[FOM] Predicativism and natural numbers

Giovanni Lagnese lagnese at ngi.it
Tue Jan 17 06:32:19 EST 2006

Nik Weaver wrote:

> No, you cannot take the concept of power set as primitive
> if you don't even know what sets are.

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

> The impatience with predicativism seen here seems to arise from
> an implicit acceptance of a platonic conception of set theory.

It's not my case.

> "The expectation ... has been that one must look
> elsewhere for _another object_ to be the pair
> of apples. But this supposed other object is
> a grammatical mirage.")

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

> [...] why in your supposed platonic universe of sets [...]

I do not believe in a platonic universe of sets.

> On this view it is obvious that we cannot simply posit
> the existence of power sets.  We have to show how
> they can be built.

I think that we have to say what a statement about subsets means.

> I do not see how a structure playing the role
> of the power set of the natural numbers could
> be constructed in any comparable way.

Do you believe in the function set N^N?


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