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From: Bruno Marchal <marchal.domain.name.hidden>

Date: Fri, 30 Jan 2004 12:48:46 +0100

Dear Stephen,

*>[SPK] No, Bruno, I like Comp, I like it a LOT! I just wish that it had a
*

*>support that was stronger than the one that you propose ...
*

[BM] Where do I give a support to comp? I don't remember. No doubt that I

am fascinated by its consequences, and that I appreciate the so deep

modesty and silence of the Wise Machine.

But the reason why I work on comp is just that it makes mathematical logic

a tool to proceed some fundamental question I'm interested in.

*>and that in addition to your 1 and 3-determinacy that there would be a way
*

*>to shift from the Dovetailer view (the "from the outside" view) to the
*

*>"inside" view such that some predictiveness would obtain when we are
*

*>trying to predict, say the dynamics of some physical system. Otherwise, I
*

*>claim, your theory is merely an excursion into computational Scholasticism.
*

The whole point of my work consists to show (thanks to math) that comp is

indeed popper falsifiable. It is just a matter of work and time to see if

the logic of observable proposition which has been derived from comp gives

a genuine quantum logic and ascribes the correct probability distribution

to the verifiable facts.

The weakness of the approach is that it leads to hard mathematical question.

*> I am sanguine about QM's "weirdness"! I see it as implying that there
*

*> is much more to "Existence" than what we can experience with our senses. ;-)
*

I agree with you. Now comp shows much more easily that it *must* be so. You

know Bohr said

that someone pretending to understand QM really does not understand

it. The same with comp, it can even be justified.

If a machine can believe something, it will be hard for her to believe in

comp and in its consequences, until she realizes that indeed if a machine

can believe something, it will be hard for her to believe in comp and in

its consequences, until she realizes that indeed if a machine can believe

something, it will be hard for her to believe in comp and in its

consequences until she realizes that indeed if .... (apology for this

infinite sentence).

*>[BM]
*

*> > comp =
*

*> > 1) there is level of description of me such that I cannot be
*

*> aware of functional digital substitution made at
*

*> > that level.
*

*>
*

*>[SPK]
*

*>
*

*> Here we differ as I do not believe that "digital substitution" is
*

*> possible, IF such is restricted to UTMs or equivalents.
*

No consistent machine can really "believe" that indeed. But this does not

mean a consistent machine will believe not-comp. The point is: are you

willing to accept it for the sake of the reasoning.

*> > 2) Church thesis
*

*>
*

*>[SPK]
*

*>
*

*> I have problems with Churches thesis because it, when taken to its
*

*> logical conclusion, explicitly requires that all of the world to be
*

*> enumerable and a priori specifiable. Peter Wegner, and others, have
*

*> argued persuasively, at least for me, that this is simply is not the case.
*

Church thesis entails that the partial (uncontrolable a priori) processes

are mechanically enumerable.

AND Church thesis entails that the total (controlable) processes are NOT

mechanically enumerable.

In each case we face either uncontrolability or non enumerability. It is

Church thesis which really

protects comp from reductionnism. That was the subject of one thesis I

propose in the seventies. Since then Judson Webb has written a deep book on

that point. (Webb 1980, ref in my thesis, url below).

See my everything-list posts "diagonalisation" for the proof of those facts.

*>
*

*>
*

*> > 3) Arithmetical Realism)
*

*> > makes the physical science eventually secondary with respect to number
*

*> theory/computer science/machine
*

*> > psychology/theology whatever we decide to call that fundamental field ...
*

*>
*

*>[SPK]
*

*> I have no problem with AR, per say, but see it as insufficient, since
*

*> it does not address the "act" of counting, it merely denotes the list of
*

*> rules for doing so.
*

Certainly not. AR is the doctrine that even in a case of absolute

catastrophe killing all living form in the multiverse, the statement that

there is no biggest prime will remain true. It has nothing to do with

axioms and rules of formal system. Indeed by Godel's incompleteness theorem

Arithmetical truth extends itself well beyond any set of theorem provable

in any axiomatizable theory.

