more from this thinker | more from this text
Full Idea
On Frege's approach (of accepting abstract objects if they fall under a concept) the existence of the number 0, from which the series of numbers starts, is of course guaranteed by the citation of a concept under which nothing falls.
Gist of Idea
If objects exist because they fall under a concept, 0 is the object under which no objects fall
Source
report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Michael Dummett - Frege Philosophy of Language (2nd ed) Ch.14
Book Ref
Dummett,Michael: 'Frege Philosophy of Language' [Duckworth 1981], p.504
A Reaction
Frege cites the set of all non-self-identical objects, but he could have cited the set of circular squares. Given his Russell Paradox problems, this whole claim is thrown in doubt. Actually doesn't Frege's view make 0 impossible? Am I missing something?
| 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] |