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?
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.