48 citations · 200 across the 26 of their papers we have counts for
6 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…
A non-standard analysis of a cultural icon: The case of Paul Halmos
Piotr Blaszczyk, Alexandre Borovik, Vladimir Kanovei +4
We examine Paul Halmos' comments on category theory, Dedekind cuts, devil worship, logic, and Robinson's infinitesimals. Halmos' scepticism about category theory derives from his p…
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…
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…
Controversies in the foundations of analysis: Comments on Schubring's Conflicts
Piotr Blaszczyk, Vladimir Kanovei, Mikhail Katz +1
Foundations of Science recently published a rebuttal to a portion of our essay it published two years ago. The author, G. Schubring, argues that our 2013 text treated unfairly his…