17 citations · 43 across the 10 of their papers we have counts for
10 papers
Marx versus Engels on infinitesimals: Chimera or triumph?
Mikhail G. Katz, Karl Kuhlemann, Semen S. Kutateladze
We document the evolution of Karl Marx's take on infinitesimals. We contrast his initial favorable stance with later criticisms, and examine the differing perspectives of Marx and…
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…
Formalism 25
Mikhail G. Katz, Karl Kuhlemann, Sam Sanders +1
Abraham Robinson's philosophical stance has been the subject of several recent studies. Erhardt following Gaifman claims that Robinson was a finitist, and that there is a tension b…
Leibniz's contested infinitesimals: Further depictions
Mikhail G. Katz, Karl Kuhlemann
We contribute to the lively debate in current scholarship on the Leibnizian calculus. In a recent text, Arthur and Rabouin argue that non-Archimedean continua are incompatible with…
A Leibniz/NSA comparison
Mikhail G. Katz, Karl Kuhlemann, David Sherry
We present some similarities between Leibnizian and Robinsonian calculi, and address some objections raised by historians. The comparison with NSA facilitates our appreciation of s…
Exploring Felix Klein's contested modernism
Peter Heinig, Mikhail G. Katz, Karl Kuhlemann +2
An alleged opposition between David Hilbert and Felix Klein as modern vs countermodern has been pursued by marxist historian Herbert Mehrtens and others. Scholars such as Epple, Gr…
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…
Leibniz on bodies and infinities: rerum natura and mathematical fictions
Mikhail G. Katz, Karl Kuhlemann, David Sherry +1
The way Leibniz applied his philosophy to mathematics has been the subject of longstanding debates. A key piece of evidence is his letter to Masson on bodies. We offer an interpret…
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…
Procedures of Leibnizian infinitesimal calculus: An account in three modern frameworks
Jacques Bair, Piotr Blaszczyk, Robert Ely +2
Recent Leibniz scholarship has sought to gauge which foundational framework provides the most successful account of the procedures of the Leibnizian calculus (LC). While many schol…