On 19 Feb 2012, at 06:16, John Clark wrote:

On Sat, Feb 18, 2012 at 5:53 AM, Bruno Marchal <marc...@ulb.ac.be> wrote:

> That solipsism. I don't see why you believe that people have to believe in comp to avoid solipsism.

Everybody, when not arguing philosophy on the internet, believes that physical actions effect consciousness and consciousness effects physical actions.

When you work on the mind body problem, you cannot take any of those expressions for granted. It would just mean that you are not interested, or perhaps aware of, the mind body problem.

In particular it is important to conceive that comp might be false. As a scientist, we cannot know that. And then there is the problem of the level of substitution, where two different form of computationalism can be quite opposed (very high level versus very low level).

Everybody also believes that a specific sort of physical action, intelligent behavior, indicates consciousness. If you accept those 2 things, and everybody this side of a loony bin not only accepts it they use it every hour of their waking life, then the Turing Test and everything else you call "comp" can be derived from that. By the way, I say "waking life" because when people are sleeping they do not behave intelligently so I assume they are not conscious.

Intelligent behavior and consciousness might be related, but should not be equated, because those are different things. Note that the theory of dreams by Maury, asserting that we are conscious of the dream at the recollection we do when awaken has been debunked by the work of Jouvet, Laberge, Dement, and that it is generally accepted that we are conscious during the dreams. The same for some comatose state. That shows that consciousness can be independent of macro-behavior. And for the micro-behavior it will depend on the choice of a substitution level.

Actually I argue that comp, when taken seriously enough, has to reduce physics to the 'theology of numbers', like biochemistry can be said to have been reduced to quantum mechanics. It makes comp refutable, by comparing the physics derived from machine's theology with the physics inferred from empirical observations.

Sentences about machines can be arithmetized (Gödel, Feferman, Löb, ... Solovay). Machines' theology is just the true sentences. Machine can prove a part, intuit a part, observe a part and infer a part of it.

> I find comp much more plausible than non-comp. I don't want at all defend non-comp, but my point is logical: we don't know, and probably cannot know, that comp is true, so it might be false.

I agree with that. Except for pure mathematics you can not know anything without doubt. I think.

I would say except for pure arithmetic. Beyond arithmetic you can already doubt.

> It is not logically impossible that we are alpha-machines, with alpha strictly bigger than omega.

If so then it is very odd indeed that we can not even deal with large but FINITE integers very well; even the smallest computer can operate with them far far better than we can.

It is a very good argument of plausibility of mechanism. One problem with this is that we can define what we means by finite, without using some prealable inuition of what is is. This is no problem for applying comp and numbers, but it is a problem for the mind-body problem, and it forces us to assume some axioms of arithmetic explicitly.

> if we are alpha-machine, we will not survive an omega-substitution.

It's also very odd that the real numbers were not intuitively obvious to everybody but instead were only discovered a few hundred years ago.

The real numbers are not that simple. They have properties which can depend on the theory used to handle them. They have simple topologies and logic, and are very useful, but there is not unanimity of what they are, and if they exist, or how. Classical math and intuitionist math diverge seriously on them. Comp clarify this by making their existence necessary in the epistemology and mandatory in the ontology. For my comp purpose, we can identify real numbers, subsets of N, or the set of total functions from N to N or or to {0, 1}.
Those are very big sets, which ontology and nature is debatable.

It's even stranger that non-computable numbers were only discovered by Turing in the 1930's

Emil Post discovered them in 1922. Others were close.

and we are not one bit better at actually pointing to one (even though nearly all real numbers are non computable) than digital computers.

We can point to many "non computable real number", called non computable function in "modern" computability theory. The function sending i on 0 if phi_i(i) converges and i on 1 if phi_i(i) does not converge is not computable, for any enumeration phi_i of the partial computable functions. There are many others, and they are organized into complexity classes, or degree of insolubility. basically most functions used to describe the behavior of universal numbers generates non computable functions (non computable real number, with the old nomenclature of Turing). The predicate total or strictly partial is more complex 'non computable number' than the one above, for example.
 There is the famous Chaitin number, etc.

> My point is not that comp is false, but that we cannot know if it is true.

My point is that we must assume its true to function.

Comp is an hypothesis concerning consciousness. Why should we must to assume it. We can assume it, but we cannot impose it to someone else. As scientist we have to keep in mind that it is an assumption.

Atheist and materialist often use comp (even a stronger version) like if it solves the mind-body problem. The least I show (I hope) is that comp can only help to formulate the problem. In particular I argue that comp reduces the mind-body problem into a appearance-of-body problem in arithmetic. In a nutshell, comp seems to be incompatible with an already weak form of materialism (the belief in an ontological primitive matter).

> So you reduce God to the Christian's conception of it.