Now, what do you mean by AR is insufficient? AR just say that arithmetical

truth does not depend on us. It does not say that some other truth does not

exist as well (although as a *consequence* of comp plus occam they do

indeed vanish). Don't confuse AR with "Pythagorean AR" which asserts

explicitely "AR and no more". We got P.AR as a consequence of comp, but we

do not postulate it in the comp hyp.

*>
*

*> I will go through your thesis step by step again and see if I can
*

*> wrestle my prejudices down into some reasonableness. ;-)
*

OK. Be sure to go to step n only if you manage to go to step n-1 before.

Don't hesitate to ask question if something is unclear. Be sure you accept

the hypotheses (if only for the sake of the argument).

Best Regards,

Bruno

http://iridia.ulb.ac.be/~marchal/

Received on Fri Jan 30 2004 - 14:42:05 PST

Date: Fri, 30 Jan 2004 12:48:46 +0100

Dear Stephen,

[BM] Where do I give a support to comp? I don't remember. No doubt that I

am fascinated by its consequences, and that I appreciate the so deep

modesty and silence of the Wise Machine.

But the reason why I work on comp is just that it makes mathematical logic

a tool to proceed some fundamental question I'm interested in.

The whole point of my work consists to show (thanks to math) that comp is

indeed popper falsifiable. It is just a matter of work and time to see if

the logic of observable proposition which has been derived from comp gives

a genuine quantum logic and ascribes the correct probability distribution

to the verifiable facts.

The weakness of the approach is that it leads to hard mathematical question.

I agree with you. Now comp shows much more easily that it *must* be so. You

know Bohr said

that someone pretending to understand QM really does not understand

it. The same with comp, it can even be justified.

If a machine can believe something, it will be hard for her to believe in

comp and in its consequences, until she realizes that indeed if a machine

can believe something, it will be hard for her to believe in comp and in

its consequences, until she realizes that indeed if a machine can believe

something, it will be hard for her to believe in comp and in its

consequences until she realizes that indeed if .... (apology for this

infinite sentence).

No consistent machine can really "believe" that indeed. But this does not

mean a consistent machine will believe not-comp. The point is: are you

willing to accept it for the sake of the reasoning.

Church thesis entails that the partial (uncontrolable a priori) processes

are mechanically enumerable.

AND Church thesis entails that the total (controlable) processes are NOT

mechanically enumerable.

In each case we face either uncontrolability or non enumerability. It is

Church thesis which really

protects comp from reductionnism. That was the subject of one thesis I

propose in the seventies. Since then Judson Webb has written a deep book on

that point. (Webb 1980, ref in my thesis, url below).

See my everything-list posts "diagonalisation" for the proof of those facts.

Certainly not. AR is the doctrine that even in a case of absolute

catastrophe killing all living form in the multiverse, the statement that

there is no biggest prime will remain true. It has nothing to do with

axioms and rules of formal system. Indeed by Godel's incompleteness theorem

Arithmetical truth extends itself well beyond any set of theorem provable

in any axiomatizable theory.

Now, what do you mean by AR is insufficient? AR just say that arithmetical

truth does not depend on us. It does not say that some other truth does not

exist as well (although as a *consequence* of comp plus occam they do

indeed vanish). Don't confuse AR with "Pythagorean AR" which asserts

explicitely "AR and no more". We got P.AR as a consequence of comp, but we

do not postulate it in the comp hyp.

OK. Be sure to go to step n only if you manage to go to step n-1 before.

Don't hesitate to ask question if something is unclear. Be sure you accept

the hypotheses (if only for the sake of the argument).

Best Regards,

Bruno

http://iridia.ulb.ac.be/~marchal/

Received on Fri Jan 30 2004 - 14:42:05 PST

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