34 citations · 61 across the 6 of their papers we have counts for
6 papers
On mathematical realism and the applicability of hyperreals
Emanuele Bottazzi, Vladimir Kanovei, Mikhail G. Katz +2
We argue that Robinson's hyperreals have just as much claim to applicability as the garden variety reals. In a recent text, Easwaran and Towsner (ET) analyze the applicability of m…
What makes a theory of infinitesimals useful? A view by Klein and Fraenkel
Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz +1
Felix Klein and Abraham Fraenkel each formulated a criterion for a theory of infinitesimals to be successful, in terms of the feasibility of implementation of the Mean Value Theore…
Cauchy, infinitesimals and ghosts of departed quantifiers
Jacques Bair, Piotr Blaszczyk, Robert Ely +10
Procedures relying on infinitesimals in Leibniz, Euler and Cauchy have been interpreted in both a Weierstrassian and Robinson's frameworks. The latter provides closer proxies for t…
Is Leibnizian calculus embeddable in first order logic?
Piotr Blaszczyk, Vladimir Kanovei, Karin U. Katz +4
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 o…
Infinitesimals as an issue in neo-Kantian philosophy of science
Thomas Mormann, Mikhail G. Katz
We seek to elucidate the philosophical context in which one of the most important conceptual transformations of modern mathematics took place, namely the so-called revolution in ri…
Tools, objects, and chimeras: Connes on the role of hyperreals in mathematics
Vladimir Kanovei, Mikhail G. Katz, Thomas Mormann
We examine some of Connes' criticisms of Robinson's infinitesimals starting in 1995. Connes sought to exploit the Solovay model S as ammunition against non-standard analysis, but t…