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.
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. 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".
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?
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.
Brent
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