34 citations · 92 across the 8 of their papers we have counts for
10 papers · 1 filter
Three case studies in current Leibniz scholarship
Mikhail G. Katz, Karl Kuhlemann, David Sherry +1
We examine some recent scholarship on Leibniz's philosophy of the infinitesimal calculus. We indicate difficulties that arise in articles by Bassler, Knobloch, and Arthur, due to a…
Two-track depictions of Leibniz's fictions
Mikhail G. Katz, Karl Kuhlemann, David Sherry +2
Leibniz described imaginary roots, negatives, and infinitesimals as useful fictions. But did he view such 'impossible' numbers as mathematical entities? Alice and Bob take on the l…
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…
Klein vs Mehrtens: restoring the reputation of a great modern
Jacques Bair, Piotr Błaszczyk, Peter Heinig +3
Historian Herbert Mehrtens sought to portray the history of turn-of-the-century mathematics as a struggle of modern vs countermodern, led respectively by David Hilbert and Felix Kl…
Fermat's dilemma: Why did he keep mum on infinitesimals? and the European theological context
Jacques Bair, Mikhail G. Katz, David Sherry
The first half of the 17th century was a time of intellectual ferment when wars of natural philosophy were echoes of religious wars, as we illustrate by a case study of an apparent…
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…