[ExI] Trilemma of Consciousness

Stuart LaForge avant at sollegro.com
Thu May 25 14:33:27 UTC 2017


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









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