[FOM] predicative foundations

Vladimir Sazonov V.Sazonov at csc.liv.ac.uk
Fri Feb 17 19:53:31 EST 2006

Quoting Nik Weaver <nweaver at math.wustl.edu> Fri, 17 Feb 2006:

> Another way to make my point about N is that I can interpret
> number theoretic assertions as being about marks on paper,
> and in this way avoid reference to natural numbers conceived
> as abstract metaphysical entities.

I do not understand what do you mean? Is, for example, 2^1000 
understood as the *marks on paper*: 2, ^, 1, 0, 0, 0, or as 2^1000 
marks |||,...,|? (I coinsider the latter meaningless as physically 
impossible as *marks on paper*.) Or may be you mean really written on 
paper symbols |,|,...,| what could be called feasible numbers (much 
less than 2^1000)? Otherwise why to mention "marks on paper" at all?

But it seemed to me that
> one has no similar trick for dealing with P(N).

Aha, you think that N is simpler than P(N). But not so simple as marks 
on paper, is not it? Please, do not oversimplify.


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