structure for 'Mathematics'    |     alphabetical list of themes    |     expand these ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of 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]