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Modern incarnations of the Aristotelic Topos

Clarence Protin
May 2021
摘要
In this essay we discuss the concepts of \emph{topos} (place),\emph{sunekhes} (continuity) and \emph{infinitesimal} as found in classicalphilosophy (primarily in Aristotle's \emph{Physics}) and their relationship tomodern topology. We show how the modern (Leibnizian and Newtonian) concept of infinitesimalhas its roots in classical thought and that the concepts of topos, continuityand infinitesimal are related. We show furthermore how Aristotle's notions oftopos can be given precise definitions in terms of modern topology and categorytheory and how they are relevant to modern problems in the foundations ofmathematics and philosophy of science.
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