Sorry for being again a bit out of phase.
On 18 Aug 2014, at 15:15, Pierz wrote:
On Monday, August 18, 2014 9:19:32 PM UTC+10, Bruno Marchal wrote:
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.
"Discourse", "unnameable", "transcendant": how the qualia sneak in
even as we try to explain them!
Yes, it is in their nature.
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.
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 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.
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".
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.
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.
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 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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