[FOM] Predicativism and natural numbers

[Nik Weaver]

Giovanni Lagnese, on doing set theory without being a platonist:

> The point is not what a set is.
> The point is what a statement about sets means.

and on the phrase "the pair of apples" not referring to a literal
object:

> I think that the point is what a statement about pairs of
> apples means.

This sounds like an approach that I might agree with.  But
there seems to be a difficulty in handling sets of sets.
If you don't have an actual object which is or represents
the pair of apples, how do you interpret a set which contains
that pair as an element?  If you have really thought this
through and feel you have a way to iterate the sort of
approach to sets you've suggested, please explain.

This is related to a difficulty I have with Martin-Lof's
concept of universes, which I will post a separate message
about shortly.

Nik Weaver
Math Dept.
Washington University
St. Louis, MO 63130 USA
nweaver at math.wustl.edu