Article/Publication Details

A Reflection on Frege’s Definition of the Number

(Original title: Zamyšlení nad Fregovou definicí čísla)
Organon F, 2010, vol. 17, No 3, pp. 339-353.
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Abstract

In his treatise Die Grundlagen der Arithmetik, Gottlob Frege tries to find a definition of number. First he rejects the idea that number could be a property of external (empirical) objects. Then he comes with a suggestion that a numerical statement expresses a property of a concept, namely it indicates how many objects fall under the concept. Subsequently Frege rejects, or at least essentially modifies, also this definition, because in his view that a number cannot be a property – it should be an object. In this article, I try to show that Frege’s first definition of number seems to be, despite his own opinion, much more promising than he supposed. I also argue that Frege’s argumentation against the (possibly) empirical character of number is by no means convincing.

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