Recent discussions, mainly with Brent and Bruno, have really got me thinking again about the issues raised by CTM and the UDA. I'll try to summarise some of my thoughts in this post. The first thing to say, I think, is that the assumption of CTM is equivalent to accepting the existence of an effectively self-contained "computationally-observable regime" (COR). By its very definition, the COR sets the limits of possible physical observation or empirical discovery. In principle, any physical phenomenon, whatever its scale, could be brought under observation if only we had a big enough collider. But by the same token, no matter how big the collider, no such observable could escape its confinement within the limits of the COR.
If we accept that the existence of a COR is entailed by assuming CTM, we come naturally to the question of what might be "doing the computation". In terms of the UDA, by the time we get to Step 7, it should be obvious that, in principle, we could build a computer from "primitive" physical components that would effectively implement the infinite trace of the UD (UD*). Furthermore, if such a computer were indeed to be implemented, the COR would necessarily exist in its entirety somewhere within the infinite redundancy of that trace. This realisation alone might well persuade us, on grounds of explanatory parsimony and the avoidance of somewhat strained or ad hoc reservations, to accept FAPP that UD*->COR. Should we be so persuaded, any putative underlying "physical computer" would have already become effectively redundant to further explanation. Notwithstanding this, we may still feel the need to retain reservations of practicability. Perhaps the physical universe isn't actually sufficiently "robust" to permit the building of such a computer? Or, even if that were granted, could it not just be the case that no such computer actually exists? Reservations of this sort can indeed be articulated, although worryingly, they may still seem to leave us rather vulnerable to being "captured" by Bostrom-type simulation scenarios. The bottom line however seems to be this: Under CTM, can we justify the "singularisation", or confinement, of a computation, and hence whatever is deemed to be observable in terms of that computation, to some particular physical computer (e.g. a brain)? More generally, can we limit all possibility of observation to a particular class of computations wholly delimited by the activity of a corresponding sub-class of physical objects (uniquely characterisable as "physical computers") within the limits of a definitively "physical" universe? This is where Step 8 comes in. Step 7 seeks to destabilise our naive intuition about an exclusive 1-to-1 relationship between computations and particular physical objects by pointing to the consequences of a physical implementation of UD*. Step 8 however is a change of tactic. First, it postulates a scenario where physical tokens have been contrived to represent a "conscious computation" (either in terms of a brain or in terms of a substitute "computer"). Then it sets out to shows how all putatively "computational" relations between such tokens could in principle be disrupted without change in the net physical action or environmental relations of the system that embodies them. Step 8 differs from Step 7 in that it seeks in the first instance to undermine the very notion that physical activity can robustly embody *any* second-order relations above and beyond those of net physical action. Accepting such a stringent conclusion would then seem to rule out CTM prima facie. The only possibility of salvaging it would lie in an explanatory strategy in terms of which computational relations take logical precedence over physical ones. Given that computational relations are effectively arithmetical, this in turn leads to the conclusion that CTM->UD*->COR (or more generally, that each implies the others). Notwithstanding this it would seem that Step 8 is not wholly persuasive to everybody, so is there yet another tack? The line of argument that I've been pursuing with Brent has led me to consider the following analogy, which I'm sure you'll recognise. Consider something like an LCD screen as constituting the "universe of all possible movie-dramas". In terms of this analogy, what are the referents of any "physical observations" on the part of the dramatis personae featured in such presentations? IOW what are we to suppose Joe Friday to be referring to when he asks for "Just the facts, ma'am"? Well, the one thing we can be sure of is that NO such reference can allude to the "underlying physics" (i.e. the pixels and their relations) of the LCD display. If this analogy holds, at least in general outline, what justification, under CTM, could remain for any assumption that our own observations and references might "accidentally" allude to some "LCD-physics" postulated, mutatis mutandis, as underlying the COR? Would it not seem extraordinary that any such underlying physics could contrive to "refer to itself" through the medium of its merely computational derivatives? This last point might seem determinative, but might there not still be a last-ditch redemption, of a physics underlying computation, in terms of "evolution"? IOW, might it not be argued that the acquisition of internal "computational" models of their physical environment confers a survival advantage on the physical creatures that embody them? But any such argument would, of course, be completely circular; assuming CTM, it begins and ends in the COR. IOW, arguing in this way would be to ignore the fact that the history of such creatures, their survival, and the environment in which this is supposed to take place, all lie within the COR, not the putative regime of any "underlying physics". THAT "physics" would necessarily be entirely inscrutable and inaccessible for reference at the level of the COR (think of the LCD analogy). And hence we simply would have no a priori justification for assuming the observational physics of the COR to be isomorphic with some notional underlying "LCD-physics". In fact, once having assumed CTM, we would have no further basis for assigning THAT physics any role whatsoever in our explanatory strategy. David -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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