On 13 Oct 2014, at 02:58, John Clark wrote:
>For your information
I like information because Information is computable.
Not all information is computable. If (a_i) =
0000001000110000101011000011100010010001101100011101100001101000...
with a_i = 1 if the ith programs (without input) stop, and 0 if not.
That the halting oracle information, and it is not computable.
>such "non-computable" feature could be "primitive" matter,
Not only is there no evidence that non-computable process exist in
the physical world
There is in Copenhagen QM. I agree there no 3p non-computable process
in Everett QM.
But, wait, we don't know if there *is* a physical world. if you work
in the fundamental, that is a very big assumption, and I have
illustrated the difficulties we have when we bring that hypothesis
together with the assumption of computationalism in the cognitive
science.
Up to now, you avoid them by stucking yourself at the step 3 or the
UDA, without being able to tell us why, exc ept with insult, mockery,
and all that panoply which makes your stucking even less serious
looking.
there isn't even any reason to think it exists in Plato's abstract
Platonia. It's true that Turing prove that there are real numbers,
lots of them, that no computational process can even approximate,
but there is no reason to think anything else can either.
Wow! Are you suggesting we should abandon the (P v ~P) axioms? What
you say might make sense in intuitionist mathematics, where you can
assume all functions being continuous, or computable (Brouwer axioms).
But I see only application in engineering and self-development. It is
handled by the S4Grz(1) logics in the machine's theology. That moves
is the solipsist move.
Note also that we don't need Turing theorem to believe in the no-
computable. the simplest proof consists in showing that the computable
functions (from N to N) make a enumerable set, and that the set of all
functions makes a set which is non enumerable.
Then we cannot avoid the non recursiveley enumerable set, like the set
of computable *total* functions. Which is enumerable, but non
computably. Even with the help of the halting oracle (which is Pi_1
complete, the totality character is Pi_2 complete). The non-computable
is structured by hierarchies of degrees of unsolvability/non-
computability. By a theorem of Post, this is related to the
arithmetical hierarchy, and the number of alternating quantifier
defining a set from a recursive relation.
Bruno
John K Clark
--
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.
