more from Paul Benacerraf

Single Idea 13412

[catalogued under 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers]

Full Idea

Not all numbers could possibly have been learned à la Frege-Russell, because we could not have performed that many distinct acts of abstraction. Somewhere along the line a rule had to come in to enable us to obtain more numbers, in the natural order.

Gist of Idea

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

Source

Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.165)


A Reaction

Follows on from Idea 13411. I'm not sure how Russell would deal with this, though I am sure his account cannot be swept aside this easily. Nevertheless this seems powerful and convincing, approaching the problem through the epistemology.

Related Idea

Idea 13411 If numbers are basically the cardinals (Frege-Russell view) you could know some numbers in isolation [Benacerraf]