On 28 Sep 2015, at 07:26, Bruce Kellett wrote in part (to Stathis) :
...
Alternatively, it could be said that your mind was distributed
across the two computers.
No. That is a silly statement.
If one of the computers were switched off, your mind would continue
running, unable to notice that anything unusual had happened.
Which simply means that the scenario you describe is operationally
just the situation of one person.
OK. One person implemented and emulated at different places by
different universal numbers implemented by different hardwares.
The only thing that making copies achieves is that the environments
will differ, so that the copies will diverge.
All right.
Consequently, they cease to be the same person after the odd
nanosecond or two. Anything else is hypothetical nonsense because
not achievable in practice.
The cease to be the same, in between themselves, but they remain both
the same as the person they were before the differentiation. OK. That
is the root of the first person indeterminacy. They might have known
that protocol, and infer the coming up of the differentiation and
understand it introduces a non-constructive or from their first person
perspective.
The situation then is just like that with the disjoint worlds of
the MWI in QM: the separate worlds are disjoint -- non interacting
-- so their existence has no bearing on you or your future. In
fact, Susskind and others have identified Tegmark's level I
multiverse with the MWI of quantum mechanics. I think this
identification is nonsense, but the relevance of the potential
copies is the same in both cases -- zero!
It is not zero if you could be any of the copies.
Demonstrate to me how this makes an operational difference. If it
makes no measurable or operational difference, then, the relevance
of the copies is precisely zero.
But in QM, and in the computationalist theory of mind, the numbers of
the relatively differentiating copies make a difference. It introduces
the need of a good statistics calculus, like in QM, and like in the
machine's self-reference logic (that I call machine's theology, and is
axiomatized by the modal logics G and G* thanks to a theorem due to
Solovay, see the reference in the paper). It is important: the theory
is there. It is not speculation. It is unavoidable.
There is reason to believe that in fact the universe is infinite
and uniform; but if it is not, which is possible, the conditional
argument still stands. So, do you think you would experience the
world differently if there were infinite copies of you and of
every possible variation of you?
No. Not that I believe that there are such copies, but even if
there were, they would be of zero consequence for anything
whatsoever.
What would it mean for probability if your mind were spread over
infinite copies?
Nothing, because it would make no operational difference to anything
-- even if such a concept made any sense at all.
The problem is that we believe our brain can be emulated by a digital
machine, we must accept that it is emulated an infinity of "times" in
a tiny part of arithmetic. Then physics has to be explained by the
coherence condition on the first person points ov view of the machine,
if only to remain consistent.
Luckily it works, the measure one is defined in G (and thus in
arithmetic) by [3]p = []p & <>t on the sigma_1 sentences. In
arithmetic it is {beweisbar(Gödel-quote(p)) & ~ beweisbar ~(Gödel-
quote(0 = 0))}, with p a sigma_1 sentence. (shape "ExP(x)" with P
decidable).
It works, as [3]<3>p put a quantum logic structure on the sigma_1
propositions. If we got the good Gleason theorem, we can extract the
probabilistic calculus. I expect the quantum one, and hope that the
symmetries and the behavior of the quantization will lead to the
standard model, or its improvement.
The advantage of this approach is that by the incompleteness split of
G and G*, and the apparition of the intensional variants, we can
explain both the non sharable qualia and the partially sharable quanta.
With computationalism RA unifies all the science, without eliminating
anything. It is a multi-level theory, where the same basic
arithmetical relations can be viewed from infinity different angles,
and it explains the relation between all the views, and that include
the physical, the psychological, and the theological, at their core
level.
The theory is testable, so let us see. It can take time, though, but
even more so if people handwave for not doing the math and the test,
actually just ignoring the theory, which is just the canonical (toy,
if you want) theology of the universal (Turing, Church, Kleene) machine.
Bruno
http://iridia.ulb.ac.be/~marchal/
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