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Full Idea
No account of an individual number is adequate unless it relates that number to the series of which it is a member.
Gist of Idea
An adequate account of a number must relate it to its series
Source
Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.169)
A Reaction
Thus it is not totally implausible to say that 2 is several different numbers or concepts, depending on whether you see it as a natural number, an integer, a rational, or a real. This idea is the beginning of modern structuralism.
| 13411 | If numbers are basically the cardinals (Frege-Russell view) you could know some numbers in isolation [Benacerraf] |
| 13412 | Obtaining numbers by abstraction is impossible - there are too many; only a rule could give them, in order [Benacerraf] |
| 13413 | We must explain how we know so many numbers, and recognise ones we haven't met before [Benacerraf] |
| 13415 | An adequate account of a number must relate it to its series [Benacerraf] |