11 citations · 31 across the 7 of their papers we have counts for
7 papers
A philosophical history of infinitesimals
Vladimir Kanovei, Mikhail G. Katz, Taras Kudryk +1
We explore the issue of providing a foundational framework for Leibnizian infinitesimals in the light of modern standard and nonstandard approaches. We outline a trichotomy of ordi…
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…
Analyzing Benardete's comment on decimal notation
Jacques Bair, Piotr Blaszczyk, Karin U. Katz +3
Philosopher Benardete challenged both the conventional wisdom and the received mathematical treatment of zero, dot, nine recurring. An initially puzzling passage in Benardete on th…
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…
The Mathematical Intelligencer flunks the Olympics
Alexander E. Gutman, Mikhail G. Katz, Taras S. Kudryk +1
The Mathematical Intelligencer recently published a note by Y. Sergeyev that challenges both mathematics and intelligence. We examine Sergeyev's claims concerning his purported Inf…
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…
Toward a clarity of the extreme value theorem
Karin U. Katz, Mikhail G. Katz, Taras Kudryk
We apply a framework developed by C. S. Peirce to analyze the concept of clarity, so as to examine a pair of rival mathematical approaches to a typical result in analysis. Namely,…