On 09 Aug 2014, at 05:34, 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. 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. 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.
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
Well, that's Gödel's discovery, with "transcendent is defined by
"satisfied by the model (N, +, *) but non provable by the machine
concerned.
That entails that the following logic, although being the meat-logic
of the set set of arithmetical beliefs, obeys completely different
logics:
[]p
[]p & p
[]p & <>t
[]p & <>t & p
And more: Gödel's incompleteness split in two, three of those logics
([]p, []p & <>t , []p & <>t & p). One part (derived from G) describes
what the machines can prove on this modality/person-point-of-view, and
one derived from G* (representable in G) describes what is true about
those modalities, including the laws that the machine cannot proves,
but still can guess or intuit, or observe ...).
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.
But nothing can do that. You ask for too much. We *assume* comp all
along, even if in the math part, we do it only at the meta-level, to
ease our comprehension. In he math part, you can forget consciousness,
and only talk in terms of beliefs, knowledge, etc. Those are defined
precisely, either directly in arithmetic, or in terms of arithmetical
notions (set of numbers).
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.
Careful. I don't say this.
All you need is the classical (analytical) most common axioms for
knowledge, or knowability:
(Knowable p) -> p
Knowable (p -> q) ->. [Knowable (p) -> knowable (q)]
and for the richer introspective form:
knowable(p) ->. knowable(knowable(p)).
I study very special machine, who have simple correct arithmetical
beliefs. Then, applying theaetetus definition (knowing p = justifying
p, with p true) gives a logic obeying the standard theory of
knowledge, and you can use it to talk with the machine, noitably on
the difference between 3p and 1p, etc.
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.
It is the same as attributing consciousness to any other one person
than oneself. You need just to accept the axiomatic definition
beliefs, knwoledge, etc. It fits, like we fits between us right now,
despite this never prove anything. But this we know, we assume comp,
and neither in the UDA, nor in the AUDA, we pretend having provided a
proof that comp is true, or that the classical theory of knowledge is
true. the nice thing is that we show them empirically refutable, as
their restriction to the sigma_1 UD must give the logic of the
observable. And unfortunately it fits, so *classical* comp is
confirmed (not proved), and not yet refuted.
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.
But then with comp, your own statement should be seen as a statement
about some (very) complex number. All statements in physics are also
just statement about numbers and numbers relations.
I guess you are not aware of the crucial distinction between
extensional mathematics, and intensional mathematics, which take into
account the body of the sentences/machines making sentences, with
notion of (self) reference.
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.
Indeed. I do not hide this. It is a key point. Comp entails it belongs
to arithmetic, up to a theological act of faith; when saying "yes" to
the doctor. You put your life in a number on that occasion. That is
why I insist it is theology. Then in AUDA, we get what was needed:
machine looking inward *are* confronted with many sort and types of
non justifiable (by them) truth, about them.
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 you do it when you bet on comp and say "yes" to the doctor. Then
with Gödel we get that a machine can guess a reality (<>t, by Gödel
completeness theorem it is equivalent, with model playing the role of
reality), and justifies, as we do, that if that reality exists, it
can't be proved: <>t -> ~[]<>t.
We can also define the mystic part of the machine by all the
intensional variant (see above) of G* minus G.
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.
Pure arithmetic. Even pure sigma_1 arithmetic (the UD*). We get it
because the comp act of faith, connect consciousness, or its
invariance, to computer science theoretical notions.
It is a fact that computer science is embedded faithfully in the
arithmetical truth. No theories at all unifies that.
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.
Mathematics does not include consciousness. It is that once a number
is Turing universal, or sigma_1 complete, its view of arithmetic is
provably beyond mathematics.
Mathematics (we need only arithmetic) is only the 3p view "outer
view", but theaetetus applied to provability leads to first person
view much richer than arithmetic.
Understanding comp is understanding that we are, even just for
arithmetic, confronted with the Unknown. It leads to coming back to
the scientific attitude in theology, and perhaps the human sciences
and affairs.
I just derive consequences for an assumption, which link consciousness
and first person to 3p number-object that we can put on a disk for
awhile, and I have never hide the theological aspect of it. In fact,
it is part of comp to admit it is a theology. We can just hope for it,
or fear it, and perhaps refute it, thanks to the level of rigor and
precision it permits.
Bruno
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