On 19 January 2015 at 18:37, meekerdb <meeke...@verizon.net> wrote: On 1/19/2015 6:01 AM, David Nyman wrote: > >> There's an effective riposte to this, I believe, but it might be a bit >> subtle, so I ask you to bear with me. I think, in the first place, that >> it's beside the point to get hung up on the 'concreteness' or otherwise of >> arithmetic. Bruno's intent is rather to enquire into the possibility that >> every relation necessary to explain both observers and what is observed can >> be reduced to those of basic arithmetic or its equivalent. Such an >> admittedly remarkable possibility is itself suggested in the first place by >> the computational theory of mind and the universality of the digital >> machine. >> >> Further axioms relating to the emulation (or embedding) of computation in >> arithmetic and that of various modal logics in computation are also >> included at the outset, but remain to be justified by their effectiveness. >> This has important consequences, as we shall see. The question then is >> whether these assumptions lead in the right direction. According to Bruno >> (and I don't claim to follow him on all the detail of this) they lead in >> the direction of self-referential computations that simultaneously emulate >> or embody two distinct logical modalities (1-person and 3-person). The >> intersection of these distinct but mutually entangled logics presents novel >> possibilities of resolving previously intractable mutual reference issues >> since mind and body need no longer be seen as categorically orthogonal. >> >> That said, as you point out, it might still seem open to a doubter to say >> so what. So we have computations whose complexities purportedly embody >> 3-personal entities, complete with the detailed appearance of their >> physical environments. So these computations may simultaneously entail the >> putatively 1-personal points of view of such entities. These two logics may >> even be related in an analytic or logically necessary way. All this may be >> remarkably suggestive but are we forced to accept that actual conscious >> experience arises as a necessary consequence of all this merely >> arithmetical *construction*? >> >> This is where the subtlety comes into play. Remember that consciousness >> is here modelled as *truth*. When you really come to think about it, truth >> is *the* defining characteristic of consciousness. As Descartes realised >> (though his insight is often misconstrued) it can make no sense to doubt >> the truth of doubt itself. When we apply this to the mutual reference >> problem something truly remarkable occurs. Take the question of Smolin's >> claiming to 'see red'. This claim is now seen as occurring at the >> intersection of two logics: one 'observable', the other 'private'. However, >> although this entanglement may explain their co-variance and mutual >> reference, neither of these logics fully captures the *truth* of the claim, >> or if you prefer, what it would actually be *like* if the expressed belief >> were true. Each of them is still, as it were, a mere epistemological >> possibility, abstractly lurking somewhere in the infinitely extended >> ontology of arithmetic. >> >> But if these logics can't definitively *capture* the truth of the claims >> they emulate, they do point to where it might be found. It comes down to >> this: Is Smolin, the putative experiencer of the truth of the claim to 'see >> red', being *truthful*? Given the hypothesised mutual consistency of the >> entangled logics, this is analytically certain. Smolin is incapable of >> being other than truthful in this regard; ergo he does in fact 'see red'. >> We can, of course, deny that there is any such analytic compulsion to >> truth. But this is self-defeating, in exactly Descartes' sense. If there is >> no truth of the matter, then there is equally no red, no Smolin, no belief, >> no logic. The 'epistemological' assumptions have been ineffective and must >> be discarded. The only remainder is arithmetic itself, since that is the >> ontology we assumed at the outset. >> > > An interesting explication. If Smolin can't be mistaken when he says or > thinks "I see red" - and I agree that he can't - then it must correspond to > (or be entangled with) a specific third person computation (i.e. physics of > his brain). But we can ask why is this entanglement, this 3p > point-of-view, even needed? Isn't just Smolin, i.e. his thoughts, already > realized in the infinity of computation, and even realized infinitely many > times? If we ask for a simulation of a lot of people then it may be more > efficient to simulate a physics that gives them consistent 3p > points-of-view. But I'm not sure efficiency has any relevance in > arithmetical infinity.
