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] atconsiderable length.If even mighty Google doesn't know what Bp&p is then I'm notembarrassed 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

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