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Full Idea
It is a chicken-and-egg problem, whether the lack of zero forced forced classical mathematicians to rely mostly on a geometric approach to mathematics, or the geometric approach made 0 a meaningless concept, but the two remain strongly tied together.
Gist of Idea
Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless
Source
Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch. 6)
Book Ref
Clegg,Brian: 'Infinity' [Robinson 2003], p.61
| 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] |