I'm not sure I'm well equipped to answer your question, assuming I've understood it. My understanding of Bruno's schema is that it leads to a kind of Computational Library of Babel. You could say that it's the way a 'creator' might set about producing a lawful universe despite knowing nothing beyond simple arithmetic. My kind of god, in fact ;-) However the dissimilarities with Borges's alphabetic library are perhaps more striking than the parallels. For one thing, the hypothesis of the dovetailer (i.e. a very simple computation that happens to generate all other computations, including itself) must result in a fractal-like explosion of redundancy that threatens to defeat the imagination. Consequently the question of differential measure, of classes of similar computations, becomes absolutely central in determining which outcomes predominate and the consequences of this are far from obvious, to say the least. So as you imply, what would emerge from this is less a matter of efficiency and more one of what would tend to get the upper hand in the ensuing measure battle. Producing a detailed a priori argument for this is unfortunately well beyond my capabilities. In other words, it is ultimately only the level of truth that validates, or >> redeems, the epistemological assumptions; otherwise they remain mere >> 'free-floating' abstractions, >> > > The epistemological assumptions are about the 3p POV. Well, my whole point is that, at the 3p level, I consider the epistemological assumptions to be *provisional*. That is, whatever results from mechanism doesn't count as knowledge, in the sense in question, until it is justified or redeemed at a level that transcends the bare mechanism itself. This is what I mean by the level of truth. I expand on this a little below. But the necessary truth you refer to is about the arithmetical relations > instantiating the 1p POV. So when Smolin thinks "I see red." it is > necessarily true that this is associated with a certain computation that > instantiates "redness". But it isn't necessarily true that the is a read > object in Smolin's view - which is what he actually means when he thinks "I > see red". Whether there is a red *object* is not material to my point. The truth in question depends only on whether his statements refer to something real or true in a primary sense. All other senses, in the context under discussion, such as secondary interpretation or decomposition into 'objects' of perception, are derivative on this primary datum. > conceptually disconnected from a base ontology that has no knowledge or >> need of them. If we can accept consciousness as the model (in the >> mathematicians sense) of such a truth level, >> > > What does "truth level" mean? I don't see what the levels of truth are; > there are true sentences and false sentences and decidable and undecidable > sentences. Are you referring to true sentences in a metalanguage? And in > what sense can a consciousness model a "truth level"; sounds like a > category mismatch? I know that Bruno specifically refers to arithmetical truths in the senses you describe above. But in my view we need to think about this somewhat more broadly or generally to get a handle on 'consciousness' in the way I am suggesting. That is, the truth in question is just what would *have to be the case* to validate, not only the truth-claims of the relevant statements, but to validate their very status *as* truth-claims (as opposed to mere machinery). In other words, truth is modelled here as the criterion that differentiates epistemology from ontology. As such, it 'retroactively' validates the ascription of 'epistemological' to those features of the ontology that can then (correctly) be seen as giving rise to it. This may be circular, but perhaps virtuously, in a sense you've sometimes encouraged us to entertain. I would be interested in Bruno's comments (and indeed your own) as to the viability of extending the notion of arithmetical truth in this way. At this point, I'm somewhat persuaded that this broader sense of truth, in approximately Descartes' sense, is in fact highly relevant to what is special and, so to speak, non-negotiable about consciousness. It has the virtue that it now makes no sense to say, as Stathis wants to suggest, that the same scenario could equally well be describing an 'unconscious' (i.e. untruthful) process. we can justify our attempt to abstract, epistemologically, a multiverse of >> dreaming machines complete with their hallucinated physical environments. >> If we insist on denying this, however, the entire epistemological >> enterprise just collapses back into the heap of its base ontological >> components. >> > > The usual way to justify a theory is to have it predict some otherwise > unexpected observable fact. > True enough, but my sense of 'justification' here was more restrictive and specific. I simply meant that our ascription of an 'epistemology', in the relevant sense, to mechanism should be conditional on the truth-claims provisionally attributed to such mechanisms being 'justifiable' or 'redeemable' at some level that transcends mechanism itself. Ordinarily, this implies some level of extrinsic interpretation, as for example when you are reading this text. But in the case of a purportedly self-interpreting mechanism, there can be no such extrinsic locus. Consequently, we must seek to anchor 'interpretation' in a manner that is intimately associated with mechanism itself but somehow transcends it. In fact, my contention is that denying the effectiveness of such a level (i.e. truth as it pertains to mechanistic 'knowledge'), is tantamount to dismantling the whole attempt to ascribe an epistemology to mechanism in the first place. 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