Dear Stephen,
With your permission, I answer an offlist post you sended to me and
some others,
> Bruno, you claim that I assume a physical world. While I would agree
> with that claim to some degree, it misses the point that I am trying
> to make, just as Lee's interpretation of my idea as being about "an
> intersubjective reality". I am trying to start with those aspects that
> I can not coherently be skeptical of, the "unassailables" (to use
> Penrose's favorite term). (I am being a Curmudgeon!)
> I can not doubt that I have a 1st person experience and I can not
> dismiss that that 1st person experience has some content.
Like me. We agree.
> Additionally I am lead by logic to not be able to doubt the existence
> of otherminds - there is no coherent solipsism for finite computations
> -
> thus it is necessary that any model of consciousness must include
> means and mechanism to explain and predict how the contents of
> multiple 1st person experiences are "synchronized" such that this
> conversation itself is not only allowed by the model but can also be
> shown to be unavoidable or inevitable; that, I think, satisfies my
> argument for "necessity" of a 1st person viewpoint.
I completely agree with you.
>
> Bruno, it seems that you claim that you don't need a "pre-existing
> physical world" since such, you hope to prove, can be derived solely
> from the relations between numbers.
To be clear I have only proved that IF COMP is taken seriously enough
THEN the appearance of a "pre-existing physical world", including its
stability, lawfulness ... MUST BE derivable from the relation between
numbers. This is done. Then I got results confirming in part that comp
can be true, in proving that the logic of physical propositions is not
boolean and even has a quantum smelling (to be short).
> I will agree, for the sake of discussion, that numbers can represent
> the content of any and all 1st person viewpoints at some level of
> Existence but my challenge to you is to shown how this Existence is
> stratified such that our unassailable experience of
> "being-in-the-world" is necessary.
I completely agree with you again.
> It is easy to see that if we only consider a single mind the problems
> of synchronization and "flow" vanish - we have the ideal solipsist
> whose experiences are identified with the "relations between
> numbers". But where does meaningfulness come from?
Meaningfulness comes from the non triviality of our experiences.
Suppose someone is cut and pasted in two exemplars in city A and in
city B. From a third person point of view no bits are produced. From
the personal point of view of each exemplar, when they localize
themselves, they find no trivial answers (A or B) each of which
produces one bit of information. It is genuine information because for
each of them, their result *could* have been different. Note that such
bits are not communicable to the outside observer. (Note the importance
of the counterfactuals).
> How is it a coherent claim to have numbers representing everything
> when there is no way that the numbers can be distinguished. It seems
> to me that this "distinguishability" requires something more than just
> "relations between numbers"..
I don't understand. Please elaborate (when and if you have the time).
> I still don't get how Bruno bypasses the proofs that quantum logics
> can not be reduced to Boolean algebras... Maybe what I do not grasp is
> that Bruno is using a higher logical algebra that has quantum logics
> as a subgroup - of course we know that Boolean algebras are a subgroup
> of quantum...
Quantum logic cannot be embedded by a truth preserving translation. It
does not mean the quantum cannot be translated by some more general
translation. I will say more on the everything-list because this is
obviously a technical point. I use a theorem by Robert Goldblatt
translating quantum logic in some modal logic.
Goldblatt, R. I. (1974). Semantic Analysis of Orthologic. Journal of
Philosophical Logic, 3:19-35
> I am still troubled by the idea that we seem to think that Integers
> (recursively enumerable numbers more precisely?) are sufficient to
> code all possible experience - how do we get complex numbers? ... Wait
> a sec. I have an epiphany! Are all other forms of numbers, set,
> groups, categories, etc. embedded in the Integers by the
> identification of their descriptions with some bitstring, a Geodel
> numbering scheme?
No. Perhaps it could be, and this would give a constructive version of
my theorem, but I doubt it is possible. As a mathematician I use as
tools any portion of Cantor paradise. I believe in all real numbers,
even non-standard one. I am not at all a constructivist, and I
certainly don't identify object with their description. On the
contrary, I show explicitly that when the Universal dovetailer
"executes" (mathematically in Platonia) his infinite computation, then,
what emerge from the point of view of internal observer "simulated" all
along, will forever prevent any such identification between observable
object and their description. In particular neither a person, nor a
universe can, in any effective or constructive sense, be a computable
object. I agree this is subtle and could look like a contradiction: I
sum it often by saying things like: if I am a machine then reality
cannot be a machine. An image is: if I am so little that I can go
through all the tiny holes in the fabric of reality, then my accessible
reality will seems genuinely bigger. You can seen comp as a
self-humility principle, but it entails a "counter-self explosion".
> WOW! But what about the Berry paradox?
>
> http://www.cs.auckland.ac.nz/CDMTCS/chaitin/unm2.html
I adore all the work of Chaitin and Svozil. Those works could add many
colors to comp. In "Conscience and mécanisme" I make some of those
relations explicit. In that setting the work on computational depth by
Bennett can give also an important color: indeed the "cosmological"
aspect of our reality; the feeling of having a very long and non
trivial history can perhaps be justified from Bennett's work. But
that's complex enough, and I am now concentrating myself mainly on the
quantum logical feature of reality.
Bennett, C. H. (1988). Logical Depth and Physical Complexity. In
Herken, R., editor, The Universal Turing Machine A Half-Century
Survey, pages 227-258. Oxford University Press.
Best regards,
Bruno
http://iridia.ulb.ac.be/~marchal/
Received on Wed Jun 01 2005 - 11:18:10 PDT