On 24 Feb 2015, at 17:47, meekerdb wrote:
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]>
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.
The awe and glee of the children when they have the number ha-ha is
when they realize that they can add one to one as many times as they
want.
But the 1p come from infinity, and is actually surprised by the
number, the finiteness. Infinity is an old pal of the 1p. I think.
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.
I guess you mean 10e500 bit machine. (1e500 = 1).
Then there would be no number representable in the computer bigger
than 1e500.
?
I can represent much bigger number with much less than a megabit. You
mean that we could not described the number in extension in that
machine.
Even with no so much memory we can represent very big number, like I
illustrated with the diagonal some years ago.
What difference would that make?
It depends on your substitution level.
Either we are in the comp normal histories, in which case the logic of
what we see when we look below our substitution level is given, say,
by Z1*. We can test that.
If the test shows that "nature" violates Z1* (and the other variants)
then we can conclude that comp is wrong, or we belong to a "perverse"
simulation made from the normal worlds. This implies it is
intentional, as those running the emulation needs to constantly verify
that we don't find the mistake. It is a form of lies, manipulation and
it has some cost. If our descendent simulate us, it will be easier to
let us find the normal laws, and then we will be as much in the
simulation, than in the normal world, by the arithmetical FPI. In that
sense, we are already at all level at once.
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.
That is wrong. We cannot postulate that sqrt(2) is a rational numbers,
and that all length are commensurable. We can't decide that the
equation 2a^2 = b^2 has no trivial solutions. We really discover those
things, that you can seen as capital subroutine to figure out
scientific problems in math, economy, physics, biology, etc.
The point is to postulate as few things as possible, for explaining as
much as possible, including the difficulties of consciousness and the
appearance of matter.
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?
That is it. But the "number" can be still decoded in whatever sign is
available from the plausible universal numbers nearby. For example a
cutllefish can send that numbers on its skin, which becomes like a
giant screen, which is used for camouflage, and to impress the crabs.
And to mate.
I mean it is the output of some universal machine, and in our case,
they talk the language of arithmetic.
I use Dennett intentional stance for machine, to avoid unnecessary,
and confusing, metaphysical baggage.
Or must it be an equation or an inequality?
In my head, it is x belongs to w_y. (the yth recursively enumerable set)
But I will not trouble you with the phi_i and w_i today.
It is just the output of a computer, and in our case, of a computer
"knowing" classical predicate logic, and its own functioning (although
in a 3p way, that is why we will be interested by the intensional
variant offered by incompleteness).
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?
Not necessarily. The machine can be mute, and you just ask her a
question, and then she stops on an answer, or not.
Does it actually have to go thru asserting the steps of the proof,
or is it enough that the assertion be provable?
For our theological concern, the study of the difference between truth
and provable give already the needed information to extract the
physical laws.
Proof theory is not relevant, at this stage, but provability explains
why proof and machine theory are relevant at some stage.
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.
That is the point (modulo the conspiracy of our descendants)
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).
It works on all simulations which respect the "winning" universal
machine, that is the one with the correct measure (which might not
exist, but has to exist with computationalism). In those case the
physics observed is the same as the physics derived from self-reference.
But in normal emulation, some "bad" machine can still delude machines,
but only by an infinite work, if they want the delusion lasting
infinity. I don't find that plausible, but that is logically
conceivable, and locally that happens all the time in real life.
Truth is what remains when the liars and the parrots vanish, if
ever, ... because universal machines can make local win by lying and
parroting.
No worry, there are no evidence that our reality disobeys Z1* or X1*.
On the contrary Everett QM, and quantum logic, assess
computationalism, like Gödel's theorem protects Church's thesis.
In a sense, computationalism introduce a new invariant in physics. The
laws of physics are "universal-machine" independent. It is ontological-
theory independent. Realities proceed through universal agreement, yet
relative to each others.
Bruno
Brent
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