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.
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.
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.
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. Are you able to solve and decide all diophantine
equations?
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.
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.
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).
Bruno
Craig
Bruno
http://iridia.ulb.ac.be/~marchal/
--
You received this message because you are subscribed to the Google
Groups "Everything List" group.
To unsubscribe from this group and stop receiving emails from it,
send an email to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
http://iridia.ulb.ac.be/~marchal/
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
