On 2/23/2015 8:47 AM, Bruno Marchal wrote:
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))).
An the existential quantifier only shows that relative to the axioms there is something
that satisfies the WFF.
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.
You seem to take the same view as LizR, "You're either for my theory or you're for a
contrary theory." So I'll ask the same question, what happened to agnotsticism? Can't
ultrafinitism be true? It can certainly be true in the same way 2+2=4 is true - i.e.
consistent with some set of axioms. But then this undermines the idea that the arithmetic
existential quantifier provides the same "exists" as ostensive physical existence.
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.
What does that mean? That it's true and ultrafinitism is false? That ZFC isn't true and
sets don't exist. Does it mean plausibly true? consistent? exists? What would make me
happy would be if it predicted something surprising that we could confirm.
Brent
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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