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Leibniz's infinitesimals: Their fictionality, their modern implementations, and their foes from Berkeley to Russell and beyond
MG Katz, D Sherry - Erkenntnis, 2013 - Springer
Many historians of the calculus deny significant continuity between infinitesimal calculus of
the seventeenth century and twentieth century developments such as Robinson's theory …
the seventeenth century and twentieth century developments such as Robinson's theory …
Leibniz's syncategorematic infinitesimals II: their existence, their use and their role in the justification of the differential calculus
D Rabouin, RTW Arthur - Archive for History of Exact Sciences, 2020 - Springer
In this paper, we endeavour to give a historically accurate presentation of how Leibniz
understood his infinitesimals, and how he justified their use. Some authors claim that when …
understood his infinitesimals, and how he justified their use. Some authors claim that when …
Approaches to analysis with infinitesimals following Robinson, Nelson, and others
This is a survey of several approaches to the framework for working with infinitesimals and
infinite numbers, originally developed by Abraham Robinson in the 1960s, and their …
infinite numbers, originally developed by Abraham Robinson in the 1960s, and their …
Infinitesimals as an issue of neo-Kantian philosophy of science
T Mormann, M Katz - … The Journal of the International Society …, 2013 - journals.uchicago.edu
We seek to elucidate the philosophical context in which one of the most important
conceptual transformations of modern mathematics took place, namely, the so-called …
conceptual transformations of modern mathematics took place, namely, the so-called …
Interpreting the infinitesimal mathematics of Leibniz and Euler
J Bair, P Błaszczyk, R Ely, V Henry, V Kanovei… - Journal for general …, 2017 - Springer
We apply Benacerraf's distinction between mathematical ontology and mathematical
practice (or the structures mathematicians use in practice) to examine contrasting …
practice (or the structures mathematicians use in practice) to examine contrasting …
Fermat, Leibniz, Euler, and the gang: The true history of the concepts of limit and shadow
T Bascelli, E Bottazzi, F Herzberg, V Kanovei… - arxiv preprint arxiv …, 2014 - ams.org
The theories as developed by European mathematicians prior to 1870 differed from the
modern ones in that none of them used the modern theory of limits. Fermat develops what is …
modern ones in that none of them used the modern theory of limits. Fermat develops what is …
A cognitive analysis of Cauchy's conceptions of function, continuity, limit and infinitesimal, with implications for teaching the calculus
In this paper, we use theoretical frameworks from mathematics education and cognitive
psychology to analyse Cauchy's ideas of function, continuity, limit and infinitesimal …
psychology to analyse Cauchy's ideas of function, continuity, limit and infinitesimal …
Is mathematical history written by the victors?
J Bair, P Błaszczyk, R Ely, V Henry, V Kanovei… - Notices of the AMS, 2013 - ams.org
The ABCs of the history of infinitesimal mathematics are in need of clarification. To what
extent does the famous dictum “history is always written by the victors” apply to the history of …
extent does the famous dictum “history is always written by the victors” apply to the history of …
Historical infinitesimalists and modern historiography of infinitesimals
In the history of infinitesimal calculus, we trace innovation from Leibniz to Cauchy and
reaction from Berkeley to Mansion and beyond. We explore 19th century infinitesimal lores …
reaction from Berkeley to Mansion and beyond. We explore 19th century infinitesimal lores …
Procedures of Leibnizian infinitesimal calculus: An account in three modern frameworks
J Bair, P Błaszczyk, R Ely, MG Katz… - British Journal for the …, 2021 - Taylor & Francis
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 …
most successful account of the procedures of the Leibnizian calculus (LC). While many …