David Nyman wrote:
> Bruno Marchal wrote:
> > If you prefer I should
> > have said "associate" instead of "identifying".
> Hi Bruno, welcome back.
> The terminological distinction you now make above is important - maybe
> it's another case of Franco-English faux amis (false cognates), but
> when you say 'identify' I think it steers Peter (and others) towards
> notions of 'reification' of number.

If Bruno isn't reifying numbers, he's in trouble.

He might be able to reduce an existent physical universe
to existent numbers, but he certainly can't reduce it
to non-existstent numbers.

> To 'associate' (in your sense of
> point-for-point commensurability) digital machines with number is a
> different matter (literally) than to 'identify' (i.e. posit an absolute
> identity between) them.

Yes. But if there if Platonia consist only of numbers,
and it here is no-one to do the associating in Platonia,
there are no machines/computations/algorithms in Platonia.

> Perhaps for the future, vis-a-vis reification, we should simply
> conclude, with Father Jack: "that would be an ecumenical matter"!

This *is* ecumenicism. The buck stops here. What higher
court of appeal is there , than consideration of the nature of

> > Computability is an absolute notion (with CT), but provability is a
> > relative (with respect to a machine) notion. Put in another way:
> > computations admits a universal dovetailer which generates and run all
> > computations, but there is no universal dovetailer for proofs.
> Point taken. The EC 'axioms' may be better conceived as primitive
> computations (like the UD), not theorems.

They're metaphysics. Face it.

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