On 22 Aug 2014, at 04:18, Pierz wrote:
On Wednesday, August 20, 2014 6:04:44 AM UTC+10, Bruno Marchal wrote:
Sorry for being again a bit out of phase.
On 18 Aug 2014, at 15:15, Pierz wrote:
What I mean is, your formulation, the words you use, add a certain
numinous quality to the description of what seem (to a non-
mathematician) to be dry abstract numerical transformations. Do they
truly develop a discourse about the transcendant?
Good question.
The fact is that I could explain to you the notion of arithmetical
truth. I can define it in the same sense that I can define you what
is an Hilbert space. Arithmetical Truth, although not definable in
the arithmetic language admits definition in slight extension of
arithmetic, on which machines can points correctly too.
yet, as far the very notion of arithmetical truth is unnameable
(Tarski theorem, also found by Gödel). Nor can the machine
generates, even working an infinite time, the whole set of
arithmetical truth. If she tries, she will be lead to adding
recurrently new axioms. There are no finite or constructively-
infinite machine/theory capable of unifying the "simple"
arithmetical reality.
Or do they merely mechanically prove their inability to compute
everything?
Well, they are universal with respect to the computable, so they can
compute everything computable. of course, we knows that there are
many non computable functions. But there are other nuances: there
prpositions which they cannot prove, yet are true, and they can find
it (by betting, etc.). There are true propositions that they can not
prove, and neither bet. There are truth that the machine can bet,
yet cannot even express, without becoming inconsistent. there are
truth that the machine cannot express at all, etc.
The incompleteness does not just separate the arithmetical truth in
two parts (the provable/the true but not provable), it introduces
nuance between "justification" ([]p), "knowledge ([]p & p),
observable ([]p & <>p), sensible ([]p & <>p & p). And most of those
nuances inherit the separation with truth. That is why we end with 8
typically different views in and on the (nont nameable by such by
the machine) arithmetical reality.
If I'm to have any chance of understanding what you are on about,
I'm going to at least a translation of the symbols. I've been
reading the wikipedia entries on modal logic so I assume [] relates
to the necessity operator and <> to the possibility operator?
That is the so called alethic interpretation of the modalities. It is
the one corresponding also to Leibniz semantics, which I have
explained sometimes ago. The corresponding theory is S5 (with notably
main axioms:
<>A -> []<>A.
But in the comp context, in AUDA, the box corresponds to Gödel's
arithmetical provability predicate, which by Gödel's theorem, obeys
like a belief (we don't have the axioms []A -> A, by incompleteness,
and instead of the alethic <>A -> []<>A, we have on the contrary that
<>A -> ~[]<>A: if A is consistent then I cannot prove that A is
consistent. Solovay solved the problem of finding a modal theory
axiomatizing the arithmetical and machine self-references. he found
two logics G and G*. I can come back on this. Normally this is
explained in the seocnd part of the sane04 paper.
So can you explain what []p & <>p means? It's provable(necessary?)
that p and it's possible that p doesn't really mean much to me. I
haven't really grokked this stuff yet.
Yopu might look for Kripke in the archive. basically []p means that p
is true in all worlds that I can access, and <>p means that there is
an accessible world. The belief predicate cannot be a probability
predicate, because with G we can have cul-de-sac world, in which []p
is "vacuously true", despite p is impossible/inconsistent. By adding
the "& <>p", we ensure that p is true in all worlds that I can access,
and that there is such a world, and that defines indeed a sort of
probability one. I will come back on this.
Perhaps you see all this drama playing out in the maths not because
it is there in the maths intrinsically, not because you are a
machine, but because you are a man of imagination, seeing your own
soul in the numbers the way early astrologers saw their soul in the
stars. Maybe the fit with the analysis of qualia truly means that is
where the qualia fit. To me it's more of a sketchy fit, suggestive
perhaps, like the bear in the sky which I can see if I squint. But I
can't argue the case until I understand the maths better.
No. The link with consciousness is made clear by the "yes doctor"
hypothesis, and the rest in math, verified by peers, etc.
I submit a problem (UDA), and I show that the machines of today can
already solves the propositional part of the solution, making the
theory testable empirically.
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.
Hmm, you make a distinction here that to my mind is at odds with
current cosmological thinking. Anthropic reasoning is trivial but
can still lead to rather startling conclusions. As Tegmark has
pointed out, it might have been used to predict the existence of
other solar systems, because the distance of our planet from the sun
must be highly "tuned" to stop us burning or freezing. So without
the assumption of specialness, we'd have to predict other planets
and suns to remove the coincidence. This reasoning seems unavoidable
in relation to the apparently remarkable tuning of physical laws to
permit life. There must be other physics, and lots of them, to
explain the coincidence.
