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6. Mathematics / A. Nature of Mathematics / 3. Numbers / l. Zero

[status and nature of the number zero]

7 ideas
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]