Bruno Marchal wrote:
On 31 Mar 2015, at 07:42, Bruce Kellett wrote:
In a phrase I have used before, It did not spring forth fully armed,
like Athena from Zeus's brow. Numbers were a hard-won abstraction from
everyday physical reality. They do not have any independent existence.
In which theory? What has independent existence?
The external objective universe, of which we are part.
As someone has said, you do not come across a number "5" running wild
in the undergrowth.
I am not sure, when I run I might not count them, but five incarnate in
my feet and hands all the time, and even if I did not have legs, like a
snake, 5 would still be prime, independently of me thinking about it or
not.
You are running into the old problem of universals. You take the
approach of Plato -- the universals are needed to explain the
commonality between all sets of five things (like toes, finger,...), but
even so, you don't see the "universal 5" running in the wild -- you see
only five toes, or deer, or ...... It is equally open to anyone to take
Aristotle's line and hold that five exists only in sets of five things
-- the modern nominalist position.
Two thousand five hundred years of philosophical argument have not
settled this issue, so no-one need accept your enthusiastic embrace of
Plato's account. Other accounts are just as good (in many ways preferable).
.......
But I think we need to distinguish two senses in which something can
be said to exist. There is mathematical existence, Exist_{math}, and
physical existence, Exist_{phys}.
I agree. And those are quite different mode of existence.
I am glad we can agree on something.
Exist_{math} is the set of all implications of a set of axioms and
some rules of inference.
Not at all. That would give only a tiny sigma_1 set. Even arithmetic is
larger than that, and non unifiable in any effective theory.
I think you underestimate the power of an axiomatic theory.
.....
Exist_{phys} is the hardware of the universe.
OK. But then comp is false, there are zombies, etc.
Why do you think that is a problem? They exist only if you create them.
....
You point and say "That is a rock, cat, or whatever." In more
sophisticated laboratory settings, you construct models to explain
atomic spectra, tracks in bubble chambers, and so on. The scientific
realist would claim that the theoretical entities entailed by his most
mature and well-tested scientific theories "exist_{phys}", and form
part of the furniture of the external objective physical world.
>
> No, that's when he get wrong, with respect of the computationalist
> hypothesis.
You equivocate on this point at different times. I said previously that,
by definition, computationalism is inconsistent with physicalism. You
denied this. But what you say here is exactly this.
...
>> So there is a very clear difference between the mathematical and
>> physical worlds.
>
> Yes, but science has not yet decided which is the most fundamental.
You agree, then, that computationalism is just a hypothesis and you
reject physicalism, or the independent existence of an external physical
world, simply because that disagrees with computationalism.
I don't think that your arguments that consciousness cannot be
understood in terms of physical supervenience are very convincing. At
all the crucial points you simply appeal to the computationalist
hypothesis -- your argument is, at heart, circular.
......
>> So prime numbers might exist_{math}, but they do not exist_{phys}.
>
> Sure. I have not verified, but I do think the universal machine would
> say the same. Physical is a sophisticated internal view of arithmetic/
> There still might be too much much white rabbits, but prime numbers
> are not of the type "observable" there.
I think this claim needs some backing up. You have to actually derive at
least some basic physical laws from your UD. Pointing to prime numbers
is not enough. I think that the white rabbits will be your undoing.
Bruce
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