On 21 Oct 2012, at 18:42, Jason Resch wrote:

On Sun, Oct 21, 2012 at 8:56 AM, Bruno Marchal <marc...@ulb.ac.be> wrote:
Hi John,

On 20 Oct 2012, at 23:16, John Mikes wrote:

especially in my identification as "responding to relations".
Now the "Self"? IT certainly refers to a more sophisticated level of thinking, more so than the average (animalic?) mind. - OR: we have no idea. What WE call 'Self-Ccness' is definitely a human attribute because WE identify it that way. I never talked to a cauliflower to clarify whether she feels like having a self? (In cauliflowerese, of course).

My feeling was first that all homeotherm animals have self- consciousness, as they have the ability to dream, easily realted to the ability to build a representation of one self. Then I have enlarged the spectrum up to some spiders and the octopi, just by reading a lot about them, looking video.

But this is just a personal appreciation. For the plant, let us say I know nothing, although I supect possible consciousness, related to different scalings.

The following theory seems to have consciousness, for different reason (the main one is that it is Turing Universal):

x + 0 = x
x + s(y) = s(x + y)

 x *0 = 0
 x*s(y) = x*y + x

But once you add the very powerful induction axioms: which say that if a property F is true for zero, and preserved by the successor operation, then it is true for all natural numbers. That is the infinity of axioms:

(F(0) & Ax(F(x) -> F(s(x))) -> AxF(x),

with F(x) being any formula in the arithmetical language (and thus defined with "0, s, +, *),

Then you get Löbianity, and this makes it as much conscious as you and me. Indeed, they got a rich theology about which they can develop maximal awareness, and even test it by comparing the physics retrievable by that theology, and the observation and inference on their most probable neighborhoods.

Löbianity is the treshold at which any new axiom added will create and enlarge the machine ignorance. It is the utimate modesty treshold.


Might there be still other axioms (which we are not aware of, or at least do not use) that could lead to even higher states of consciousness than we presently have?

Yes, there are interesting transfinities below and beyond omega_1^CK (the Kleene Church first non constructive ordinal). This has plausibly, with comp, some relation with possible consciousness states (but that is not obvious and depends on definitions).

Also, it isn't quite clear to me how something needs to be added to Turing universality to expand the capabilities of consciousness, if all consciousness is the result of computation.

Gosh! It is only recent, for me, that I even think that universal machines are already conscious. I thought Lôbianity was needed. But then it is basically the same as the consciousness-->self- consciousness type of consciousness "enrichment/delusion". In a sense, abstract universality is maximally conscious, maximally undeluded, or awake, somehow.

But Turing universality is cheap and concerns an ability to imitate other machine, not to understand them, so for provability and beliefs, and knowledge there are transfinite improvement and enlargement possible. We are not just conscious, we differentiate in developing beliefs, and get greater and greater view on truth.

It is like you might be near doing a kind of "Searle error" perhaps. A computation can emulate consciousness, but the computation is not conscious, only the person emulated by that computations, she can always progress infinitely (even if "restricted" on the search of arithmetical truth), develop more and more beliefs and knowledge. Particular universal machines will develop particular parts (even if transfinite) of arithmetical truth.

But G and G*, that is the modal logic of the provability of the Löbian machines, is a treshold. Despite growing transfinitely on her knowledge(s) of the arithmetical truth, as long as they remain self- referentially correct, they will obey to G and G*, for their theory of provability. If consistent, they will for ever been able to prove that they are consistent, for example, and they can prove that for themselves. The abstract theology is invariant despite the evolution of the arithmetical content of the B in Bp. PA and ZF have very different arithmetical beliefs, but both obeys to G and G*.

Consciousness, from the first person perspective is more related to "all computations" going through my states, than any particular computations. The living self is not a computer, it is a believer, supported by infinities of computer (by UDA).

I am happy you are open to the idea that universal machine are all conscious, it is then, the state of "you" before developing any more beliefs than those making you universal. Your first person indeterminacy, in that state, is all other possible machine/dreams. The Löbian machine knows that they are universal, and so knows the price to pay, for "staying consistent", like the possibility of crashing, in front of the unknown arithmetical truth.


You are welcome.



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