On 23 Feb 2015, at 01:55, meekerdb wrote:
On 2/22/2015 4:38 PM, Jason Resch wrote:
Not as Bruno uses it: That all computations exist Platonically and
instantiate all possible thoughts - and a lot of other stuff.
That's arithmetical realism, not computationalism. However, to
believe in the notion of Turing machines or Turing emulability
requires assuming at least something like the peano axioms.
I think there's a difference between arithmetical realism and
assuming there's a universal dovetailer that exists in at least the
Platonic sense.
We need only the existence (in the usual arithmetical sense) of the UD
and the computations. The existence of the UD is a theorem of PA, or
even RA.
Assuming the Peano Axioms means assuming they are 'true', not that
anything exists.
Once you assume PA, you derive the existence of many things, like
numbers, finite computations, and sequences of computations, etc.
For example s(0) = s(0), by identity axioms, and from this you can
derive already that the number 2 exists, by the existential quantifier
rule F(t) ==> ExFx): Ex(x = s(s(0))).
And I put 'true' in scare quotes because to show that there are
true but unprovable arithmetic propositions requires assuming that
the numbers are infinite, which I think it just a convenience, and
not a metaphysical necessity.
It is a mathematical necessity. if you assume a finite number of
numbers, you can prove 0 = 1 at the metalevel.
So to you use your remark as a critics, you would need an
ultrafinitist axioms, which indeed contradicts arithmetical realism,
and RA, PA, etc.
If you need to resort to ultrafinitism to escape the consequence, you
are defending computationalism, as virtually nobody believes in
ultrafinitism.
To be sure, I do not defend computationalism. I just study its
consequences, and I show that a classical version of comp is testable.
I do find computationalism plausible, though. But this is between us,
and I don't intend to defend computationalism (and this will not
prevent me to criticizing invalid argument against comp, or invalid
argument for comp, etc.). In fact it is the resemblance between the
comp solution to the mind-body problem and QM (without collapse) which
makes me feel that computationalism is plausible. Classical
computationalism? I am just quite astonished that this has not yet
been refuted.
Bruno
Brent
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