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Full Idea
Frege's point was that by treating 0 as a number, we run into none of the antinomies that result from treating 'never' as the name of a time, or 'nobody' as the name of a person.
Gist of Idea
Treating 0 as a number avoids antinomies involving treating 'nobody' as a person
Source
report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Michael Dummett - Frege philosophy of mathematics Ch.8
Book Ref
Dummett,Michael: 'Frege: philosophy of mathematics' [Duckworth 1991], p.96
A Reaction
I don't think that is a good enough reason. Daft problems like that are solved by settling the underlying proposition or logical form (of a sentence containing 'nobody') before one begins to reason. Other antinomies arise with zero.
9838 | Treating 0 as a number avoids antinomies involving treating 'nobody' as a person [Frege, by Dummett] |
9564 | For Frege 'concept' and 'extension' are primitive, but 'zero' and 'successor' are defined [Frege, by Chihara] |
10551 | If objects exist because they fall under a concept, 0 is the object under which no objects fall [Frege, by Dummett] |
8653 | Nought is the number belonging to the concept 'not identical with itself' [Frege] |
9837 | 0 is not a number, as it answers 'how many?' negatively [Husserl, by Dummett] |
10574 | Unless we know whether 0 is identical with the null set, we create confusions [Fine,K] |
10853 | Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg] |