σ,F))dσ≤+∞ is equ...
Frechet distance between weighted rooted trees
The aim of this note is to extend the notion of Frechet distance over the set of weighted rooted trees. The weighted trees naturally appear as skeletons of planar domains. The defined distance allows for defining a dista...