30 citations · 199 across the 25 of their papers we have counts for
5 papers · 2 filters
Gregory's sixth operation
Tiziana Bascelli, Piotr Blaszczyk, Vladimir Kanovei +6
In relation to a thesis put forward by Marx Wartofsky, we seek to show that a historiography of mathematics requires an analysis of the ontology of the part of mathematics under sc…
Toward a history of mathematics focused on procedures
Piotr Blaszczyk, Vladimir Kanovei, Karin U. Katz +3
Abraham Robinson's framework for modern infinitesimals was developed half a century ago. It enables a re-evaluation of the procedures of the pioneers of mathematical analysis. Thei…
Interpreting the infinitesimal mathematics of Leibniz and Euler
Jacques Bair, Piotr Blaszczyk, Robert Ely +10
We apply Benacerraf's distinction between mathematical ontology and mathematical practice (or the structures mathematicians use in practice) to examine contrasting interpretations…
Small oscillations of the pendulum, Euler's method, and adequality
Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz +1
Small oscillations evolved a great deal from Klein to Robinson. We propose a concept of solution of differential equation based on Euler's method with infinitesimal mesh, with well…
Leibniz vs Ishiguro: Closing a quarter-century of syncategoremania
Tiziana Bascelli, Piotr Blaszczyk, Vladimir Kanovei +4
Did Leibniz exploit infinitesimals and infinities `a la rigueur, or only as shorthand for quantified propositions that refer to ordinary Archimedean magnitudes? Chapter 5 in (Ishig…