Dear Bruno,

- CRH implies COMP
- COMP implies the negation of CRH

> Universality, Sigma_1 completeness, m-completness, creativity 
 >(in Post sense), all those equivalent notion makes sense only through
 >complementary notion which are strictly sepaking more complex (non RE, 
productive, ...).
 >The self-introspecting universal machine can hardly miss the inference 
of such "realities",
 > and once she distinguishes the 1, 1-plural, 3-person points of view, 
she has to bet on
 >the role of the non computable realities (even too much getting not 
just randomness,
 >like QM, but an hard to compute set of anomalous stories
 > (white rabbits, coherent but inconsistent dreams).

Why does the machine have to bet on these complementary non-RE 
histories? I do not quite see how this arises from 1 and 1-plural POV; 
after all, it could be just rec. enumerable continuations?

Schmidhuber's/Tegmarks Computable Universe Hypothesis seems very 
attractive: it gives rise to structure, _evolves_ self-aware 
sub-structures, and gives reasonable (?) measure, for instance 
Schmidhuber's speed prior.

This also takes care of the white rabbit.

> It's a bit like "understanding" (putting in a RE set) the (code of) the total 
> computable
 > functions, forces us to accept the existence of only partially 
computable functions,
 >which sometimes (most of the time, see the thesis by Terwijn) have a 
non recursive domain.

> OK, the ontic part of a comp TOE can be no *more* than Sigma_1 complete, 
 >but a non self-computable part of Arithmetical truth and analytical 
 >is needed to get the *internal* measure, we can't even give a name
 >to our first person plenitude and things like that.

I think this answers part of my question above. The ontic part is only 
the Sigma_1 complete stuff; we assume the others for our measure - but 
my claim is that they do not give rise to first person experience.

I think the central question is this: _what_ does the Arithemetic Truth 
of whatever simulate? Reality at a granular level (like in the CA 
approach, Zuse's Rechnender Raum) - that is what I would assume - that 
reality at the lowest level is a number-relation; but that awareness 
only arises in these domains as a higher oder abstraction.

I think you assume that the Sigma_1 sentences give the OMs directly, is 
that correct? So in your view there is no underlying reality; QM and 
stuff like that is only an "illusion". Am I correct in how I interpret 
your theory?

> Perhaps this is why the Intelligible has been discovered (Plato) before the 
> "ONE" 
 >(Plotin). It is far bigger. With comp you can restrict the ontic to 
the Universal Machine
 > (the baby ONE),

Ok, I'm with you this far.

> but its intelligible realm is well beyond its grasp.

For me, the intelligible can be only a (proper?) subset of the ontic. 
How could something that does not exist (ontic) be intelligible? Or 
would you say that this is mathematical imagination?

> All this is related to the fact, already understood by Judson Webb, 
 >that comp is truly a vaccine against reductionist theories of the mind.

I have the Webb book on my desk and have glanced occasionally inside, it 
  looks like a wonderful book, but I have not yet had the time to study 
it in detail.

But I wonder - why do you say that comp is not reductionist? For me comp 
is reductionist - mind as the working of computation (I am pro 
reductionist, that is not a negative word in my view).

So, two questions:

1) At what level do your Sigma_1 sentence operate? OM's directly (I 
would interpret your paper in this way) or low level (more like a 
classical physical/digital physics view)?

2) You say that the ontic part is computable (in this sense, I would say 
  COMP does _not_ refute CRH?) Because what "is" that is not ontic? That 
would be contradiction in terms?


Günther Greindl
Department of Philosophy of Science
University of Vienna


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