On 1/6/2012 18:57, Bruno Marchal wrote:

On 05 Jan 2012, at 11:02, acw wrote:

Hello everything-list, this is my first post here, but I've been
reading this list for at least half a year, and I'm afraid this post
will be a bit long as it contains many thoughts I've had on my mind
for quite some time now.

Welcome acw. It looks like you wrote an interesting post. But it is very
long, as are most sentences in it.
I will make some easy comments. I will come back on it later, when I
have more time.

Thanks, I look forward to the full response.


A bit about me: I'm mostly self-taught in the matters concerning the
topics of 'everything-list' (Multiverse hypotheses, philosophy of
science, 'rationalism', theory of computation, cognitive science, AI,
models of computation, logic, physics), and I greatly enjoy reading
books and papers on the related subjects. My main activities center
mostly around software development and a various other fields directly
related to it.

OK. Self-teaching is often of better quality than listening to others.


It's fine and allows one to better study some matters, but it also may lead to gaps in knowledge if one isn't aware of the gaps.


I will give my positions/assumptions first before talking about the
actual topic I mentioned in the subject.

One of my positions (what I'm betting on, but cannot know) is that of
computationalism, that is, that one would survive a digital
substitution.

OK. As you know that is my working hypothesis. As a scientist I don't
know the truth. I certainly find it plausible, given our current
knowledge, and my main goal is to show that it leads to testable
consequences. Mainly, it reduces the mind body problem into an
arithmetical pure body problem.


Neither do I claim to know the truth, or should anyone else, if someone claims to know it, they may be telling a lie, voluntarily or not. Our senses aren't that reliable to claim absolute knowledge about the world and even when talking about mathematical truth, the incompleteness theorem applies to everyone.

Instead of truth, I tend to assign a theory a high confidence value, or to consider it more probable than others, but the only thing that we can really do beyond that is testing, falsification or verification of our expectations/theories.

It sort of was the main goal of my post - to show that there are some practical ways to test COMP that one might be able to do some day.



There are however many details regarding this that would have to be
made more precise and topic's goal is to elucidate some of these
uncertainties and invite others to give their ideas on the subject.


Why computationalism?

Chalmers' "Absent Qualia, Fading Qualia, Dancing Qualia" thought
experiment/argument shows that one can be forced to believe some
seemingly absurd things about the nature of consciousness if
functionalism is false (that is, if one assumes that conscious nature
depends on more than just functional organization, such as some
"magical" properties of matter).

Taking it from functionalism to computationalism isn't very hard
either, all it takes is assuming no concrete infinities are involved
in the brain's implementation and the CTT(Church Turing Thesis) does
the rest.

OK. And if you make explicit that COMP assumes only the existence of a
level, then you see that COMP, as discussed on this list, is a weaker
hypothesis that all the comp discussed in the literature. That is why I
refer to the generalized brain. The level can be so low that the
"generalized brain" is an entire galaxy or even a multiverse quantum
state. This does not make the assumption trivial, the main reversal,
between Aristotle theology and Plato theology still follows.

Too low a level and functionalism is no longer very practically testable, but the consequences of COMP (reversal) would still apply if it's true. In my example (the experiment) from the previous post, I tried to assume a reasonable (mid(atomic)/high(neurons or higher)) substitution level, in that it could be tested someday. Such a mid/high-substitution level allows for the mind's implementation to become substrate independent (SIM), but if the new implementation isn't too exact, would the continuation likely or not: it should be conscious, but would it be likely to experience a continuation into a SIM after saying 'yes' to the doctor? Would it be more likely to end up "amnesiac" and just choose not to become a SIM?

I've discussed the matter of errors or inexact 'copies' in the previous post and will wait for your response on that part before going into more details again. In a way, I think it might be more reasonable to consider the mind's implementation and the environment's implementation separately (even if environment+mind are at least one (and infinity of) TM in COMP) as the environment has more chance to vary and only indirectly leads to conscious experience, or that it might be more of a wildcard.

