[FOM] Predicativism and natural numbers

[Giovanni Lagnese]

Nik Weaver wrote:

> the concept "of length omega", which need not refer
> to any special object and which I think is initially available.

The concept "of lenght omega" is not initially available, because it is not 
clear before you define it.
The concept "unending" is clear, but not the concept "of lenght omega".
"Of lenght omega" does not mean simply "unendig". It means "minimal 
unending". This is the point.


> I can imagine no process which would enable me to
> identify a structure which could play the role of the
> power set of omega and which could not be further
> enriched by a longer process.

I can say that you can not identify a structure which could play the role of 
omega and which could not be further enriched by a longer process...


> we can imagine omega
> --- the key phrase being "a complete and clear mental survey" --- 
> in a way that we cannot imagine the power set of omega.

My intuition of omega is not so complete.

But I think we do not need a complete intuition of a collection C to 
quantifying in C.
I think are sufficient Brouwers's continuity principles.

GL