Yes I suppose I have. Christians and other religious franchises should own the word "God" as they think its so important and use it so much. So when I want to talk about that I will use the word "God" but when I want to talk about something else, like truth or numbers or Millard Fillmore, I will use another word. I give them "God", there are plenty of other words I can use when I want to talk about something very important but is not a omnipotent being who created the universe.

The problem is that if we withdraw the research of God from the academy, some other science will begave as if it was a theology, and this without saying, which is worth. Today many scientist perverts the very idea of science by daring to make unrigorous crazy theological extrapolation from their theories, be them theists or atheists. Even for the layman, there is a general belief that modern science has solved everything, when, in my opinion, it has not yet really address the fundamental questions. It is still taboo, like if it was a shame to confess ignorance, the preliminary step to formulate a problem.

> I use the term in the sense used by the scientists before politics stole the concept and develop the fear selling. I gave you the axiom of God: It is the one responsible for the existence of anything



> we cannot prove its existence (so it asks for an act of faith)--- god's transcendence.

That impossible to prove His existence bullshit is just stuck on and plays no part in the core concept, it need not be that way. If God is omnipotent he could certainly make his existence obvious to even the stupidest most unobservant person if he wanted, in fact I think He would need to expend a considerable part of that omnipotence to hide himself from us.

The God of the correct machine (arithmetical truth) is not omniscient, and is omnipotent only in a trivial way. Now, with comp, there are arguably three God, the usual ONE, the divine intellect, and the universal soul, or Inner God. There are complex tradeof abilities among them. The divine intellect already overwhelmed the ONE, and is overwhelmed itself by the Soul. There is a sort of tension between them, which figures the arithmetical reason why souls falls (from heaven to earth), and how they can come back (that's a mechanical process, but still not an algorithmic one, because the machines cannot find a name for that algorithm, without falling again).

When you say: "If God is omnipotent he could certainly make his existence obvious to even the stupidest most unobservant person if he wanted", you are still using a quite "official" version of it. If you are OK with defining God by what is responsible for the existence of anything, and if you agree with comp, then arithmetical truth, the set of all true sentences about machine and machines is a sort of candidate for the job. For this one it makes no sense to say he want to be known by us, except perhaps to explain why we teach it to the kids, but they understand it well: it is already living in their head somehow. No machine can escape it, despite the infinite layers of lies which can make it losing its transparency in almost all deep and rich computations.

He should be bloody obvious. However I can certainly see why certain humans would push the idea that His nature can't be found by reason and that faith, believing in something for no good reason, is a wonderful virtue.

It is deadly fatal error in the long run. I think.

These religious mountebanks have a really nice little swindle going, they turn the inability to prove one word of what they say into a advantage.

That's is deeper than you thought. But I agree it is also the reason of the theological trap, which leads to crap religion. That's a reason more to be serious about it, even if the correct theology appears negative (like Neoplatonist theology): God is not this, nor that, etc.

Talk about turning lemons into lemonade!


> we cannot give it a "name"

I don't know what you mean by this, humans have named all the thousands of Gods they have invented over the centuries.

Which gives the thousand human miseries. That is not a coincidence. It is a bit like believing that the set of all sets is a set. A comp *legend* is that all possible creature will met someday somewhere. All from bacteria to gods, of all universes, or all multiverses. Absolutely all except one.

> we cannot not believe in it

I think I do a pretty good job in not believing in it.

Are you back to the Christian conception of God?
If you agree that "God" is the reason of existence, then what you say is equivalent to saying we cannot understand this, and you agree already with an axiom believed by many religious people., and meta- explainable in the comp theory, by Tarski-like non definability theorems.

> With comp God can be arithmetical truth

Then just call it what it is, arithmetic.

Arithmetic is too much often confused with the arithmetical theorems of some rich theory, like PA or ZF.

The word "God" adds nothing and just invites confusion and misinterpretation.

It helps to translate Plotinus in arithmetically based concepts. This shows at the least Plotinus and neoplatonist to be consistent, but it makes it refutable too, because that theology contains physics.

It has vastly too much baggage so it's time for "God" to be retired and join other obsolete words like "methinks","cozen","fardel", "huggermugger", "zounds" and "typewriter".

Then we will never been get rid of the 'too much baggage'. Theology will remain in the hand of the manipulators and fear sellers.

> If you believe that the Christians have the right conception of God, then you are a sort of Christian.

Hey, let's not get nasty.

OK. Sorry.

The Christians are not the worst, though. Thanks to many of them, a big heritage of Plato, and the best of Aristotle, has been transmitted. A big part of science comes from the refutation of Aristotle theories. In science it is not a problem to be wrong. But letting theology in the hand of the 'politics' prevents it to improve, and it transforms science itself into a fake theology. This rotten the whole human science, notably in making people believe that others can think for them. Universal machines already know better, I would say.



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