While I cannot ever know if concrete infinities are involved
in the mind's functioning (leaving aside various forms of observer
selection from some Plentitude, such as Marchal's UD* or Arithmetical
Platonia, or possibly some larger ontology, although if higher
infinities do exist ontologically, I don't think there is any way for
a way for a system that isn't even as powerful as an UTM (Universal
Turing Machine) to be able to know if they have a access to a genuine
oracle of a more powerful system; to be more specific, in the state we
are now, we have finite memory), neuroscience does indicate that we
(our brain) is a (partially self-modifying) neural network and that
each component (neuron) of this network can be simulated
digitally.

That's a good evidence. But I would not say yes to a doctor if he misses
the functional composition and state of the glial cells. I can imagine
that my consciousness is "in" the neural network, but some deeper
personality traits can be dependent of the glial cells.

That might be true, although more research would have to be done to know for sure how much glial cells matter. I wonder if you'd be you if you lost one very minor personality trait (let's say one encoded by 5 neurons+their glial cells). We tend to lose a lot more during a single day. A SIM would be less likely to forget due to his implementation being less error-prone (and backups).




Not only that, it also seems to be very resilient to noise
and component loss, it's also very adaptable (neuroplasticity).

Like everything in nature, it is highly redundant.



Various research shows that the substitution level might even be
higher than the neuron level, in the sense that the abstract
functionality performed by the brain still stays nearly the same after
more high-level substitution. An example of this view is described in
the Jeff Hawkins' "On Intelligence" book and in abstracted models of
the visual system where instead of neurons one can just use larger
components which perform some forms of bayesian inference based on the
input given. AGI research hints that the mindspace (the space of
possible minds) may be much larger than we ever thought, and this is
only talking about that of finite computational minds, which obviously
have no concrete infinities in their implementation. I have a very
hard time imagining what an infinite mind could be, how it could even
think a single thought, how it could maintain unity of consciousness,
or be embedded in time, hence I will assume most minds are finite and
have bounded or unbounded memory.

OK.


We are currently memory bound due to
evolution/physical limits, but an AGI(Artificial General Intelligence)
living within some TM(Turing Machine) or a very robust potentially
infinite universe could have unbounded memory (which is finite at any
given time, but potentially growing, depending on the actual program).


I don't think humans are memory bound. They use their environment to
extend their memory all the time, from cave's wall to magnetic tapes. It
is not different from a universal (Turing) machine using bigger and
bigger portion of its tape/environment in the course of a computation.


I only considered the internal memory storage (the brain), but if we consider the entire environment (and assuming the environment isn't memory bound, which seems to be the case - it's expanding at least at the speed of light, however unfortunately, it doesn't seem trivial to be able to take advantage of available resources past a certain limit as 2 very distant objects can be moving away from each other at speeds faster than the speed of light), you're right. If COMP is assumed (and unusual continuations), there are ways to even get around those limits.


CTT tends to follow from the belief that 'abstract finite rules
applied on abstract finite objects can be applied and they will always
give the same abstract result in any possible universe', which is
fairly close to some form of Platonism, however there is substantial
(mathematical) evidence for CTT being true. The evidence is in the
form of the equivalency of a large class of abstract machines (for
more on this you can read Boolos, Burgess and Jeffrey's "Computability
and Logic").

That's a powerful empirical evidences indeed, especially that those
abstract universal system can be very different, like
number+addition+multiplication, combinators, quantum topology, billiard
balls, Conway's game of life, Penrose pavements, etc.
But the conceptual reason which makes me think the most that CT might be
true is the closure of the set of partial computable functions for the
Cantorian diagonalization procedure. Diagonalization is a killer of
universality-pretension, but it fails on the universal (with respect to
computability) machines. Unlike the fact that it succeeds for
provability (Gödel) or definability (Tarski), or infinity (Cantor), we
cannot use it to find more powerful computation system (with respect to
the class of computable functions).

