more from William W. Tait

Single Idea 9984

[catalogued under 4. Formal Logic / F. Set Theory ST / 7. Natural Sets]

Full Idea

Why can't we have a series (as opposed to a linearly ordered set) all of whose members are identical, such as (a, a, a...,a)?

Gist of Idea

We can have a series with identical members


William W. Tait (Frege versus Cantor and Dedekind [1996], VII)

Book Reference

'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.51

A Reaction

The question is whether the items order themselves, which presumably the natural numbers are supposed to do, or whether we impose the order (and length) of the series. What decides how many a's there are? Do we order, or does nature?