On 2/24/2015 5:21 AM, Bruno Marchal wrote:
On 23 Feb 2015, at 20:46, meekerdb wrote:
On 2/23/2015 7:58 AM, Bruno Marchal wrote:
On 23 Feb 2015, at 01:16, meekerdb wrote:
On 2/22/2015 2:52 PM, LizR wrote:
On 23 February 2015 at 10:17, meekerdb <[email protected]
<mailto:[email protected]>>
Computationalism is an extraordinary claim.
The claim that what goes on inside brains is at some level Turing-emulable seems not
necessarily extraordinary - or do you think it is?
Yes. It's not crazy or outlandish, but I don't think it's ordinary either.
It seems like a fairly standard assumption by many scientists and philosophers, but
I can believe it's wrong - but some reason to do so would be nice rather, than just
a "statement from authority". as given here.Y
(If the conclusions Bruno has drawn from that assumption appear extraordinary those
aren't "claims", just deductions which can presumably be shown to be wrong through
the application of logic, assuming they are ub fact wrong. He's provided a detailed
description of his assumptions and deductions, so go to it.)
I doubt Bruno has made an error of deduction. But I find his interpretation that
identifies "provable" = "belief" dubious.
I do not identify "believable" with "provable by PA". I say only that if we assume
computationalism, then the result will apply to all rational believer in PA. They can
be quite different from PA, like ZF. the results apply as long as the machine is
consistent, and believes in the axioms of PA. It would not work on you, only in the
case your arithmetical beliefs are inconsistent with the theorems of PA. So, to make
your remark here relevant, you should give us a theorem of PA that you disbelief.
That every number has a unique successor.
Then you disbelieve already in the axiom of RA, and I have no clue what you
mean by number.
Sure you do. You learned about numbers before you ever heard of infinity. Suppose, as
people on this list have sometimes proposed, that we and the world we perceive is a
digital simulation in a computer vastly more powerful than the ones we've built. Suppose
this computer is 1e500 bit machine. Then there would be no number representable in the
computer bigger than 1e500. What difference would that make?
The problem is that in physics and computer science we do postulate that every natural
numbers have a successor.
And we postulate real numbers, complex numbers, quaternions, octonions, sets, continua,
and the rights of man. We can postulate whatever we like to construct a theory.
And even the Plationist idea that arithmetic exists in the sense necessary to
instantiate the world we see is doubtful.
There is no world. But if you agree that 2+2=4 independently of time, mass, space
(which is the natural understanding of math proposition), and if you agree or assume
computationalism, then some numbers will behave like if they believe in worlds, and
will develop physics, etc.
What does it mean for a number to believe something? I earlier said you identified
"believe" with "provable" but you denied that - although it seems to me you use it that
way.
I say that a machine believes p if the machine asserts p.
What does it mean for the machine to assert p? Just to print out a number? Or must it be
an equation or an inequality?
Then, as I want machine trying to understand themselves, I limit myself to ideally
correct (with respect to the arithmetical reality) machine which believes already to PA
axioms and to the validity of the usual inference rules.
Isn't that a requirement that the machine prove the assertion from PA? Does it actually
have to go thru asserting the steps of the proof, or is it enough that the assertion be
provable?
You can say that they are zombies, assuming some magic matter, but it is more
interesting to look at the physics they develop, and compare with our inferred physics.
That some things may happen at random isn't.
Now that /is/ an extraordinary claim, in my opinion. What would be a suitable
underlying means by which the universe might operate, that it makes things happen at
random? I can imagine things that might appear random to us, but are actually the
result of deterministic forces operating on scales we can't probe - e.g. string
vibrations. But genuinely random - that seems to me to require extraordinary
evidence. So far we only have evidence for "apparently random" as far as I know.
Some backup for the above two extraordinary claims would be welcome.
(1) that brains aren't Turing emulable at any level
You seem to be saying that to assert a claim is extraordinary is equivalent to
asserting it's negation. So if I say claiming there's a teapot orbiting Jupiter is
extraordinary, you'll ask that I back up that extraordinary assertion? What happened
to agnosticism? I don't think I made any extraordinary claim; unless mere doubt of
Platonism has become extraordinary.
It is better to use "realism" instead of Platonism, which is related, but different.
Arithmetical realism is believed by all scientists, and almost all philosophers.
Platonism is a different matter, as it implies something like "no more than the
numbers, or that the world of ideas". Arithmetical realism is in the assumption (in
Church thesis notably). Platonism is among the counter-intuitive conclusions.
(2) that there is a mechanism by which the universe might generate truly, rather
than apparently random events.
I'm not sure it's possible to have a mechanism that generates truly random events. I
think that's like asking for an algorithm that produces truly random numbers. -
although it may turn on the meaning of "mechanism".
Well, if you enlarge mechanism by replacing computable function by function, then, by
Cantor, you get 2^aleph_zero genuine random functions, but there is no evidence that
this exists in nature
There's no evidence in nature that there are infinitely many natural numbers
either.
But I do not postulate that nature is the fundamental reality. I prove the contrary, in
the computationalist frame.
Which leaves the question whether it is a reductio of computationalism.
It looks like you want me to believe that ~comp is consistent. But I do believe this at
the start. In fact if comp is consistent,then that consistency is not provable in the
comp theory.
My goal is to explain (to myself, notably) where consciousness, or the belief in a
reality, comes from. I also show that postulating a physical reality does not work for
this, unless you add in the primitive matter some non Turing emulable functions, or some
non FPI retrievable infinities, which both would contradict comp + occam.
Suppose we added "primitive matter" (whatever that is). It would mean the doctor would
use some matter in his substitution. But I don't see that it would change the inferences
about ideal machines, what they would assert, and what physics they would predict. In
that case it seems your conclusions would all still apply in any simulated world (such as
the computer games my son creates).
Brent
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