That's strong evidence indeed. As a side note, I think universality would be lost if one tries to go hypercomputational (formally), but it also seems unlikely we'll ever be able to physically implement it (in the case COMP is false), or be able to truly know that we actually have a hypercomputational oracle on our hands.


Some other interesting results are how everything that we
can talk about regarding formal systems can be encoded and formalized
by a TM-equivalent machine. Of course, this doesn't mean that a
system is consistent, merely that we can't talk more about it than a
machine could (within some system, you can of course assume stronger
systems and so on). Personally I'm willing to assume PA(Peano
Arithmetic) consistent and that valid sentences in it have a truth
value, although I cannot /know/ that for sure, I'm only betting on it
being consistent.

Well, you are not alone. Virtually all mathematicians assume PA
consistent, and even the consistency of stronger systems (in which you
can prove the consistency of PA by "quasi elementary method". You can
prove the consistency of PA from transfinite induction up to a
reasonably little ordinal (epsilon_0), or you can convince yourself of
the consistency of PA by appeal to the intuitive (but accepted in math)
notion of arithmetical truth (which can be defined in reasonable set
theory).

In a way, I do wonder what exactly would it mean for PA to be inconsistent, or its standard model to not exist. Not entirely sure there would be any math that would be left standing, except maybe some logic.

I'm aware of Gentzen's proof about PA's consistency by transfinite induction, although I still need to do more studying to better understand some of its details.

> This shows that humans are richer Löbian machine than PA, very
> plausibly. Nevertheless, with the COMP assumption, we might defend
> the idea that we might not be so much stronger than PA.

Possibly, although humans can just take a formal system and assume its truth, then reason within it. It's hard to a human to claim to know for sure that a system is consistent, it seems to me to be as much as a bet as COMP.

For much stronger formal systems such as some set theories that talk of higher infinities, it might even be harder to claim to know their truth as they can talk about behavior of infinite processes (non-halting), which is far from what we can assume.

Yet, I do think such stronger formal systems are very useful as far as taking shortcuts about finding the behavior(such as convergence) of such processes - I don't think you can ask a scientist to give up his analysis or differential equations just because there's a small chance of ZFC not being consistent.

I also tend to try to think a bit differently about the levels of truth a human can know. Direct experience is truth, although not always communicable - it is also the truth of the lower-level of systems that support the human's existence. Mathematical truth where we reason formally about some system is also truth (if a system is consistent and sound, but we cannot always know), but it's non-experiential, and having a wrong belief about it wouldn't make your lower-level self inconsistent, although you'd be wrong if you were asserting it as truth - it's a bit like how a Turing Machine which encodes a theorem prover for some system can talk about what's provable (or isn't provable) within it, but isn't the formal system itself. If one identifies directly with the system, it's not hard to make the same mistake found in some conclusions about the "Chinese Room Argument" or "China Brain Argument".

On the other hand, I do think that PA formalizes well how we think about arithmetic and it likely matches our beliefs (unless you're an ultra-finitist, and thus reject the induction axiom or the natural numbers, but rejection of such an axiom is rather strange, as one could perform induction manually for any k steps, but then one assumes eventually that there is some finite k+1 step where it fails). In that way, truths about PA can be lifted and used as truths about the world (in science and more), and if COMP is true, truths about computability have very far-reaching consequences.

> Also, there is no interesting theorem in math which cannot be proved
> in PA, except in mathematical logic and
> higher algebra (category theory).

What about results that can be shown to have very small proofs in Second Order logic, but have non-trivial (longer than we'll ever be able to write) proofs in first order logic (Boolos' "A Curious Inference") or that Goodstein's sequence's termination cannot be proven in PA, as well as certain facts about non-primitively recursive computable total functions?


I'm agnostic about the consistency of stronger set
theories that imply higher infinities, although it is very useful to
be able to talk about them, regardless of their ontological existence
- they might even have useful computational consequences: such as
assuming certain types of processes will converge to some specific
value and so on (surely calculus/analysis is scientifically very
useful), although of course, with stronger systems we risk
inconsistency even more.

