Sheldon Smith on Newton’s Derivative: Retrospective Assignation, Externalism and the History of Mathematics

Topoi 42 (1):333-344 (2023)
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Abstract

To illustrate the view that a speaker can have a partial understanding of a concept, Burge uses the example of Leibniz’s and Newton’s understanding of the concept of derivative. In a recent article, Sheldon Smith criticizes this example and maintains that Newton’s and Leibniz’s use of their derivative symbols does not univocally determine their references. The present article aims at challenging Smith’s analysis. It first shows that Smith misconstrues Burge’s position. It second suggests that the philosophical lessons one should draw from the practice of the historians of philosophy are more ambivalent than what Smith thinks.

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Individualism and the mental.Tyler Burge - 1979 - Midwest Studies in Philosophy 4 (1):73-122.
Word and Object.Willard Van Orman Quine - 1960 - Les Etudes Philosophiques 17 (2):278-279.
Other bodies.Tyler Burge - 1982 - In Andrew Woodfield (ed.), Thought And Object: Essays On Intentionality. New York: Oxford: Clarendon Press.
Theory change and the indeterminacy of reference.Hartry Field - 1973 - Journal of Philosophy 70 (14):462-481.

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