Hi Kim,

I'm afraid I probably don't understand your question. It seems to me  
you are using in an informal context some  terms like if they have  
precise meaning.
I will make a try, so as to be clearer on the point raised by Günther  
and Abram.

On 26 Dec 2008, at 22:49, Kim Jones wrote:

> On 27/12/2008, at 7:56 AM, Bruno Marchal wrote:
>> nd sometimes, even that is not enough, and you have to climb on the
>> higher infinities. I think Kim was asking for an example of well-
>> defined notions which are not effective. The existence of such non
>> effective objects is not obvious at all for non mathematicians.
>> Your interpretation was correct too given that Kim question was
>> ambiguous.
> I wanted to know if you can have:
> 1. A system with a defined set of rules but no definite description
> (an electron?)

Perhaps with a bit of imagination I can give sense to this. It raises  
an important question: can we simulate the observable behavior of an  
electron with a classical computer? I think that the answer is NO. For  
example if the electron is in a superposition state UP+DOWN, and you  
observe it with the {UP, DOWN} obervable, you will see it UP or DOWN  
with a truly random probability 1/2. It can be proved that such a  
truly random process cannot be simulated on a classical computer.
What you can simulate with a classical computer is the coupled system  
PHYSICIST+ELECTRON. In that case, the result of the simulation is the  
MW-situation PHYSICIST UP + PHYSICIST DOWN, and the probability 1/2  
comes from the fact that the physicist has been duplicated. So the  
probability is a first person point of view.

> or
> 2. A system with a definite description but no rules governing it   
> (???)

Theoretical computer science is born dues to the complexity of  
defining what "definite description", and "rules" can mean. Without  
delving more in computer science I can only point to informal example.

It can be argued that the set of true propositions in Arithmetic admit  
a definite description. For example we can defined it easily in naïve  
set theory, and we can have a pretty idea of what that set consists  
in. But we cannot generate such a set with a computer, and it that  
sense there can be no rule governing it. Most set of numbers are of  
that type. They escape the computable realm. For example the Universal  
dovetailer will generate only a tiny (but very important) part of  
arithmetical truth, indeed, with Church thesis, it can be said it  
generates the whole of the computable part of arithmetic. In math  
there are many things that we can define and talk about, but that we  
cannot compute. This makes the difference between constructive or  
intuitionist mathematics and classical mathematics.

> Based on Abram's original distinction, as a way of separating the two
> types of machine that Günther specified.

I would be pleased if someone can explain this link. Let me quote  
Stathis Papaioannou:

> From the SEP article:
> "Turing did not show that his machines can solve any problem that can
> be solved "by instructions, explicitly stated rules, or procedures",
> nor did he prove that the universal Turing machine "can compute any
> function that any computer, with any architecture, can compute". He
> proved that his universal machine can compute any function that any
> Turing machine can compute; and he put forward, and advanced
> philosophical arguments in support of, the thesis here called Turing's
> thesis. But a thesis concerning the extent of effective methods --
> which is to say, concerning the extent of procedures of a certain sort
> that a human being unaided by machinery is capable of carrying out --
> carries no implication concerning the extent of the procedures that
> machines are capable of carrying out, even machines acting in
> accordance with 'explicitly stated rules'. For among a machine's
> repertoire of atomic operations there may be those that no human being
> unaided by machinery can perform."
> Is this just being pedantic in trying to stick to what the great man
> actually said? What is an example of a possible operation a machine
> could perform that a human, digital computer or Turing machine would
> be unable to perform?

I probably mention such an example above: to generate a truly random  
event. And the old Copenhagen QM, which admits a reduction of the wave  
packet,  could have inspired for a time the believe that nature can do  
that. But after Einstein-Bohr-Podolski (EPR) paper, even Bohr realised  
that the collapse of the wave cannot be a "mechanical" phenomenon, and  
most Copenhagians will have to say that the quantum wave function  
describe knowledge state, and not nature or physical systems. With  
Everett everything becomes clearer: nature does not collapse the wave,  
and thus, does not provide any examples of a machine generating truly  
random events. Randomness appears in the mind of the multiplied  
observers, exactly like in the mechanical self-duplication experience.  
That is why Everett and comp fits so well together.

Of course Everett could be wrong, and comp could be wrong, and  
naturalism could be right: but it is up to the naturalist to say what  
is the machine's atomic operation that a Turing machine cannot  
complete. If it is the generation of a truly random event, and if this  
is based on the wave collapse, then I can understand (but you will  
have to solve all the problem raised by the collapse, you will have to  
abandon the theory of relativity like Bohm and Bell suggested, etc.).  
Or you say like Searle that "only special machine can think:  
biological brain". In that case we have to suppose something very  
special about the brain: it generates consciousness. But this is just  
a blocking argument: it could be interesting only if it points on  
something special in the brain that a digital machine cannot imitate.  
Without such specification it is just equivalent with the *assumption*  
that the brain is not a digital machine.

To escape the consequence of comp, a naturalist has to specify either  
a non causal mechanism (like generation of truly random events), or  
actual infinities, like a neuron with an analog infinite information  
state. But non causal events and actual infinities are not the kind of  
things that naturalist find appealing. I really know only Penrose for  
suggesting the existence of such non computable events in nature.
To escape comp, it is thus more honest to invoke supernatural thing,  
like in some (non platonist) "religion".

I am quite open to the idea that comp could be wrong, and I respect  
all those who believes so, but I will not hide that I do find the  
arguments based on nature against comp quite unconvincing if not being  
just dishonest hand waving directed by wishful thinking or taste.

Except the very speculative and quasi-abandoned quantum wave collapse,  
nothing in nature points on any atomic machine operation which would  
be non-Turing emulable. Needless to say, collapse of wave is not  
really in the spirit of the everything-list type of TOE, but that is  
not an argument, of course.



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