On 09 Aug 2014, at 06:48, meekerdb wrote:
On 8/8/2014 8:34 PM, Pierz wrote:
In "The Conscious Mind", Chalmers bases his claim that materialism
has failed to provide an explanation for consciousness on a
distinction between 'logical' and 'natural' supervenience, where
logical supervenience simply means that if A supervenes on B, then
B logically and necessarily entails A.
Because we can logically conceive of a (philosophical) zombie, then
it seems that consciousness cannot logically supervene on the
physical.
This kind of argument is very weak. "Logically" anything can be
true that doesn't entail "x and not-x", i.e. direct contradiction.
When a philosopher slips in "can logically conceive", it is the
"conceive" that does all the work. No one could "logically conceive"
of particles that were two places at once, or became correlated by
future instead of past interactions - until quantum mechanics was
invented. It's at base an argument from incredulity.
There is simply nothing in the physical description that entails or
even suggests the arising of subjective experiences in any system,
biological or otherwise. This is a well-trodden path of
argumentation that I'm sure we're all familiar with. However, since
it does appear that, empirically, consciousness supervenes on
physical processes, then this supervenience must be "natural"
rather than logical.
I agree.
It must arise due to some natural law that demands it does. So far
so good, though what we end up with in Chalmers' book - "property
dualism" - hardly seems like the nourishing meal a
phenomenologically inclined philosopher might have hoped for.
Bruno's version of comp seems like more nourishing fare than the
the watery gruel of property dualism, but Chalmers' formulation of
logical supervenience got me thinking again about the grit in the
ointment of comp that I've never quite been able to get comfortable
with. This is only another way of formulating an objection that
I've raised before, but perhaps it encapsulates the issue neatly.
We can really only say we've "explained" something when explicated
the relationships between the higher order explanandum and some
ontologically prior basis, demonstrating how the latter necessarily
entails the former. Alternatively we might postulate some new
"brute fact", some hitherto unknown principle, law or entity which
we accept because it does such a good job of uniting disparate,
previously unexplained observations.
Now the UDA does a good job of making the case that if we accept
the premise of comp (supervenience on computational states), then
materialism can be seen to dissolve into "machine psychology" as
Bruno puts it, or to emerge from arithmetic. But the problem here
is that we can no more see mathematical functions as necessarily
entailing subjective experience as we can see physical entities as
doing so. It is perfectly possible to imagine computations
occurring in the complete absence of consciousness, and in fact
nearly everybody imagines precisely this. I would say that it is an
undeniable fact that no mathematical function can be said to
logically entail some correlated conscious state. Rather, we must
postulate some kind of law or principle which claims that it is
just so that mathematical functions, or certain classes thereof, co-
occur with or are somehow synonymous with, conscious experiences.
In other words, we are still forced back on a kind of natural
supervenience. But the problem here is that, whereas with matter we
may be able to invoke some kind of ontological 'magic' that "puts
the fire into the equations" to quote Hawking, with pure
mathematics it is hard to see how there can be any such natural law
that is distinct from pure logic itself.
I think the way to look at it, is to ask how and why evolution
invented consciousness. It's pretty clear that not *all*
computation produces consciousness. So what is it about the
computation in human brains that produces consciousness. I
speculate that it's because it's computation that is about
something. It's computation that is representing, reflecting on and
predicting the world. That world is perceived by our sensory
systems and evolution built this representational system on top of
the sensory system. So when we recall something we experience
images of it. When we think about playing some music we experience
sounds. It has been my reservation about Bruno's step 8 that he
considers a dream state in order to avoid the question of it's
relation to the world, to being about something. I think the world,
which Bruno calls physics, is necessary as the object of
consciousness.
I agree.