? There must certainly be other geographies, but other physics? I
don't think this follow. On the contrary, with comp, physics is the
same for all machines. It can be true that for all machines, physics
is slightly different when dead, that's an open problem, but the
fact that quantization appears on all persons views, suggest that
there might be different physical realms.
So geography *is* the laws, at least to down to the level of the
constants that can vary (the "brute facts" of our standard model).
So the thing is, how will I know what belongs to the laws and what
to geography?
This the question that comp answer the best. the physics, with comp,
is as necessary than arithmetic. It is what is truelly invariant
from one universal to another. That is related to the fact that the
comp TOE is anything Turing equivalent. I choose numbers, and
sometimes combinators to avoid the risk of some number idolatry.
There may be observers in other universes with other sets of
physical constants and therefore different laws.
Not really. Only in "normal simulation".
I get what you're saying - we could create a simulation with
different laws, but any conscious inhabitant will always "escape"
the limits of the simulation and dwell in the measure of all
simulations. Fine, but see below.
OK.
I suppose you can always slip through the net by saying that the
real laws are the deeper ones that explain the different sets of
constants.
Wel, either the constants are determined by the consciousness flux
in arithmetic, and then they are laws, indeed, or the consciousness
flux can differentiate on different constants, and then they are
geographical. of course to day, we just don't know.
Yet, the shadows of some reason why some constant might be needed
appears already. But well, is very technical.
But that recourse does make you susceptible to the charge that any
set of laws whatsoever that we happen to discover will be OK with
comp, because whatever they are, that must be what the measure of
computations going through my state predicts! And also it might not
be tenable because it makes the laws so remote from the observer as
it were. I mean, if the laws derive from all the computations that
pass through a particular conscious state, can those laws really
reside outside not only of the observer's apparent universe, but of
their multiverse? That would lead to an awfully low substitution
level wouldn't it? Because to simulate the observer completely,
you'd have to simulate right back to the sum of all multiverses of
this type (I think).
No, the laws emerge from all the computations which are below his
substitution level, but above that level, those laws implement some
approximation of the abstract person they are, so that such a person
can manifeste itself relatively to a stable environment/universal
numbers.
OK, I think I have gleamed from the above responses the answer to my
question. Let me see if I have it right. According to comp, the laws
arise from the measure on FPI. If comp is not to directly contradict
real live physics, then this must directly relate to the FPI in QM
(MWI). In other words, the probability measures we observe in QM
must ultimately be derivable from the arithmetical measures. Now
cosmology and string theory are suggesting that it is highly likely
that there is a level II multiverse, i.e., a multiverse of
multiverses, each with its own different set of constants deriving
from the differing configurations of calabi-yau manifolds (in M
theory). You say above that there is only one law of physics, which
seems to me to be incorrect if these cosmological theories prove true.
Why? No. If M theory is correct, it is the M theory which has to be
derived from arithmetic (through comp). It is open if we get a unique
universe (but there are few chance), a unique multiverse, or a unique
multi-multiverse.
However, it would depend on what you mean by the laws. Normally by
laws we mean the observable laws of our environment, which string
theory suggests are local conditions. If comp suggests that the
local laws are driven purely by arithmetic, then it seems to me that
it would be directly contradicted by findings which support the
hypothesis of a level II multiverse.
Agreed.
In other words, the predictions of comp and string theory differ. If
that is the case, I'd be putting my "bets" on string theory (sorry
Bruno).
No problem. String theory is just QM + more precision (and some light
on the marraige between QM and GR, but that is not yet clear for me).
Comp and QM goes hand in hand, and it is too early to say we can
decide from comp if String theory is better than Loop Gravity (say).
If by laws you mean the "meta laws" that generate the local laws in
various multiverse regions, then comp has an out.
Yes, it is more like that.
Now above you say that the consciousness flux may be able to
differentiate on different constants, which suggests you are hedging
on this and open to the possibility that comp may define some meta
law rather than merely the laws we happen to know.
By definition, physical laws are supposed to be universal, in the
physical realm. If they are not, I call them contingencies (type <>A).
It is more geography, than universal (physical) truth.
