On 17 Aug 2014, at 14:43, Pierz wrote:
Thank you Bruno for your response. Honestly I don't know if I'd say
yes to the doctor.
Nor do I.
Actually, even if comp is true, I might say "no", because I might not
trust the doctor's skill, or the choice of the level.
It's cowardly of me, but I think I'd like to see the device work on
someone else first. If they appear to be fine after the operation
then I guess I'll go under the knife - and have to swallow the
logical consequences whole!
Me too.
Your reply helps. I suppose what I feel is missing from the account
is the *necessity* of qualia, because it seems to me that everything
that exists, necessarily exists, and as it stands in the comp
account, the necessity for there to be an interior to mathematics
remains mysterious.
All machines introspecting itself, in the standard sense of Gödel, or
Kleene, is bound up to develop discours about something unnameable
which transcend them. But when you study the mathematical sructure of
that transcendent reality, it fits with previous analysis of qualia
and quanta.
My guess is that comp is wrong, but it may be that it is still a
whole lot more right than materialism. It may be wrong in the same
way that general relativity and QM are "wrong", i.e., correct, but
to some limit. My next step is to read the Amoeba's Secret and see
if I can start to wrap my head around the S4Grz and the []p & p -
the maths is still largely a mystery to me.
OK. It is also in the second part of the sane04 paper.
However I wanted to put some less argumentative and more curious
questions to you about the way you imagine the comp-driven universe
to be (yes, there's no universe, I know, but I lack words: this
apparent "space" we inhabit?). The question comes up in the comp
account about the physical explanation for the origin of the Löbian
organism the self-consistency of whose mind creates the appearance
of matter (allegedly). Liz and Brent were throwing around this "if a
tree falls in the forest" question on the MGA thread. The account
whereby the observer arises out of the long, deep history of matter
sure looks convincing. What is the status of this alternative origin
story if the observer is actually grounded in Platonia? I seem to
recall you talking about the idea that the observer's self
consistency demands that it also find a consistent account of itself
in the "material hypostases". OK, I can go with that, but something
here still troubles me. We can't surely dismiss these origins as
fictive any more than we can dismiss the other observers we find in
our environment as fictive. How do you see the relationship between
these accounts (the exterior physical and the machine
psychological)? It occurs to me that in some ways the anthropic
explanation of the fluky coincidences of the laws of nature
resembles the machine psychology account - in that the requirements
of existing as a complex self-aware machine in a sense "cause" the
laws of the universe to be what they are. The need for logical
consistency constrains the environment and its laws in very
specific, complex ways. It's almost strange that it's taken us so
long to realize just how extraordinary it is that the "laws" work,
that they are capable of creating the complexity and beauty we see.
Only a huge, unfathomable amount of selective work could lead to a
structure like the calabi yau manifolds etc, with its staggeringly
elegant capacity to generate complexity from simplicity. So... that
work I describe would be the infinite computations in the UD, and
just as all the complexity in the UD is surrounded by a vastly
greater region of garbled junk, so the physical account relies on a
similar surrounding region of incoherence. Which makes me wonder:
are the two accounts just mirror images somehow? Are the garbled,
dead, sterile, incoherent universes the reflection of those infinite
sterile computations? Is there an observer of these dead regions? Or
are the observers like fleeting Boltzmann brain or quantum fuzz in
the void: incoherent, fleeting, barely aware, but just there enough?
I hope I make sense...
The anthropic account might "explain" the particularity of geography,
perhaps trivially (we are made of carbon, so there must be a carbon
producing machinery in the neighborhood, ...). This can use Bayes, and
"ASSA (absolute self sampling assumption). The physical *laws* should
be extracted from the measure on all computations going through my
state, and should be normally the same for all universal machine.
Then the arithmetical realism suggests the existence of approximation
of physical realities, without observers. The falling leaf will make a
sound (a 3p wave), but of course, without observers, there will be no
perception or qualia actualized there. Those realities can even have
the correct relative measure, which means here that if it was the case
an observer would be there, it would be stably there from his first
person points of view. A bit when sending a man on Mars. He can
believe that what he see existed there before he walk and see it on
Mars, a priori.
Now a second thing. Comp suggests, or predicts, Many Worlds, and
says physics arises from the measure of the observer computations.
