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.
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.
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. :-)
Brent
"The duty of abstract mathematics, as I see it, is precisely to
expand our capacity for hypothesizing possible ontologies."
--- Norm Levitt
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