On 2/4/2012 14:38, Stephen P. King wrote:
On 2/4/2012 8:58 AM, David Nyman wrote:On 4 February 2012 12:22, Bruno Marchal<marc...@ulb.ac.be> wrote:No, I am not. I bet that comp is TRUE, but I don't see COMP as requiring that the physical world is supervening on numbers (up to isomorphisms) as primitives. So you have to explicitly show what is not valid in the UDA1-8. You miss something, let us try to find out what. I am not missing a thing, Bruno. You are missing something that is obvious to the rest of us. If someone else can confirm this, and put some light on what Stephen is saying, I would be pleased.Bruno, I used to think that you were indeed missing "something that is obvious to the rest of us". I don't think so any longer, because I understand now that you are presenting a theory and your arguments consequently derive strictly from the axioms and assumptions of that theory. I don't pretend to understand all aspects of that theory of course, but through discussion and the contrast of ideas I have come a bit closer than when I started. I don't know if it will help at all for me to state here my understanding of what might motivate the theory in the first place, but I'll try. Firstly, as you have so often said, the informational/computational theory of mind (CTM) is more or less the default assumption in science. Indeed this conclusion seems almost unavoidable given that brain research seems to imply, more or less unambiguously, the correlation of mental states with relations, rather than relata. However, CTM in its uncritically-assumed form continues to be combined with the additional assumption of an Aristotelian primitively-physical state of affairs. This leads directly either to denialism of the first-person, or alternatively to some ill-defined species of property dualism. These consequences by themselves might well lead us to reject such primitive-physicalism as incoherent, even without an explicit reductio ad absurdum of the unambiguous association of conscious states with "physical computation". Either way, in order to retain CTM, one is led to contemplate some form of neutral monism. The question of what form such a "neutral" theory should take now arises. Since the theory is explicitly *computational*, the axioms and assumptions of such a theory should obviously be restricted to the absolute minimum necessary to construct a "computational universe" (in the traditional sense of "universe") or rather to indicate how such a universe would necessarily construct itself, given those axioms and assumptions. The basic assumption is of a first-order combinatorial system, of which numbers are the most widely-understood example. Given the arithmetical nature of such a universe, construction and differentiability of composite entities must necessarily derive from arithmetical assumptions, which permits the natural emergence of higher-order structural integration via the internal logic of the system. Of particular note is the emergence in this way of self-referential entities, which form the logical basis of person-hood. Since the reality of first-person localisation is not denied in this theory (indeed the theory positively seeks to rationalise it), the system is not posited as having merely third-personal status, but as possessing a first-person self-referential point-of-view which is associated with consciousness. Perhaps it is this aspect of the theory which is the most tricky, as it cuts across a variety of different intuitions about consciousness and its relation to the phenomena it reveals. For rather than positing a primitively-physical universe which "instantiates" conscious states, the theory must reverse the relation and posit conscious states that "instantiate" physical phenomena. In so doing, it exposes itself to empirical refutation, since those phenomena must be, at least, consistent with ordinary observation (although they also predict, in the limit, observations of high improbability). It is this last issue of instantiation which seems to be one of main bones of contention between Stephen and yourself, though I'm not sure why this is the case. From my own perspective, unsophisticated though it may be, it seems reasonable that the emergence of "truly physical" phenomena should indeed be the result of "personal instantiation" in the conjunction of consciousness and computation. After all, when do questions as to what is "truly physical" emerge, other than in the context of what is "truly experiential"? The rest is calculation. DavidDear David, Does my claim that our primitive ground must be neutral with respect to any properties make any sense? It like the zero of arithmetic from which we can extricate any set of positive and negative quantities in pairs such that their sum is equal to zero. What I see in Bruno's interpretation of COMP is that it permits for the primitive to have a set of properties (numbers and + and *) to the exclusion of its complementary opposites. Since this is a violation of neutrality, thus I see a fatal flaw in Bruno's Ideal monist interpretation. Onward! Stephen
One can wonder what is the most "general" theory that we can postulate to explain our existence. Tegmark postulates all of consistent mathematics, whatever that is, but is 'all of consistent mathematics' consistent in itself? Schmidhuber postulates something much less, just the UD, but strangely forgets the first-person or the what the implementation substrate of that UD would be (and resorts to a Great Programmer to hand-wave it away). Before reading the UDA, I used to think that something like Tegmark's solution would be general enough and sufficient, but now I think 'just arithmetic' (or combinators, or lambda calculus, or ...) or is sufficient. Why? By the Church-Turing Thesis, these systems posses the same computability power, that is, they all can run the UD. Now, if we do admit a digital substitution, all that we can experience is already contained within the UD, including the worlds where we find a physical world with us having a physical body/brain (which exist computationally, but let us not forget that random oracle that comes with 1p indeterminacy). If we are machines, then we can only experience finite amount of information given some finite interval of time, some of this information may be incompressible, due to 1p indeterminacy, thus we could experience "reals" in the limit, despite there only being finite computations at any given time. This essentially means that any mathematical object which can be described in Tegmark's "Ultimate Ensemble" and that can contain us, is already part of the 1p experiences of those existing within the UD and we can look at 1p experiences, as well as the UD* trace as being part of the greater "arithmetical" truth (or any other theory with equivalent computational power, by the Church-Turing Thesis).
This is why I think "arithmetic" is as good as any for a neutral foundation, and we cannot really distinguish (from the inside) between these foundations by the CTT. However, there might be other possible foundations, if you wish to postulate concrete infinities, but even if they existed, how could we tell them apart, it doesn't seem to be possible for someone admitting a digital substitution, which has a finite mind (at any finite point in time). If you can show that those other foundations are necessary and they affect our measure/continuations, or that concrete infinities are involved in the implementation of our brain, it could prove COMP wrong. There is another problem with taking a set theory as foundational rather than arithmetic - some set theories have independent axioms and they can be extended by adding either an axiom or its negation, and they result in different set theoretical truths. This doesn't really happen with computation - if there's anything absolute in math, it's computation (although different theories about what arithmetic is will result in different things the theory can talk about, but it won't make computation any less absolute).
As a side-note, I don't see why the primitive physical world is necessary, from the 1p, we can only know that we have senses and from the senses we can infer the existence of the external world. If consciousness is how some (possibly self-referential) arithmetical (or computational) truth feels from the inside, it does not seem impossible that there would not be computations representing some physical (just not primitive) world and that world would contain us and our bodies/brains, and the existence of such computations would be a theorem in arithmetic.
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