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
