[FOM] predicative foundations

[Aatu Koskensilta]

On Feb 16, 2006, at 2:12 AM, Nik Weaver wrote:

> I can describe N in a metaphysically uncontroversial way in terms of
> making marks on paper.

But these "marks on paper" can't be actual marks on paper, but must be 
something
like "possible" marks on paper. The justification for N in these terms 
is circular,
because we have to assume that something like "possible marks on paper" 
make sense,
which is just as problematic or unproblematic as the natural numbers 
themselves.
Similarly to hold that the totality of subsets of, say, 
A={0,1,...,2^128} is determined
because eg. every such subset "can" be given by explicitly listing its 
elements is just
begging the question: the existence of the totality of these listings 
is just as problematic
or non-problematic as the existence the totality of the subsets A, 
because the "can" must simply
amount to mathematical existence, there being no question that, 
actually, we are in no position
to survey such a totality of listings.

Aatu Koskensilta (aatu.koskensilta at xortec.fi)

"Wovon man nicht sprechen kann, darüber muss man schweigen"
  - Ludwig Wittgenstein, Tractatus Logico-Philosophicus