On 07 Dec 2010, at 05:54, Rex Allen wrote:

On Mon, Nov 29, 2010 at 12:09 PM, Bruno Marchal <marc...@ulb.ac.be> wrote:
On 29 Nov 2010, at 05:15, Rex Allen wrote:
On Sat, Nov 27, 2010 at 4:06 PM, Jason Resch <jasonre...@gmail.com> wrote:
you admit then, that a computer which interprets bits the same way as a brain could be conscious? Isn't this mechanism? Or is your view more
the Buddhist idea that there is no thinker, only thought?

Right, my view is that there is no thinker, only thought.

Ah! The key point where we differ the most. Person is the key concept for
those who grasp mechanism and its consequences.
At least you don't eliminate consciousness, but you do eliminate persons.

Once one has abandoned libertarian free will, I don’t see that the
concept of “persons” matters much anyway.

Yes. That is what I fear a bit with your theory. It is an open problem with mechanism to distinguish persons, and if there are many persons or only one, but the concept is primordial, if only because "matter" is a person building thing, in some sense. And we get it by the fact that correct machine cannot see that Bp is equivalent with Bp & p.

Meillassoux’s solution uses Cantorian detotalization to counter
proposed resolutions to Hume’s “problem of induction” that involve
probabilistic logic depending upon a totality of cases.

Meillassoux's main point with this digression into Cantorian set
theory is that just as there can be no end to the process of set
formation and thus no such thing as the totality of all sets, there is
also no absolute totality of all possible cases.

Down the rabbit hole of infinite regress. Doesn’t seem promising, and
doesn’t seem necessary.

Meissaloux seems to ignore that the set of partial computable is closed for the Cantorian diagonalization. That is the key technical point which makes Church thesis possible and *digital* mechanism so powerful (and computer
science a science).

If one doesn’t accept that conscious experience is the result of
computable functions, then I don’t see that this is relevant.

We have to be careful/ With mechanism consciousness is not the result of a computation, or a computable function. It depends on all computations, and that dependence itself is not computable. Consciousness depends more on truth than computation. That is why the "p" appears in Bp & p. "B" is computable, but "p" alone is not. True("p") is not even definable.

So the Church-Turing thesis is basically that "everything computable
is computable by a Turing machine."


Further, since an algorithm is a finite string of characters from a
finite alphabet, the number of computable functions is countable.


You can’t use Cantorian diagonalization in this case because doing so
would require you to write a computable function that could generate a
list of the other computable functions, and then create it’s own
output for input “n” by sampling the nth output of the nth computable
function and adding 1 - with the problem being that because of the
halting problem you can never generate a list of *only* the computable

But you can do that. You can enumerate the programs. What the diagonalization will show is that although the programs are mechanically enumerable, the total program, capable of being controlled, are not. That is why the Universal dovetailer has to dovetail, it cannot know in advance which programs will stop or not. The diagonalization does not prove that the total programs are not ebumerable, but it shows that it is not mechanically enumerable. Universality makes you partially not controllable. It is a key for giving sense to the whole UD*, and AUDA.

Which means that Meillassoux’s idea won’t work *if* one assumes that
conscious experience is computable...since in that case there is, in
some sense, a set of possible conscious experiences.

That does not follow. Consciousness is distributed on the border of the UD*. That is not a computable structure, even with oracle.

But if one doesn’t start from the assumption that conscious experience
is computable, then your point has no bearing on Meillassoux’s
argument.  Right?

I don't know.

And, as an accidentalist, I don’t assume that conscious experience is

Are you saying that you necessarily say no the digitalist surgeon? Or that you could say "yes", or "no" accidentally, and what would that mean? Again, try to avoid the expression "conscious experience is computable", because, once you say yes to the doctor and reason a little bit, you should understand that not only consciousness is not computable, but it is even not descriptible in computational terms. Consciousness relies on truth, which is highly not computable. Note that if you are ready to smoke salvia, somehow you are already saying yes to a brain intrusive doctor, which happens to be a plant.

While some sequences of experience may have aspects that lend
themselves to being accurately described via computable functions, I
see no reason to accept that *all* aspects of *all* experiences are
thus describable.

Your intuition are coherent with the intuition of the universal machine looking inward. Consciousness is not amenable to anything we could describe in any finite or infinite ways.

So...an interesting argument, but I think not applicable.

I don't do any philosophy. I keep my opinion on such matter private. I just say that IF we are machine THEN physics emerges (entirely, curiously enough) from the numbers, and this in a sufficiently precise way that we can test it experimentally. That is all my point, except that I show also the beginning of the extraction (with AUDA).

If for some reason you believe that it is *impossible* that the brain functions like a digital machine at some level of its description, then the consequences of mechanism does indeed not apply to your "theory". But don't say that you reject the doctor's proposal because consciousness is not computable, because saying yes to the doctor is precisely what will make consciousness not computable indeed.

In AUDA, the full (first order) terrestrial intellect (qG) is PI_2 complete, making it highly not computable, not decidable, etc... The full (first order) *divine* intelligible hypostase (qG*) is PI_1 complete even with God (well Arithmetical Truth) as Oracle. It is beyond the whole arithmetical hierarchy. Recursion theory is really the theory of the ladder(s)of non computability, that's extends far beyond the computable, and what UDA shows is that universal machine's consciousness are confronted with *all that*.



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