On 28 May 2013, at 17:52, John Clark wrote:
On Mon, May 27, 2013 Russell Standish <li...@hpcoders.com.au> wrote:
> John - you are being disingenuous here. Bruno has explained this
[Bp&p] at
considerable length.
If even mighty Google doesn't know what Bp&p is then I'm not
embarrassed in not knowing either.
You might search on "Theatetus" instead, as Russell suggested.
It is the older theory of knowledge. It is the idea that knowledge is
subjectively the same as belief, except that, *by definition* the
belief is correct.
The very old Wittgenstein, the one who wrote "On Certainty",
eventually got it, and realize implicitly somehow he was wrong until
there.
The greek used it to develop the dream argument. You can find similar
argument in chinese and indian philosophies.
Now, by Gödel's theorem, provability (Gödel's beweisbar arithmetic
predicate Bew, which is sigma_1 complete and thus represent a
provability predicate enough rich to emulate all Turing machines, i.e.
to be universal in the Church-Turing-Post sense) does NOT obey
Bew('p') -> p, with p an arbitrary arithmetical sentence. I write Bp -
> p for the longer expression (and later this is amde precise by
theorem on the modal logics G and G*)
If PA, or any correct Löbian machine, would prove all Bp -> p, this
would entail they would prove Bf -> f, with f the constant
propositional 'false'), and so they would prove ~Bf, and they would
contradict Gödel's second incompleteness theorem.
But this means that the logical expressions Bew('p'), and Bew('p') &
p will obeys different logics, and it can be shown that for the Löbian
machines (and even more general class of entities) such logic obeys
the classical theory of knowledge, axiomatized by the modal logic S4.
Indeed they are entirely formalized by S4 + K(K(p->Kp)->p)->p. K for
"I know".
So, incompleteness makes the definition of Theatetus working well for
the case study of a simple notion of knowledge for the ideally correct
machines.
There are many interesting theorem, like the fact that the knower
cannot attribute a name to itself, that it feels like not being a
machine, and is somehow right on that, that he is a fixed point in a
relation between believe and truth, etc.
John,
UDA is supposed to explain that physics is in your head,
and
AUDA is supposed to explain that physics (and much more) is in the
head of *all* universal machine/number.
(the Lôbian one are just more chatty about all this).
It makes sense for people who, in this list, try to get a theory of
everything, explaining, without begging the question, from where
matter and consciousness comes from, and how they are related.
What I argue is that if we assume we can survive with a physical
digital brain, then physics get reduced to a relative measure problem
on all computations, or Turing emulable processes, as defined in
arithmetic.
I use arithmetic but any first order logical specification of a
universal system would work.
This will be translated by a refinement of Bp & p, in fact by Bp & p &
Dt. With p restricted to the sigma_1 proposition (UD-accessible). Dt =
~Bf = self-consistency. This will again give the same extensional view
of arithmetic, but a quite different intensional, or modal, one. This
is too long to justify here. But this works, and give an arithmetical
quantization from which you can see the shadow of the "quantum linear
symmetrical core of physical reality". Linearity should ensure the
existence of the first person plural deep histories.
Actually, arithmetical quantization appear with the Bp & p, Bp & Dt,
and Bp & p & Dt, (all p sigma_1) making possible many nuances.
Bruno
John K Clark
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