On 12 June 2012 17:36, Bruno Marchal <marc...@ulb.ac.be> wrote:

Yes, but the expression "from the current state of any universal
>> machine" (different sense of universal, of course) already *assumes*
>> the restriction of universal attention to a particular state of a
>> particular machine.
> But is that not the result of the fact that each machine has only access
> to its own configuration?

That's too quick for me.  To say that "each machine has only access to its
own configuration", is still merely to generalise; to go from this to *some
particular machine* requires one instance to be discriminated from the
whole class.  So what, you may retort, "your" states just "discriminate
themselves as you".  The problem to my mind, with looking at things in this
way, is that for there to be a *universal* knower, each state must *
primarily* belong to "you qua that knower" (which is what makes it
universal) and only secondarily to "you qua some local specification".  If
this be so, it is circular to invoke those secondary characteristics, which
become definite only after discrimination, to justify the discrimination in
the first place.

ISTM that the two of us must actually be thinking of something rather
different when we conceive a universal person or knower.  For you, IIUC,
this idea is consistent with many different states of consciousness
obtaining "all together"; consequently the viewpoint of this species of
universal person can never be reducible to any particular single
perspective.  I'm unsatisfied with this (as presumably was Hoyle) because
it leaves me with no way of justifying "why am I David" that isn't
circular.  I can of course say that I'm David because the given state
(here, now) happens to be one of David's states of mind, but the problem in
this view is that this is completely consistent, mutatis mutandis, with
Bruno's saying exactly the same. By contrast, Hoyle's heuristic allows me
to say I'm David because a state of David happens momentarily to be the *unique
perspective* of the whole.  As Schrödinger puts it, not a *piece* of the
whole, but in a *certain sense* the whole; Hoyle's heuristic makes explicit
that "certain sense".

I suspect that the difference between us is that it is not your intention
to justify the feeling of change directly from your mathematical treatment,
but rather to demonstrate the existence of an eternal structure from which
that experience could be recovered extra-mathematically.  You often refer
to the inside view of numbers in this rather inexplicit manner (forgive me
if I have inadvertently missed your making the details explicit elsewhere).
 Hoyle however seemed to be directly concerned with rationalising this
feeling by associating it with a unique dynamic process operating over the
system as whole.  That's the difference, I think, and it may be


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