OK. But a lot in "real analysis" is arithmetic in disguised. I heard
Maccintyre saying this, and that view is also defended by Torkel Franzen
in his lovely book "inexhaustibility".

Some of it might be translatable to PA. I'll have to read the works you mentioned to get a better understanding of it.


Post-edit note: When I speak of TMs in this post, I mean any
Turing-equivalent machine as by CTT. It might have been better for me
to have used UM(Universal Machine) or UN(Universal Number) instead of
TM, as the particular choice of universal machine implementing the
computation is irrelevant, just that some UTM-equivalent machine exist
and the UTM runs UD at least, or merely UD running directly as some
specific Turing-equivalent machine. I've seen the terms used in this
list, and I'm not always sure they are exactly the same concept, but
they seemed to me (although I may be wrong when the term LUM(Lobian
Universal Machine) is used, that seemed to me to be more about
specific formal systems that are used to model truth that can also be
generalized to persons).

OK. LUMs have just a little more provability (not computability) power.
In fact provability itself can model computability. In that case a
theory like Robinson Arithmetic (RA, it is PA without the induction
axioms) is already Turing universal. But it lacks serious introspection
ability, which are present for PA and ZF (which are Löbian, they obeys
Löb's theorem). More on this later, probably.


I'm currently reading some of Boolos' books on the matter, when I'm done I plan on re-reading AUDA. Looking forward to your elaboration on it as well.



The assumptions so far: Mind, COMP, CTT, Cons(PA).

Well, as I explain COMP, it contains the mind, CT and cons(PA)
assumption. In fact it assumes even more: it assumes that PA is not just
consistent, but arithmetically sound. But all mathematicians assumes
this (consciously or not).




The 'Mind' assumption is just that I have a 1p (first person) internal
view, or consciousness. It had to be stated as if you only assume a
3p(third person) world, there is no reason to believe that the 1p view
exists. To someone else that only considers that ONLY the 3p view
exists (let's say, some physical reality for the sake of the argument,
or 'materialism'), explaining the existence of 1p seems impossible, so
they eliminate it away with Occam's razor by saying that all this 1p
view talk is the person being defective/delusional "by design"(not in
the sense of "Intelligent Design", just due to how it happened to
evolve) and there's no such thing as 1p. The major problem with that
is the 3p world is only inferred to exist using the 1p view, so belief
in a mind is natural, but then so is the inference of the 3p world.
At least it seems to be that using 1p and by induction to get to 3p
and then to notice that there doesn't seem to be a reason for 1p to
exist from the 3p view and thus to conclude that 1p doesn't exist
would make the reasoner's beliefs inconsistent.

To believe that 1p are delusional is self-defeating. The 1p have been
methodologically eliminated by the Aristotelian, but this has led to the
reification of nature, and the abandon of the fundamental human science
to political authorities, and to making of the mind-body problem, and
then its hide under the rug. But her-and-now-consciousness or 1p views
are our only certainties. The rest is (3p)-
theories/conjectures/postulates.



I agree with most of that, but I'm not entirely about the politics part. In another way though, I do wonder how can someone claim to have no phenomenology and then claim that it only seems they have a 1p view, because the 3p view says that that must be the case. In another way, it may be that one trusts the 3p view more than the 1p view, which is strange because the 3p view only exists because the 1p view is able to reason about it (in COMP, both exist of course (as computation and arithmetical truth about it), but it also says that one should care about 1p as much as they care about 3p).




From these assumptions one can use Marchal's UDA (Universal Dovetailer
Argument) and MGA(Movie Graph Argument) to notice that if we are
conscious and we have a digital substitution level then any notion of
"physical" reality loses its meaning/explanatory power, and that
physics is just local relative numerical phenomenology, or just a
shared 1p reality, you also get a plentitude for free (in UD*, in AR)
and 1p indeterminacy similar to that of MWI(Many Worlds
Interpretation), and also confirming observed facts(QM).

