I’m very suspicious of using logical results such as Penrose's use of Goedel’s
Incompleteness Theorem (GIT) to limit the possibility of strong AI machines.
I’m not even comfortable with going the other direction, employing the Heisenberg
Uncertainty Principle as a physical basis supporting/establishing GIT. It is far
too easy to commit a category error, projecting properties manifest at one level
into another categorical level, which may or may not evidence such properties.
At least one definition of emergence has no trace, no predictability whatsoever.

http://antimeta.wordpress.com/2009/02/06/the-strong-free-will-theorem/
"However, it seems to me that Conway and Kochen go on to make some bad
interpretations of what this theorem says about freedom, determinism, and
interpretations of quantum mechanics. They say, “our theorem asserts that if
experimenters have a certain freedom, then particles have exactly the same
kind of freedom.” This is true for a very specific type of freedom (namely,
non-supervenience on the past) but their theorem says nothing else about any
other kind of freedom, or whether their freedom has anything to do with the
kind of freedom that matters. It may be that this kind of freedom is an
important component of free will in the ordinary sense, but it may be that
free will essentially requires not just non-supervenience, but also some sort
of complex structure that just isn’t possible for the motions of individual
particles."

SH: I think the last sentence in the above paragraph is another way of stating
that the emergent properties at a more complex level are not predictable from
the more primitive level(s), or conversely, that the more complex level has
the same properties carried into it from/(contained in) the less organized level.

Taken from Conway's paper:
"It asserts, roughly, that if indeed we humans have free will, then
elementary particles already have their own small share of
this valuable commodity. ...
Some readers may object to our use of the term "free will"
to describe the indeterminism of particle responses. Our provocative
ascription of free will to elementary particles is deliberate, since
our theorem asserts that if experimenters have a certain freedom,
then particles have exactly the same kind of freedom. Indeed,
it is natural to suppose that this latter freedom is the ultimate
explanation of our own."

SH: This approach reminds me of animism, [from the Wiki]
"Hylozoism is the philosophical conjecture that all or some material
things possess life, or that all life is inseparable from matter." or
I think more accurately, "Panpsychism, in philosophy, is either the view
that all parts of matter involve mind, or the more holistic view that
the whole universe is an organism that possesses a mind (see pandeism
and panentheism). It is thus a stronger and more ambitious view than
animism or hylozoism, which holds only that all things are alive."

SH: Without nitpicking too much over definitions, let's assume
(before Conway) that free will belongs to living things, especially
mammals; they have consciousness generated by a brain which
exhibits a mind. Humans as well as lemmings are also assumed to
have instincts as well as the assumed free will.

How is Conway going to separate the free willy aspects of his elementary
particles from the other properties or characteristics which imbue the
decision making process of a mind? I mean that I don't think that Conway
can make a reasonable argument which says the source of free will originates
in elementary particles but not other aspects of brain generated consciousness
such as instincts. Or another way to put it is how is only the free will
property isolated and transmitted to the more complexly organized choice-making
mind, but that the other properties besides choice-making that the mind exhibits
(other than) ->= free will, how are they isolated and excluded from being
transmitted as trace manifestations of properties (why only and exactly free will)?

Humans have consciousness which is necessary to support free will. What is
the explanation that if humans have free will as an aspect of consciousness,
ultimately derived from freedom of the elementary particles source, why are
not elementary particles also the ultimate source of other aspects of (human)
consciousness. Why would humans acquire only the free will property from
elementary particles source and not the other properties of consciousness?

What I'm getting at is that if elementary particles are the source of human
free will, and free will requires a living brain to generate consciousness and
the mind which renders decisions, then the elementary particles also require
the same necessary and analogous properties at their own level of complexity.
I think it would be a category error to assert that some entity at a primal
level which has free will doesn't also need a mind or consciousness mechanism
(even if just remotely analogous to human mind) in order to generate such a choice.

