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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The Foundations of Arithmetic: A Logico-Mathematical Enquiry Into the Concept of Number.Gottlob Frege - 1950 - New York, NY, USA: Northwestern University Press.
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