2 citations · 7 across the 9 of their papers we have counts for
9 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…
Of pashas, popes, and indivisibles
Mikhail G. Katz, David Sherry, Monica Ugaglia
The studies of Bonaventura Cavalieri's indivisibles by Giusti, Andersen, Mancosu and others provide a comprehensive picture of Cavalieri's mathematics, as well as of the mathematic…
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…
When does a hyperbola meet its asymptote? Bounded infinities, fictions, and contradictions in Leibniz
Mikhail G. Katz, David Sherry, Monica Ugaglia
In his 1676 text De Quadratura Arithmetica, Leibniz distinguished infinita terminata from infinita interminata. The text also deals with the notion, originating with Desargues, of…
Evolution of Leibniz's thought in the matter of fictions and infinitesimals
Monica Ugaglia, Mikhail G. Katz
In this paper we offer a reconstruction of the evolution of Leibniz's thought concerning the problem of the infinite divisibility of bodies, the tension between actuality, unassign…