Now when I've put this objection to Bruno in the past in slightly
different words, claiming that it is hard to see any way to
reconcile the language of mathematics with the language of qualia,
Bruno has invoked Gödel to claim that mathematics is more than mere
formalism, that it embodies a transcendent Truth that is beyond
that which can be captured in any mathematical formulation. At
least, that is the best summary I can make of my understanding of
his reply. He also claims to have discovered the 'placeholder' for
qualia within the mathematics of Löbian machines: the gap between
statements which the machine knows to be true and those which the
machine knows to be true and can prove to be so. It's a fascinating
argument, but it seems at the very least incomplete. The fact that
a machine making self-referentially correct statements will be able
to assert some (true) things without being able to prove them does
not compel me in any way to believe that such a machine will have a
conscious experience of some particular phenomenal quality. It may
be true that correct statements about qualia are correct statements
which can't be proven, but this does not mean that statements about
qualia are statements about unprovable mathematical propositions. I
might claim that Chaitin's constant is 0.994754987543925216... and
it might just happen that I'm right, through divine inspiration,
but Chaitin's constant is not a quale of mine. Bruno can point to
this space in his formalism to say "that's where the qualia fit",
but there is a similar leap of faith involved to actually put them
there as we make when attributing qualia to emergence from neurology.
Gödel's theorem might show that mathematics is more than mere
formalism, but it does not allow us to make the leap to mathematics
being more than abstract relationships between numbers. There will
always be some true, unprovable statement in any set of axioms, but
this statement will still be about numbers, not about feelings. If
we start to say mathematics is more than that, we are making a
metaphysical, and indeed mystical claim, and I believe we have also
expanded mathematics to become something else, something that we
can no longer truly claim to be maths as that is usually understood.
Now of course the "gap" between the maths and the qualia (I don't
like the obfuscating and often confused language of Craig's posts,
but I think "Gödel of the gaps" is a pretty good turn of phrase, if
indeed he is pointing to the same thing as me) is actually imported
into comp with the initial assumption of qualia supervening on
computational states. That postulate is of course unexplained,
mystifying and, when taken to its logical end as Bruno has done,
mystical. But when all is said and done, we're still left with it
as a "brute fact", if anything more naked than it was at the
beginning of the argument. More naked because it is even less clear
how we are going to get a natural law to bridge the gap between the
putative ontological basis of consciousness and consciousness
itself when that basis is pure mathematics.
That doesn't bother me as much. If you look back how we have
explained gravity, electromagnetism, atoms, thermodynamics,all
that hard science that is held up as the paradigm of explanation,
you see that at bottom is just precise, predictive description.
John von Neumann said, "The sciences do not try to explain, they
hardly even try to interpret, they mainly make models. By a model
is meant a mathematical construct which, with the addition of
certain verbal interpretations, describes observed phenomena. The
justification of such a mathematical construct is solely and
precisely that it is expected to work." That's why I think that
the "hard problem of consciousness" is hard because people think
that when we have a theory that works we still won't have an
explanation - but we will, just as good and bad explanation as we
have for gravity and electromagnetism.
OK. And with comp, the arithmetical self-reference, *and its many
relation with truth, is the best you can hope for. You get the
compleet explanation why more is just dishonest theology (assuming
comp!).
After all, what is mathematics? If it includes all consciousness,
is inseparable from it, if it encompasses love, pain, the smell of
rain, and everything else it is possible to experience, then we are
really talking about the mind as a whole, and the claim of a
reduction to arithmetic starts to look at the very least
misleading. Arithmetic is just the sugar coating that gives the
rationalist a better chance of swallowing the psychedelic pill.
Bruno seems to be able to make arithmetic pretty mystical - calling
parts of it angels and God. :-)
sigma_0 and sigma_1 set of numbers represent machines, computations,
effective or constructive objects.
pi_1 sets, sigma_2 sets, ... are non computable, non effective
notions, yet definable without problem, and I call them angels, to
distinguish them with gods, which like the set of all arithmetical
true sentences, or the set of all knowable sentences, are above the
union of all pi_i and sigma_i, and are not definable by the machines.
They can still point to it in a myriad of ways.
Gödel proved that if a machine is consistent then she cannot prove
that she is consistent.
Yet, the key is here, Gödel-Hilbert-Bernays-Löb proved that a machine
can prove that if she is consistent then she cannot prove that she is
consistent. Solovay found the theories which axiomatizes the all
propositional provability logic (G and G*), and Boolos, and Goldblatt,
(separately) also Kusnetzov and Muravitski (together), independently
found the logic of the non representable knower, the first person
S4Grz. You still need the Z and X variant to get the observable. In
fact the Z1* and X1* logics.
Bruno
Brent
"The duty of abstract mathematics, as I see it, is precisely to
expand our capacity for hypothesizing possible ontologies."
--- Norm Levitt
http://iridia.ulb.ac.be/~marchal/
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