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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]
17444 | Husserl said counting is more basic than Frege's one-one correspondence [Husserl, by Heck] |
21214 | We clarify concepts (e.g. numbers) by determining their psychological origin [Husserl, by Velarde-Mayol] |
9819 | Psychologism blunders in focusing on concept-formation instead of delineating the concepts [Dummett on Husserl] |
9851 | Husserl wanted to keep a shadowy remnant of abstracted objects, to correlate them [Dummett on Husserl] |
9837 | 0 is not a number, as it answers 'how many?' negatively [Husserl, by Dummett] |
9575 | Husserl identifies a positive mental act of unification, and a negative mental act for differences [Husserl, by Frege] |
9576 | Multiplicity in general is just one and one and one, etc. [Husserl] |