Now I've only just started thinking about this, so my reasoning may
well be wrong, however... if there are other multiverses with
different constants, it is certain that some of those universes will
have three dimensions like ours and that such universes, being
infinite, will generate from time to time local conditions outwardly
identical to ours, yet with different trajectories due to the
(probably only slightly) differing laws. So observers will not be
able to remain isolated from other multiverses which generate
similar conditions. And it seems to me therefore that to any
observer, the "constants" will appear to wander over time according
to the measure of universes. In other words, quantum uncertainty
should apply to the configuration of the calabi-yau manifolds.
Whereas if comp were wrong, then the observer would be locked within
her specific set of physical laws and such fluctuation wouldn't occur.
I think that is correct.
But then, following on from this reasoning, I can't see any reason
why comp should preclude the existence of other universes with
totally different types of environment, following different laws,
because such universes would not overlap in the platonia with ours.
In principle, it would not seem to be any different from a
geographical difference - my environment has slightly different
"laws" from yours even on earth.
They exist in UD*, but without incidence on the measure.
For example, ice melts when left outside in my environment but maybe
not in yours (if you're Moscow man for example). Of course we know
that the laws are really the same, but only because we have
understood the underlying regularities. It seems to me the same
principle might apply all the way down to the constants and sets of
particles, and even beyond that to the possibility of environments
with laws unimaginable to us. I can't see why such a thing is
precluded if you allow for "the consciousness flux differentiating
on different constants".
OK, but only in the case those constants can fluctuate without
preventing my consciousness to get the right measure, in which case
those constants are not really constants, but parameters, obeying
deeper laws.
IF Z1* would have seen it modalities collapsing ([]p = p = <>p), then
I would have thought that comp makes the whole of physics into
geography. But Z1* gives a quatum quantization, making comp open to
the idea that the quantum principle is a really a fundamental, lawful,
feature of physics.
Perhaps then comp does have a quite concrete prediction: that this
specific set of physical constants is the only one in which life can
exist. Although admittedly it's a pretty hard prediction to test.
Unfortunately it is an open problem.
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.
OK that may be true, but without an observer, nothing will exist to
select out that computation from the chaotic infinities.
Right. It is not a physical reality in the strict sense of the comp
definition of physics (the 1p measure), but such digital
approximation does plays role when having observers, and those
having non observers, like a simulation, at the quark level, of
earth, + asteroids killing all life in the early days, still exist
in arithmetic.
I don't know how you can say that the leaf meaningfully exists,
because other computational threads will destroy the leaf instantly,
do every conceivable thing to it, and then who can say there's a leaf?
because we can agree with some 3p definition of leaf, and sounds,
and agree that in that computation, a leaf is falling, and create a
sound, and we can see that nobody can hear it. We might be able to
hear if we build some interface with that computations, normalizing
it in our (hopefully) stable physical reality.
Without an observer's measure it has no stability
Come on. A computation is a stable relation which exists among
number. nothing can be more stable than that. It is of the type "17
is prime".
You're right. I'm speaking too loosely. Still, the notion of those
computations having any meaning as a "leaf falling" seems dubious to
me. But I need to meditate on this a bit more. :)
OK. You might help yourself with some good book on computability
theory. The fact that computation are arithmetical object is not
obvious, and admittedly counter-intuitive. That was better understood
before the advent of concrete computers!
and can only be projected artificially into the computations by some
observer who already has the concept of a leaf. Frankly I'm
surprised to hear you argue this.
It follows from the "arithmetical realism", (the belief that 17 is
prime is absolutely true), and from the discovery that addition
+multiplication (and a bit of logic) is Turing complete.
"My" theory, is really only elementary arithmetic, or the two axioms
Kxy = x ; Sxyz = xz(yz), and nothing more. At the metalevel, you can
connect the sense/consciousness by the acceptance of the "yes doctor".
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).
Yet as I said, there are different geographies, and it gets hard to
distinguish conditions from laws.
At least comp provides a simple criteria. Whatever is not a
consequence of arithmetic is geographical.
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.
OK
(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.
Not to me. I probably need to clarify what I mean by this idea. "24
is not prime" is not a brute fact because it is a truth that arises
from and within the entire interconnected logical/numerical of number.
Hmm... It is just the statement that the row
IIIIIIIIIIIIIIIIIIIIIIII can be divided in a finite numbers of parts
so that you get a rectangle both both side equal or bigger than 2.
Let us try:
IIIIIIIIIIII
IIIIIIIIIIII
OK, we did it, so 24 is not prime.
Is 23 prime?
I let you try to convince me on this.
In a platonist, classical logical, sense, you are right. All true
and provable propositions are somehow equivalent, and thus related.
