3. Due to Church Turing and #2, the underlying implementation of
the computer (the programming language, the physical material,
the laws of physics, the universe it happens to run in) are
irrelevant, only the functional equivalence at the low-enough
level (substitution level) is important to preserve
consciousness (note that nothing to this point has changed
anything about our assumption of reality, the ontology, etc.)
4. Assuming arithmetical realism (which implies the existence of
all computations) and #3, this implies all conscious states
exist in arithmetic. (this makes redundant the assumption of
physical universes that are distinct from physical universes,
here we modify our ontological assumptions about what a physical
universe is)
It does not make redundant the assumption of physical universes
because you have not defined the "functional equivalence" and how
it relates to the world outside the brain. The brain presumably
is receiving and processing information and action in this
world...otherwise its computations will be just arithmetic and
have no referents. It will be like the rock that computes
everything.
I noticed a typo in what I wrote, I meant to say "this makes
redundant the assumption of physical universes that are distinct from
*/arithmetical/* universes". Hopefully this addresses your point.
5. Given #4, and the fact that an infinite number of
indistinguishable programs implement your conscious state (e.g.
different below your substitution level), and given that these
programs may diverge in the future, then making predictions
about future experiences
Future experiences of...what?
Observers.
You have relations among states of Turing machine or similar
computer, and you claim they are conscious. But you are helping
yourself to a picture in which this computer is embedded in your
head which is embedded in a physical world which gives meaning to
the computations.
But with step #5 our head is embedded in an ensemble of similar but
distinct universes.
(the focus of physics) now becomes a statistical question
regarding the distribution of unique programs existing below
your substitution level.
Statistics refers to samples from a probability distribution.
How is a probability distribution relevant to these programs
Given that teleportation is possible, there is a distribution of
future states which any of those observers might become (where they
could next find themselves).
We have now reached the "reversal" (the laws of physics can be
derived from the arithmetic concerning conscious programs which
exist arithmetically, here we acknowledge that no observer
exists in any single universe).
So from the evolution of the view of what is meant by physical
universe, we see there are at least 3 connotations:
A) The first view where a universe is a causally isolated
physical structure which may or may not contain observers
B) The second view where a universe is a relatively stable
(perhaps shared) observation in the mind of some observer(s)
C) The third view where there exists a unified set of
metaphysical laws, applicable to all observers, and in principle
these laws can be derived from the arithmetic of self-reference,
there is no longer the notion of an observer which belongs to a
universe as each observer is supported by an infinity of
similar, but distinct computations
How similar do they have to be in order to be the same observer?
I believe this is undefinable according to Bruno, though I am not
sure on what basis he reached this conclusion.
So when you say "the theory is that the physical universe is a
statistical construct over all the computations running through
your conscious self", you are correct that this is the logical
end and conclusion of the theory of computationalism. But when
I said you could implement any consciousness in any universe
where it is possible to build a Turing machine, I am talking
about the "level A" type universe. (which I acknowledge to be
redundant and eventually eliminated in the theory, but use this
example for pedagogical purposes).
So any external universe is part of that construct through
your consciousness. So appealing to an external universe
running a simulation does not help at all.
Remember, consciousness is the sum over all
computation that pass through that particular
conscious state, so in this theory your AI, be it in
silicon or the Game of Life, cannot be conscious,
because it is a single computation.
That all subjectively indistinguishable computations
going through that state are a possibility means the
consciousness cannot identify itself with any one
particular thread of computation. In this sense that
consciousness is not the same as one of the programs
passing through that state. But to say the consciousness
is not identical with one of the computations is
different from saying that computation is not conscious.
The trouble here is that that is an unproven assumption.
It follows from there being a level of digital substitution (the
computationalist assumption). Let's say we can substitute your
consciousness with a computer that emulates each atom in your
neuron to a precision of 20 decimal places. This means we could
also substitute your consciousness with a computer that emulates
each atom using a precision of 50 decimal places, or 100. Your
consciousness would be no different. However, given enough time
these simulations would eventually diverge.
You are still helping yourself to an external physical world in
which this artificial brain is embedded. Suppose instead it is
embedded in nothing, in a perfect void? Or suppose it is embedded
in a world of Newtonian physics? Or suppose it is embedded in a
random world in which only things that are improbable in our
world are realized? Will it still function as your
consciousness? If so, what makes it "yours"?
That it is subjectively indistinguishable. I think Saibal Mitra
explain this in "Changing the past by forgetting" (
https://arxiv.org/abs/0902.3825 )
If the future of any conscious moment depends on the
statistics over the infinite number of computations running
through that state, then a single computation gives a
conscious moment that does not have a coherent future.
I think we are in agreement here. The experiences of a single
computation would/could eventually discover it has deviated from
the normal expected statistics.
Neither does a single computation exist in a coherent world,
since physics, and the appearance of matter, is also the
result of the statistics over the infinite number of
computations.
Once we replace our "level A" view of physics, with the
realization in "level C" that there is no physical world,
That isn't what "C" says.
There are still worlds, and there the appearance of a physical world,
but the appearance falls out of arithmetic, rather than physics.
(assuming computationalism and arithemtical realism).
What this says, "The third view where there exists a unified set
of metaphysical laws, applicable to all observers, and in
principle these laws can be derived from the arithmetic of
self-reference" is that there is no difference between
metaphysics and physics. It is the dream Einstein that he
discovers that the Creator had no choice.
The creator having no choice you get to with just arithmetical realism.
Jason
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