[ExI] Trilemma of Consciousness

[Colin Hales]

See below.

On Fri, May 26, 2017 at 12:33 AM, Stuart LaForge <avant at sollegro.com> wrote:

> Some of you might remember my mathematical musings on the computability of
> consciousness linked to here:
> http://lists.extropy.org/pipermail/extropy-chat/2016-December/091135.html
> http://lists.extropy.org/pipermail/extropy-chat/2017-January/091224.html
>
> My idle boast of being able to easily prove the undecidability of the
> generalized Turing test based on Russell's paradox was premature as I was
> thwarted by the funny fact that modern set theory has two additional
> axioms specifically designed to disallow Russell's Paradox. You can read
> about that here:
> https://proofwiki.org/wiki/Russell's_Paradox
>
> So despite the zombie detector being intuitively true, I was unable to
> prove it rigorously using set theory. So I had change my tact completely.
> Here is the latest sketch of my proof:
>
> Theorem: Consciousness can only be one of the following: 1. a property of
> all Turing machines, 2. an undecidable property of some Turing machines,
> or 3. not a property of Turing machines at all.
>
> Proof
>
> Axiom 1: Let F(n) be the nth computable function with n being an
> admissible numbering of all possible computable functions.
> Axiom 2: Let K be the subset of F(n) such that all K share a semantic
> property k.
> Definition 1: Let k be called trivial if all F(n) have property k.
> Definition 2. Let k be called null if no F(n) has property k.
> Axiom 3: Let Dt be the decision problem as to whether a given F(n) belongs
> in K.
>
> Theorem: By axioms 1-3, definitions 1-2, and Rice's Theorem, Dt is
> decidable if, and only if, k is trivial or null.
>
> Corallary: The set K of conscious functions is noncomputable.
>
> Q.E.D.
>
> In other words, the generalized Turing test is decidable IFF all computer
> programs are conscious or none are. Or equivalently, the GTT is
> noncomputable.
>
> Thoughts, anyone?
>
> Stuart LaForge
>
>
>
Consciousness is completely missing from current set theory. It can be
added. But I don't have the maths skill to sort it out formally. I wrote
this up in my book. Perhaps you have the math skill?

I'll hand it over ... maybe you can make some progress.

Consciousness is about the 1st-person perspective. In set theoretic terms
this means that whatever the mathematical treatment, it is all about

1) "Being" a subset X within a hosting set U (A class of sets to be
discovered)
then
2) Finding out, based on the relationship between set members within U, a
way of characterising how everything that is NOT-X might 'appear' (whatever
that means in set theoretic terms) to X from within U. That 'view' is
completely inaccessible except from the perspective of being X, inside U.

Nothing in set theory ever formally looks at this. It's a completely green
field.

Answer this question: What must the kind U of set members and relations
between U set members (or groups of) such that there's an identifiable
class of set U that might result in it being 'like something' to be X
within U.

NOTE 1: Important aspect. Once identified, a computer-based
numerical/symbolic exploration, of this new "X within U being like
something" aspect of set theory, is a valid scientific exploration of the
nature of consciousness. However, it is NOT an instance of consciousness.

NOTE 2: Whatever that class of U is, our universe is a member of that class
of sets. This is an empirical fact: proved by the existence of an observer
(us humans) as empirically proved by the existence of science, and in
particular the science of consciousness.

NOTE 3: The facts of the situation in NOTE 1 does not entail that U cannot
be classed computation.The regularity in U is obviously validly interpreted
as computation. NOTE 1 says that a _computer_ exploration of U is only
that. (Like a flight simulator is not an instance of flight).

HINT1: In this new class of set (and I suspect this is a very special kind
of set) where 'it being like something from within' can result, the
relations that are the origins of consciousness are that of "aggregate
_virtual_ set membership". That is, collections (populations within X, part
of X) can 'act as if' other set members (within NOT-X) exist that don't
actually exist. X can 'paint a view of NOT-X. In that act, NOT-X becomes
'visible'. Whatever 'view' of NOT-X this provides to X, real causal
relations between the fine-structured set U members means that the virtual
construct within X inherits a kind of 'virtual causality', where future
(actions) are taken based on the 'appearances' experienced by X, and
there's no actual obvious link because the only entity with access to 'why'
is X.

HINT 2: Success and Empirical Proof.
To empirically prove you've succeeded all you need to do is come up with an
X within U that predicts what X looks like to another member of kind X, say
Y. In humans, Y would look at X and see specific kinds of electromagnetism
in the brain. That is, to another Y within U looking at X in the act of
having consciousness delivered to X, it looks like brain electromagnetism.
Why electromagnetism? It's the only thing to choose that has been proved
100% correlated to consciousness for the entire era that science has
examined the origins of consciousness. 'Being' electromagnetism (behaving
in a certain way) delivers a 1st person perspective. somehow.. something
that is amenable to this new set-theoretical treatment.
=======================

I don't have the time or the skill to do this new set theory. But I'm
working out how to build it, which needs no theory, just knowledge of how
the brain does it with electromagnetism. I can build that.

Somebody has to do this new part of set theory.

Off you go. Just put me in the acknowledgements. :-) Remember me when you
get your Nobel prize.

cheers
colin
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