18 citations · 56 across the 5 of their papers we have counts for
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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…
Leibniz's well-founded fictions and their interpretations
Jacques Bair, Piotr Blaszczyk, Robert Ely +2
Leibniz used the term fiction in conjunction with infinitesimals. What kind of fictions they were exactly is a subject of scholarly dispute. The position of Bos and Mancosu contras…
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…
Interpreting the infinitesimal mathematics of Leibniz and Euler
Jacques Bair, Piotr Blaszczyk, Robert Ely +10
We apply Benacerraf's distinction between mathematical ontology and mathematical practice (or the structures mathematicians use in practice) to examine contrasting interpretations…
Is mathematical history written by the victors?
Jacques Bair, Piotr Blaszczyk, Robert Ely +9
We examine prevailing philosophical and historical views about the origin of infinitesimal mathematics in light of modern infinitesimal theories, and show the works of Fermat, Leib…