Even false proposition can be related (trivially) to true
propositions, like in the true fact that "24 is not prime" ->
Goldbach conjecture & Rieman hypothesis! (trivial!).
It's a truth in no way independent from every other mathematical
truth,
So we basically agree. this makes them even more independent from
you and me.
and in fact you have to swallow all the truth whole because each
part of it necessitates the whole.
Yes, in some sense, but nobody asks you swallow all of it in two
seconds, and sinc eGödel, we know that all machine can swallow only
a tiny part of it, even with eternity as a given.
You can prove and explain the statement in an infinite number of
ways. But in say string theory, the fact that "space has 11
dimensions" is "just so", take it or leave it. You can justify
believing it by virtue of what it explains, but nothing explains it.
Nothing against string theory of course, but I contrast that
situation with your example.
It means that string implies 11 dimensions is true independently of
you and me, and of the truth or applicability of strings to physics,
or to something else (the bosonic string theory can be used to prove
a theorem by Lagrange and Jacobi in pure number theory).
Then the raw consciousness here and now seems to me to be a first
person sort of brute fact.
More so, yes. Descartes' conclusion. I should have qualified my
statement by saying that no brute facts exist except for everything!
I mean that there is one brute fact, infinity itself,
You are quick here. But what you say please me, as I tend to believe
that consciousness has some relation with infinity, but this is out
of the topic, I think.
the great It, Being, God or whatever. And the first person moment is
our little piece of that brute fact.
OK. It is more than a "piece" of it, I think, but I relate with the
image.
Well then, it is our place in it and our perspective on it. Better?
It is complicated. I would say it is the place and perspective, but in
relation with truth. But I am aware I use non trivial information from
logic. We will have to come back on this.
But there is nothing specific we can ever identify, nothing finite,
that is not really defined by its relations with everything else.
That's what QM tells us - a particle can't even exist in one place
without exploring every other position in spatial infinity - the
part is defined by the whole and implies the whole.
Hmm... OK.
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.
Aha, so maybe we agree.
Yes. That might be possible too :)
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).
You have the disadvantage of rigour here :) I just guess. Can you
explain why infinities are a problem for Gödel's incompleteness?
Because we have no proof today that those special infinities, which
crops in the machine 1p physics, does not yield a non Turing
emulable reality. Physical gods cannot yet be excluded. After all,
we do have arithmetical Gods (entities, which can be Löbian, or not,
there are many types) which are not Turing emulable.
Keep in mind that understanding comp makes us more ignorant. It
enlarges our ignorance like no discovery ever did. That's indeed why
it has to make us modest. Doubly so in theology and Everything
theories.
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.
Right!
OK, nice.
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.
Ha ha yes! The younger one is, the more curious about the next world
cup, but I hope to be more curious about the great mystery of death
than any of that by the time I get to facing my own end. A friend of
mine was talking to me yesterday about meditating and watching his
thoughts die, how they protested and tried to hold on before fading
away into the void, and how he would simply watch them go. And I
said, "yes and one day you will watch and let die the great thought
that was you and your life". So it is.
I think you know we can even train ourselves to do that, by working
on dream lucidity, for example, or by different sort of exercises
and arts, or by different plants consumption, which seems to help.
Hard to know if the experience will correspond with the dying
experience, but at least we can learn how large the brain
consciousness states spectrum can be. Altered state of consciousness
can provide a sort of stereo-view on consciousness.
Ah well I've had plenty of training then! :) With the plants (and
the fungi) and the dreams. I used to dream lucidly almost all the
time - not always full blown lucidity of course, but I was aware at
least dimly in most dreams that I was dreaming. But it hasn't been
that way for years now. When I did lucid dream more I never saw it
as being about "controlling" the dream state, as some proponents do.
Agreed. Lucidity and control are orthogonal. Or they do overlap, but
only a little bit. It took me years for NOT flying in a lucid dream.
Frankly that never works; all you can do is influence. I saw it as
training for death, though you are right: I have no actual idea if
it has any correspondence with dying.
Salvia seems to make explicit links, or convincing links in that
respect, but ... a priori there is no reason to believe more a plant
than a government ... The experiences remains interesting tough, but
only for enlarging the doubting. Platonists knows that an experience
ever proves anything. Experiences only suggests this or that
assumptions, but they remains assumptions.
Bruno
PS I will think bout how to explain more of the modal logics, and its
relation with computability and provability and machine's
introspection, and UDA, ...
Bruno
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
...
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