But string theory suggests many physics(es!). So this is intriguing.
Are we humans (and other animals in this multiverse) bound to one
set of physics as it were, while perhaps other (more complex?)
observers occupy a world with different laws?
Normally, no. The physical laws are ... laws, with comp, and so are
the same for all observers (universal machine).
But we do get arithmetical quantization in more than one hypostases
([]p & p, []p & <>p, []p & <>p & p, with p sigma_1 and see at the G*
level).
So, we might still get more than one physical realm. Maybe the physics
coming from []p & p is the physics of heaven, but I am not sure of that.
Because it seems we have only one of two options. Either the other
possible physics are all sterile, or there is something about the
types of mathematical structures that we are that keeps us bound to
this particular set of observer states, not letting us "slip over"
into universes with different laws?
The laws will always assured the existence of computations in which
you survive, and have that quantum MW aspects, but in some
consciousness state we might live some "phase transition" between
different physical realms. Obviously, we cannot get a physical reality
in which there is no observers at all. Eventually that will depend of
what is in the core set of laws.
Might we not be capable of a kind of mathematical state change that
would see us metamorphose, wake up in a world with different laws?
Might death and birth not be such state changes?
Death might be like ging from []p & <>p to []p & p, but I am not sure.
I am open to what you say, but I can't derived this from the universal
machine interview, yet.
(This last suggestion no doubt getting too mystical for many whose
self-appointed job it is to crush any idea that smacks of the Big
Guy Upstairs who we've had so much trouble with in the past, but
you're not afraid of the G-word it seems, so I ask anyway (not that
survival of death has to bring God with it, but some people are
sensitive about these things.))
My own pet idea at the moment is a simple rule that seems at the
least strongly suggested by scientific experience to date and to me
just intuitively compelling. It is simply that there are no brute
facts.
OK. Although with comp, I think we can without fear put the elementary
arithmetical truth in brute fact. "24 is not prime" is a sort of brute
fact to me.
Then the raw consciousness here and now seems to me to be a first
person sort of brute fact.
Or another way of saying this is that there are no "hard"
ontological boundaries, no places where that which exists nakedly
abuts non-existence, in the way that a brute fact is encased as it
were in a boundary of nothingness beyond which one cannot travel. So
far, wherever we look we find that apparently hard boundaries are
illusions. Every apparently closed system turns out to be incomplete
(yes Gödel again), to be contained as a special case within some
more encompassing whole.
But those closed systems are the theories, or machines, brains,
observer. They are incomplete with respect to arithmetical truth, and
"reality". By definition "reality" or "god" provides the "hard
ontological boundaries". With comp, arithmetical truth is enough for
the 3p reality. This, from inside, will indeed escape all possible 3p
boundaries.
I believe this is true infinitely and in all "directions".
That is correct for the internal view in arithmetic, which contains
the physical and mental realm.
And so when people pin their hopes on string theory as a Final
Explanation, I don't believe it, just as I don't believe the spatial
dimensions will stop at the current count of 11. They can't, if my
idea is correct, because that 11th dimension would be a hard
boundary. The flower of knowledge will keep opening and opening.
This is an open problem to me. Gödel's incompleteness might still not
be applicable to the physical realm, as infinities crops up there.
Possible, but we do not yet know that (even in the comp frame).
And so I also do not believe in the boundary of death, the ultimate
brute fact. So - maybe I won't say yes to the doctor but yes to
Doctor Death instead, preferring to embrace the transformation than
to perpetuate the machine in its current form.
That's a position close to the comp enlightenment of the universal
machine :)
Once you have the cognitive ability to consciously say yes to a comp
doctor, by virtue of comp (and not by virtue of added magic like god
and/or primitive matter), then you have the cognitive ability to know,
assuming comp, that as far as immortality is the "goal", the digital
brain is not needed. With an artificial brain, you will just extend
artificially the samsara, and miss the nirvana, to speak in buddhist
terms.
People will undergo brain transplant, not for being immortal, but for
keeping high the probability to see the next soccer cup, or the grand-
grand-children getting married ... Buddhist would call this
attachment, as their goal is to cut the cycle of lives.
Bruno
On Sunday, August 10, 2014 4:01:00 AM UTC+10, Bruno Marchal wrote:
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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