Bruno Marchal wrote:
> Le 22-août-06, à 08:36, Tom Caylor a écrit :
> > I believe that we are finite, but as I said in the "computationalsim
> > and supervenience" thread, it doesn't seem that this is a strong enough
> > statement to be useful in a TOE.  It seems that you cannot have YD
> > without CT, but if true I would leave Bruno to explain exactly why.
> >
> I am not sure I have said that YD needs CT. CT is needed to use the
> informal "digital" instead of the "turing", "java" "python" seemingly
> restriction.
> For someone not believing in CT, "digital" could have a wider meaning
> than "turing emulable".
> Now CT needs AR. CT is equivalent with the statement that all universal
> digital machine can emulate each other.

i.e "If a Universal Digital macine exists, it can emulate
another one". No ontological commitment there.

>  To make this precise (or just
> to define universal machine/number) you need to believe in numbers.

To make something precise you need a precise *definition*.

For a formalist, there is nothing to numbers except definitions (axoms,
etc),. The numbers themselves do not have to exist. So there is
still no necessary ontological commitment in CT.

> (But just in the usual sense of any number theorist).

Which will depend on whether the individual number theorist is
a Platonist, Formalist, or whatever.

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