Axiomathes 30 (5):577-588 (2020)

Abstract
Frege’s famous definition of number famously uses the concept of “extension”. Extensions, in the Fregean framework, are susceptible to bringing many difficulties, and, some say, even paradoxes. Therefore, neo-logicist programs want to avoid the problems and to replace the classical Fregean definition of number with Hume’s Principle. I argue that this move, even if it makes sense from a computational point of view, is at odds with Frege’s larger philosophical project. For Frege, I claim, extensions were an important part of his philosophical program of logic-as-an-universal-language. This is why Frege places his project in line with Leibniz’ philosophical project of finding a lingua characterica universalis.
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DOI 10.1007/s10516-019-09468-5
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References found in this work BETA

Frege: Philosophy of Mathematics.Michael Dummett - 1991 - Harvard University Press.
Frege’s Conception of Numbers as Objects.Crispin Wright - 1983 - Critical Philosophy 1 (1):97.
The Julius Caesar Objection.Richard Heck - 1997 - In Richard G. Heck (ed.), Language, Thought, and Logic: Essays in Honour of Michael Dummett. Oxford University Press. pp. 273--308.

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