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Single Idea 9838

[filed under theme 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / l. Zero ]

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.


The 7 ideas with the same theme [status and nature of the number zero]:

Treating 0 as a number avoids antinomies involving treating 'nobody' as a person [Frege, by Dummett]
For Frege 'concept' and 'extension' are primitive, but 'zero' and 'successor' are defined [Frege, by Chihara]
If objects exist because they fall under a concept, 0 is the object under which no objects fall [Frege, by Dummett]
Nought is the number belonging to the concept 'not identical with itself' [Frege]
0 is not a number, as it answers 'how many?' negatively [Husserl, by Dummett]
Unless we know whether 0 is identical with the null set, we create confusions [Fine,K]
Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg]