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date: 23 August 2019

Abstract and Keywords

This article examines the so-called problem of generality in Euclid’s Elements. More specifically, it asks whether there is a ‘more general’ point of view from which magnitudes and numbers might be treated without distinction, and if so, whether Euclid violated the Aristotelian prescription by treating general features (typically the operative core of “proportions”) in specific cases in Book V (for magnitudes) and in Book VII (for numbers). The article first considers the general context of the problem of generality, taking into account the object domains in Euclidean mathematics, and some of the modern strategies proposed to solve it. These strategies rely on historical reconstructions and often make use of evidence taken from Aristotle, but tend to have a purely utilitarian relationship to such evidence. The article also discusses Aristotle’s conception of scientific knowledge, the problem of the katholou, and his view of generality in mathematics.

Keywords: problem of generality, Euclid, Elements, generality, magnitudes, numbers, Aristotle, scientific knowledge, katholou, mathematics

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