On 15 May 2014, at 22:22, Craig Weinberg wrote:
On Thursday, May 15, 2014 2:19:01 PM UTC-4, Bruno Marchal wrote:
On 15 May 2014, at 14:40, Craig Weinberg wrote:
On Wednesday, May 14, 2014 6:34:55 PM UTC-4, Bruno Marchal wrote:
On 14 May 2014, at 03:45, Craig Weinberg wrote:
I'm showing that authenticity can be empirically demonstrated, and
that the failure of logic to detect the significance of
authenticity can be empirically demonstrated, but that neither
authenticity or the failure of logic to detect it can be detected
within logic. At least Godel shows logic's incompleteness, but
that is just the beginning. What logic doesn't know about what
logic doesn't know I think dwarfs all of arithmetic truth.
Gödel has shown the completeness of first order logic, and this
means that what we prove in a theory written in such logic, will
be true in all interpretation of the theory, and what is true in
all interpretations, will be provable in the theory.
Then Gödel proved the incompleteness of *all* theories about
numbers and machines, with respect to a standard notion of truth.
This means that the truth about number and machines are above what
machines can prove, and thus what human can prove, locally, if we
assume computationalism.
But computationalism is a theory about numbers and machines, so we
cannot truthfully assume it.
no. It is a theory about your consciousness, and its relation with
possible brains. It becomes a theory about numbers, but that is the
result of a non trivial reasoning, and the acceptation of the
classical theory of knowledge.
Does Wiles solution to Fermat's last theorem prove that humans can
use non-computational methods, in light of the negative solution to
Hilbert's 10th problem?
No.
Why not? I doubt I'll understand your answer but I might be able to
get someone else to explain why he thinks you're wrong.
Well, you can invite him to make his point. The problem is that
somehow, in some sense, humans can use non computational rules, like
heuristics and metaheuristic, which are non algorithm. But that is
also a big chapter in AI, and machines can also use heuristic without
problem, and it change nothing about the truth or falsity of comp. In
fact the first person "[]p & p" is also a non algorithmic entity. So,
use à-la Penrose Gödelian argument are usually confusion between []p
and []p & p, or []p in G and []p in G*.
Penrose thinks that it does:
"The inescapable conclusion seems to be: Mathematicians are not
using a knowably sound calculation procedure in order to ascertain
mathematical truth. We deduce that mathematical understanding - the
means whereby mathematicians arrive at their conclusions with
respect to mathematical truth - cannot be reduced to blind
calculation!"
Good. That's when Penrose is correct. No machines at all can use a
knowably sound procedure to ascertain a mathematical truth.
By adding "knowably" Penrose corrected an earlier statement. But
then he does not realize that now, his argument is in favor of
mechanism, because it attribute to humans, what computer science
already attributes to machine.
If computer science attributes it to machines (and I would say that
it is only some computer scientists who do so)
because some are not aware of the difference between []p & p and []p.
then it cannot use a knowably sound procedure to do that, therefore
it is a belief rather than a correct attribution.
Yes. you even need an act of faith. I never defend the "truth" of
comp. It is a belief like everywhere in science when we apply it to a
reality.
If we allow mechanism to be true by faith, I don't see how any
argument within mechanism can be used to prove that mechanism cannot
be disproved.
The point is that mechanism can be disproved.
The arguments against Penrose seem to me pure unscientific bigotry:
"Theorems of the Gödel and Turing kind are not at odds with the
computationalist vision, but with a kind of grandiose self-
confidence that human thought has some kind of magical quality
which resists rational description. The picture of the human mind
sketched by the computationalist thesis accepts the limitations
placed on us by Gödel, and predicts that human abilities are
limited by computational restrictions of the kind that Penrose and
others find so unacceptable." - Geoffrey LaForte
Well, if you have evidence that we don't have those limitations,
please give them.
That's what I'm giving. I saw someone's exhibit at the consciousness
convention a few weeks ago which included a musical translation of
Wiles proof - a proof which he says would not be possible for a
computer to produce, given the negative answer of Hilbert's 10th
problem.
Those are not related.
Are you able to solve and decide all diophantine equations?
I can't, but Wiles proves that humanity as a whole might.
But all machines as a whole might as well. No need of magical carbon,
a priori.
He seems to be saying "I don't like it when people imagine that
being human can ever be an advantage over being a machine. Machines
must be equal or superior to humans because of the thesis that I
like."
Being a machine is an advantage, for reproduction and use of
information redundancies. Instead of terraforming the neighborhoods
we can adapt ourselves in much more ways. We have more clothes, and
ultimately we know where they come from, and where we return.
You're saying that we are identical to machines on one hand but that
if we are machines we will be able to be and do things that we could
not do now. That says to me that you are 1) intuiting properties of
non-machines that are not discoverable by math, and 2) attributing
those properties to us because it is natural to assume that humans
are not machines.
We do it now at the molecular level, but betting on the fact that we
are some machine, at some not to low level, makes us possible to
explore the universe more easily.
Universal machine are always unsatisfied, and are born to evolve.
There is a transfinite of path possible.
But there are a lot of humans who seem quite satisfied. They
actively resist dissatisfaction and protect their beliefs, true or
not.
Good for them. I guess they don't look inward or are not interested
in the search of truth.
Then either they aren't universal machines, or it doesn't mean
anything to say that universal machines are always unsatisfied.
Well, even human are used sometimes for their non universal ability.
And Gôdel completeness is what machine discover themselves quickly,
they can justify it rationally.
Yet some of what they justify is not merely justified within their
own experience or belief, but veridically in intersubjective
experience over many lifetimes.
That too, from passing from the arithmetical []p (and []p & <>p) to
the non arithmetical []p & p (and []p & <>p & p), with p sigma_1.
I almost only translated what you said in arithmetical terms, and it
works very well, as this entials your insitence that sense is not
formalizable in arithmetic. (It also refute your statement that this
fact refutes comp).
To me, what you're saying sounds like "I figured out that what you
are saying is wrong." but then not explaining it.
I explain it. You makes words to defend the idea that you are not a
machine, and I explain that I am not convince this refute comp,
because the machines already do similar sequence of words. That
refutes your proof, simply. And indeed you are just showing that you
have a first person notion, and that is indeed not a machine, all
machines know that already.
Bruno
Craig
Bruno
Craig
Bruno
http://iridia.ulb.ac.be/~marchal/
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