Good :)





Why a plentitude and which plentitude?

A long time ago, I used to often think "Why these specific physical
circumstances?" or the more general "Why these physical laws/universal
law?" Eventually I came to read Tegmark's Ultimate
Ensemble/Mathematical Universe Hypothesis - if the universe can be
described/contained in a consistent mathematical object, why then not
just assume that it is one. If you assume this, Occam's Razor or its
formalized versions (such as Solomonff Induction) will say that your
hypothesis is rather complex.

OK. That's the main motor of the everything-list.



Assuming all possible (consistent mathematical) structures is the
simplest possible hypothesis. The problem with this is that this
'whole' might be a bit too large or inconsistent in itself (like
Russell's Paradox), and like I've said before, there is no way for us
finite humans to know an oracle when we see it. If we're a bit more
modest, we can use the only mathematical notion that we know to be
truly universal - computation as by CTT.

OK. The main problem also is in the self-localization in the possible
math structure. Comp entails a first person indeterminacy which
distribute us in the mathematical reality, and what we perceive might
NOT be a purely mathematical structure, but something "supervening" on
it from the inside view. This is a point missed by people like Chalmers,
Tegmark, Schmidhuber, etc.

What does 'what we perceive might NOT be a purely mathematical structure' mean? Qualia? Or the undefinable truth? Maybe in a less related way, we could imagine partially non-computational physics (even without assuming any 'jump') where appearances are some seemingly non-computational structure being computed in the limit - such as computable reals, this would make digital physics false in its naive formulation, but true in the sense that there always existed a TM that computed those states (even though it may run very deep).



The first papers I've read that described used computation (CTT) to
describe a plentitude were Schmidhuber's "Algorithmic Theories of
Everything", which describes the Universal Dovetailer (and assumes
COMP), the program that can run all possible programs(in the limit),
and by CTT which shows the existence of an universal TM, it describes
a computational plentitude.

Unfortunately it bugged me a bit that he avoided using some Platonia
or some form of AR(Arithmetic Realism) to put the UD in and just used
some "Great Programmer" that runs the program in some magical
undefined land. If anything this land only seems to grant 'existence'
and nothing more - my Occam's Razor sense was tingling a bit.


OK. It misses also the first person indeterminacy. he did not seems to
have accepted here when discussing on the list.

If one takes 3p as primary and 1p as non-existing (I don't know what his view is on this), I can see how it's easy to reach that conclusion. If 1p is accepted, just arithmetic is sufficiently rich.


Some time after that I've read Egan's "Permutation City" novel, which
seem to informally do what Marchal does with his UDA+MGA, although not
in a formal rigorous way, but enough to give a strong intuition for
it, but I think it still keeps assuming only a finite, bounded
universe, given the novel's conclusion (or merely it being one of
those improbable observations that nevertheless exist, or a "white
rabbit") - would it be an assumption of PA being inconsistent such as
in his "Luminous" and "Dark Integers" short stories - it's still
something which I have trouble imagining: if there is an abstract
structure (supported by arithmetic modulo some number) of finite size
k which is consistent, why cannot a structure of size k+1 exist - it's
my belief in mathematical induction (induction schema) that makes this
hard to imagine.

OK


I think conscious/self-aware beings which are embedded in time
(probably a requirement for consciousness) are likely to come to such
inductive beliefs by themselves if they think hard enough, although I
don't think that having such a high-level belief affects low-level
consciousness - for example, there are ultrafinitists which don't
believe in natural numbers beyond some unspecified finite limit (I
don't know how they justify their beliefs, but I think it has to do
with assuming a finite material reality).

I guess so. In this list, such an ultrafinitist physicalism has been
defended, contra comp, by Thorgny Tolerus, if I remember well.


