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Full Idea
Husserl contends that 0 is not a number, on the grounds that 'nought' is a negative answer to the question 'how many?'.
Gist of Idea
0 is not a number, as it answers 'how many?' negatively
Source
report of Edmund Husserl (Philosophy of Arithmetic [1894], p.144) by Michael Dummett - Frege philosophy of mathematics Ch.8
Book Ref
Dummett,Michael: 'Frege: philosophy of mathematics' [Duckworth 1991], p.95
A Reaction
I seem to be in a tiny minority in thinking that Husserl may have a good point. One apple is different from one orange, but no apples are the same as no oranges. That makes 0 a very peculiar number. See Idea 9838.
Related Idea
Idea 9838 Treating 0 as a number avoids antinomies involving treating 'nobody' as a person [Frege, by Dummett]
| 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] |