I don't think Conway can talk about this situation in isolation from the
structure needed (which he attempts to do) that entails free-will at the
macrocosmic level. If there is a structure for free will at the macrocosmic
level, then there also needs to be a corresponding foundational structure
at the microcosmic level. Basically, that will require attributing primitive
consciousness/awareness in the foundational structure so that free will can
be embedded within it (the microcosmic level). Or Conway has to explain why
specifically, free will is a unique microcosmic outlier which is exempt from
analogous foundational structures for free will required at the macrocosmic level.

From the grander view, the universe scientifically started without life,
without organic consciousness. Supposedly it had no free will. Then over
the millenniums life emerged and there is to my knowledge still no very
well-established theory for the miracle of life, or how inorganic became
organized and organic and so ultimately consciousness with the possibility
of a mind possessing free will emerges. One explanation is to assume that
the universe instead started with a primordial pervasive consciousness
(panpsychism), which is not a well-received theory. Both ideas hit a dead
end: we cannot know if the universe was created from/as a deterministic event
or from/as an uncaused first cause. Appropriately, my final indictment about
the lack of critical thinking shown in Conway's paper is the logical fallacy
of false cause; correlation does not imply causation and Conway does not
demonstrate that the microcosmic is the true cause of free will. Free will
or its absence can be correlated at both the macrocosmic and microcosmic
levels and both have a deeper underlying cause (parent, and not necessarily
God) to the merely correlated properties which may exist at both spawned levels.

In plain language I think Conway engaged in yet another proof of whether
there is a God or whether there is not a God, when no such proof exists or
can exist. I mean "God" as an existential labeling shortcut to knowing the
Reason for Existence. How could one possibly prove that something which doesn't
actually exist, does not actually exist?! I don't mean that Conway literally said
this, but that it's consequential that his claim potentially suffers from the same
Incompleteness malady due to a chained reasoning sequence of local paradox produced
contexts of contradictory QM interpretations.
Conway's proving tool, QM, is like using a screwdriver when a wrench is required
and is inappropriate, similar to how Penrose's attack on strong AI with GIT, failed.
---------------------------------------------

http://stonescryout.org/?p=1603
The statement of the (strong) Free Will theorem is:
The Free Will Theorem. The axioms SPIN, TWIN and MIN imply that the
response of a spin 1 particle to a triple experiment is free—that is to
say, is not a function of properties of that part of the universe that
is earlier than this response with respect to any given inertial frame.

"Conway and Kochen prove this theorem by contradiction, that is they assume
the theorem is not true and show that leads to a problem, in this case the
the *contradiction comes in the form of the Kochen-Specker paradox*."

arXiv.org > quant-ph > arXiv:0711.1473
Quantum Physics
Title: Quantum Scholasticism: On Quantum Contexts, Counterfactuals,
and the Absurdities of Quantum Omniscience
Authors: Karl Svozil
What happens if one insists on the use of two–valued states outside of a single
context by considering quantum propositional structures still allowing "a
few" two–valued states? In this case, the invocation of counterfactuals and
the "scarcity" of two–valued states accounts for some consequences which,
depending on the disposition of the recipient, appear "mindboggling" to absurd.
By bundling together propositional structures giving rise to such "mindboggling"
properties, one arrives at the KS conclusion. For such finite compositions of
observables, the mere assumption of a globally defined truth table results in
a complete contradiction. Alas, by contemplating the situation not bottom–up as
usual, but top–down; i.e., from the point of view of KS, it is not too difficult
to derive "mindboggling" statements from absurdities. Indeed, the principle of
explosion (stating that ex falso quodlibet, or contradictione sequitur quodlibet)
which, due to the pasting construction of Hilbert lattices, holds also in quantum
logic, implies that *"anything follows from a contradiction."*

motl said [re Conway's]: The free will theorem is a very cute sharpened reformulation
of the hidden variables no-go theorems that can be phrased in the following way:
'If experimenters have free will, then so do elementary particles.'

SH: I think to be significant then the converse needs to be true that
'If elementary particles have free will, then so do experimenters.'?