I'll see about looking up his posts. I've talked with one ultrafinitist in the past, but I still have a terribly hard time understanding how one can use it to talk about ontology. It seems sufficient if you only want to talk about finite-state machines, but much harder to talk about math, physics or philosophy in it. In another way, I feel that it would only be acceptable if one could show PA inconsistent ( Vladimir Voevodsky seemed to contemplate such a view in: http://video.ias.edu/voevodsky-80th ), but then, what could replace it?

The way I see it: certain mathematical (or computational) structures
will contain within themselves observers like us (or even us), and
those structures can be seen as having states which are temporally
related(a naive example: f:N->N, u:N->N, f(0)=U0, f(n)=u(f(n-1)),
where U0 is some initial state, U is some computable function
calculating the next state given some previous state, usually giving a
greater complexity to the output; note that I'm not claiming this to
be the case for us, if you want it to apply better to us, instead of
the function 'u', you may think of it as a class of functions that
support you, selected at random from a countably infinite set.
Although I do expect the criticism that an /uniform/ probability
cannot be defined on such a set).

They do exist, but are not always sigma-additive, which does not prevent
the use of some probability calculus.


I'd be interested to read a paper on this.


Some time after reading Egan's works, I've read Russell Standish's
"Theory of Nothing" book which discusses some of these ideas in more
detail, but gives more importance to the observer, with the Anthropic
Principle and his derivation of the laws of QM as being observational
laws. Not that long after, I've read Marchal's UDA+MGA/AUDA and some
of his other papers.

I was very impressed by the argument - it seemed to provide exactly
what was missing from Schmidhuber's idea - the notion that the
observer cannot be magically attached to some program running an
universe: if computationalism is true (and a person has a 1p view),
then the observer is only attached to whatever infinite ensemble of
programs which happen to contain the 'body' of his mind (1p
indeterminacy), not one particular piece of (virtual) matter.

Good.



It seemed to me like a (relatively more) formalized version of the
ideas presented in "Permutation City" (which I think came before
Tegmark, Schmidhuber or Marchal's works, although I would love to be
corrected if I'm wrong about this).

I published the whole thing in 1988 (the Toulouse paper, but I present
it orally in many places in the seventies). Also in 1991 (in artificial
life proceedings). Egan's permutation city is 1994.



I was under the impression that Tegmark was one of the first that thought that idea, but I suppose it just means that no well-known authors had published it at that time. I find it a bit strange that your idea(UDA+MGA) has remained so little well-known, despite that there has been a lot of talk about computationalism and functionalism in general. I can see why it wouldn't be that popular because it shows some forms of materialism false, but then, isn't that also Tegmark's assumption that matter is just math anyway?


Another very interesting idea that
Marchal has seems to be of consciousness/observation as arithmetical
truth (or similar universal system capable of representing
computation), it gives you whole worlds contained in timeless
arithmetic, and it also gives you the 1p view. My only problems so far
with it are that there were some parts of the AUDA which I either
didn't understand too well (and might need to read more logic books
then re-read AUDA again) or which I failed to interpret correctly
within the proper context. There is a possibility that some of my
questions that I will ask are due to my current incomplete
understanding of the AUDA. After understanding some of the
consequences of the UDA, I was fearing that the 1p reality of a
conscious observers might be too jumpy (too many "afterlives" due to
many consistent continuations outside of the current computations that
support us) or even worse, border on white noise, thus you get very
frequent zombie-like consciousness - this might even be worse if we
allow a continuum to exist (such as sets of cardinality aleph_1 or
more, if Continuum Hypothesis is to be assumed true).


That's what I call the (first person) white rabbit problem. Too many
parallel realities, and a possible inflation of predictions. But that's
what make the comp hyp eventually testable. QM has also first person
white rabbits, despite the Feynman formulation almost explains how they
go away. Comp has to succeed similarly, and AUDA shows indeed why that
is possible.


Using the quasi-quantum logics? Or some RSSA-like assumption? I may get back to this after re-reading AUDA (once I think I've read enough logic books).


