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27 papers · 1 filter
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…
Episodes from the history of infinitesimals
Mikhail G. Katz
Infinitesimals have seen ups and downs in their tumultuous history. In the 18th century, d'Alembert set the tone by describing infinitesimals as chimeras. Some adversaries of infin…
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…
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…