On 26 Dec 2008, at 20:24, Abram Demski wrote:
>
> Bruno,
>
> In one sense those examples are things for which (finite) reasoning
> fails, but I would still say that they are governed by (finite) rules
> and possess a (finite) description--
Yes but we have to bet we share the standard interpretation of it. And
the notion of finiteness itself cannot de described in a finite way.
Then things get more complex and need higher infinities to be described.
> the problem is "merely" that it
> takes infinite amounts of time to derive the consequences of those
> rules/descriptions.
And 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. The real question is what does this have to do with
Günther's proposal that we should distinguish natural or physical
machine from the digital machine, unless it is followed by an
explanation why such machines should say no to the doctor.
I mean when you said:
<<Right, that can't be done-- maybe such a system exists, but if so then
our rationality basically fails to apply to it. So as Gunther says,
the broader version of mechanism "can be granted by every
scientifically minded person".>>
To escape or criticize the consequences of the UDA, you have to say
explicitly in what sense those natural machines are not Turing
emulable, or why they have to say no to the doctor.
I have nothing against non-computationalism, but I am not convinced by
any who points on nature. Nature, it seems to me, behave as if it has
already bet on comp more than one times. Our cells bet on self-
replication all the times, and they substitute their functional
components more quickly than current machines. And the nervous systems
appears when chatty amoebas discovered the cables. Universality is
cheap.
The "scientifically minded person" of today take for granted both
mechanism and materialism, I'm afraid. I point on the difficulties and
the general shape of the solution. I warn against the risk of
eliminating the person for "saving" the MAT. (In Europa and Africa we
have idea about what that could mean).
The universal dovetailer dovetails on the reals and the oracles too,
so, to escape comp with "hypercomp" sort of weakening of mechanism
does not really work, most of the self-reference logic remains stable
on it. Yet, you can invoke some tools for escaping comp, but it is
highly difficult to do that and being confident in the consistency of
the theory. This is like constructing a magical nature, just to say no
to the doctor.
And then, is it not wonderful? The theory of everything can assume
just the positive integers with succession, addition and
multiplication. It does not eliminate the persons and it justifies
the logical evolution of the physical laws so that we can measure our
degree of "mechanism", in a sense. With Everett QM, it seems to me
that nature confirms again the "disturbing?" consequence of Mechanism,
which is that propensity to self-multiply.
Bruno
>
>
> --Abram
>
> On Fri, Dec 26, 2008 at 11:49 AM, Bruno Marchal <marchal.domain.name.hidden>
> wrote:
>>
>>
>> On 25 Dec 2008, at 22:27, Kim Jones wrote:
>>
>>>
>>>
>>> On 26/12/2008, at 5:23 AM, Bruno Marchal wrote:
>>>
>>>>
>>>> On 25 Dec 2008, at 08:05, Abram Demski wrote:
>>>>
>>>>>
>>>>> Bruno,
>>>>>
>>>>> I agree with Gunther about the two types of machine. The broader
>>>>> machine is any system that can be logically described-- a system
>>>>> that
>>>>> is governed by rules and has a definite description.
>>>>
>>>> Then Church thesis entails it is not broader, unless you mean that
>>>> the rules are not effective.
>>>>
>>>>
>>>>
>>>
>>> I might be missing something here, but somebody please give an
>>> example
>>> of a system that is NOT governed by rules and possesses NO definite
>>> description.
>>
>> Arithmetical truth. That is, the set of all true sentences of
>> elementary arithmetic.
>> The set of Gödel number, or description of never stopping programs or
>> machines.
>> The set of descriptions (in any universal language) of any non
>> trivial
>> machines.
>> At the first order level: all the arithmetical hypostases.
>> Sigma_2 truth, Sigma_3 truth, Sigma_4 truth, Sigma_5 truth, Sigma_6
>> truth, etc. (the union of which gives arithmetical truth)
>> Analytical truth (far beyond arithmetical truth).
>> Mathematical Truth (if that exists).
>>
>> Kim, all those exemples provide well defined set of objects, (except
>> the last one) but there is no way to generate them by any machine,
>> nor
>> can we axiomatize them in any effective way. No effective complete
>> "Theory" for any of them.
>>
>> Alas, there is a need of some math to prove this. If you are patient,
>> when we get the seven step of UDA, I will have to give you at least a
>> tool (diagonalization) capable of easily showing the existence and
>> the
>> non effectivity of those non mechanical mathematical realities.
>>
>> It is needed to be more precise on "effectivity" to discover the non-
>> effectivity.
>> Mechanism is not a reductionism, (as I explain often to John Mikes)
>> because Universal machines behaviors depends on those non effective
>> things. Creation and life appears on the border between the
>> computable
>> and the non computable. It is similar to the border of the Mandelbrot
>> set.
>>
>> Bruno
>>
>> http://iridia.ulb.ac.be/~marchal/
>>
>>
>>
>>
>>>
>>
>
>
>
> --
> Abram Demski
> Public address: abram-demski.domain.name.hidden
> Public archive: http://groups.google.com/group/abram-demski
> Private address: abramdemski.domain.name.hidden
>
> >
http://iridia.ulb.ac.be/~marchal/
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Received on Fri Dec 26 2008 - 15:56:54 PST