Single Idea 13411

[catalogued under 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers]

Full Idea

If we accept the Frege-Russell analysis of number (the natural numbers are the cardinals) as basic and correct, one thing which seems to follow is that one could know, say, three, seventeen, and eight, but no other numbers.

Gist of Idea

If numbers are basically the cardinals (Frege-Russell view) you could know some numbers in isolation

Source

Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.164)


A Reaction

It seems possible that someone might only know those numbers, as the patterns of members of three neighbouring families (the only place where they apply number). That said, this is good support for the priority of ordinals. See Idea 13412.

Related Idea

Idea 13412 Obtaining numbers by abstraction is impossible - there are too many; only a rule could give them, in order [Benacerraf]