However, since I am writing this right now, you can guess that my
reality is fairly stable and non(observably)-jumpy ;)
It seemed to contradict comp a bit, but then I made another assumption
(which I find hard to believe in, but one must reason): the
substitution level could be too low and thus we're tied to this
particular set of computations in that most of our measure is here,
and other continuations are just rare.

That's a possibility indeed. Most probably, if comp gives exactly QM,
our subst-level is given by the Heisenberg uncertainty relations.
Basically the quantum state up to Heisenberg intervals.



This seemed be bad news for the
one getting a full brain transplant as it might make their reality
jumpier, but on the other hand, the one getting the brain transplant
will still act like a normal human would,

Not sure.


'Not sure' in the sense that the transplant is impossible or that behavior will be wrong if taken at a higher subst level (such as neuron)?


thus I cannot ascribe it any
part-zombie status (only due to the potentially jumpy nature), they
would, like I would, write up their email, observe the world and
conclude that they are not jumpy.

What I ended up settling with is that one has to assume some sort of
relative self-referential measure, that is, one will (most probably)
observe the world that is consistent with one's mind's structure and
current state.

Exactly, and this leads to AUDA, where everything (including physics) is
based on self-reference.





It was my impression that AUDA attempts to do that, but I will need
to re-read it after I study more logic.

OK. Good books are Boolos 1979 and Boolos 1993. Also, Smorynski 1985.




I'm currently half-way through "Computability and Logic"(1974,2007) and I've non-sequential parts of "Logic, Logic, and Logic"(1998). I plan on starting on "The Logic of Provability"(1993) after being done with "Computability and Logic". As for Smorynski's, is that "Self-reference and modal logic"? I might read it if I can find it, although it seems to be out-of-print and used copies of it seem to be quite expensive.



However, if comp is true, I
don't think jumpiness can be eliminated, merely made more rare by
virtue of what the observer is and how he is embedded in the
world. UDA+MGA+AUDA implies universes could be regarded to be
1p-plural observations which are the shadow on an infinity of "3p"
ensembles of computations, thus have the appearance of objective 3p.

More rare in the normal worlds. Which leads to the comp immortality
(with the quantum immortality as a special case).


Can true cul-de-sac's even exist? It doesn't seem to me, at least intuitively. I've also seen a "no cul-de-sac" theorem mentioned on this list, but I have yet to find exactly what post describes it.



To summarize my view on: COMP as shown in the UDA+MGA+AUDA, despite
its limitation to 'merely computations' seems to me to be an
incredibly rich plentitude, even richer than Tegmark's
MUH(Mathematical Universe Hypothesis), due to the proper attention
given to 1p.

OK.




It may seem smaller because you can say "eh, it's just
arithmetic", but in a way, for a finite observer, they cannot easily
believe in knowing that something is beyond COMP, and yet in COMP,
the 1p observer isn't even tied to any particular structure, but to an
infinite ensemble of computations, and the observer's next moment is
always selected within this ensemble.

Which happens to be very rich and to possess a highly non trivial
structure.



In another way, it seems to me
that COMP is a much stronger claim than MUH, despite being smaller.

OK.



(MUH being mostly: restrict modal realism to mathematical realism: my
structure admits a consistent mathematical description, thus by Occam,
all possible consistent descriptions exist. It does beg the question
of the consistency of the multiverse can be considered a consistent
object which can be part of 'all' the consistent universes or not,
creating a problem similar to Russel's Paradox. This might be solvable
by assuming less (such as COMP), or using some privileged meta-logical
level to talk about theories (sort of like one does in
meta-mathematics).

OK.

OK.

I stop here to read the rest when I have more time. Oh, I will answer
some questions at the end.

[big snip, to comment later]


Thanks for replying. I was worried my post was too big and few people will bother reading it due to size. I hope to read your opinion on the viability of the experiment I presented in my original post.




To Bruno Marchal:

Do you plan on ever publishing your thesis in english? My french is a
bit rusty and it would take a rather long time to walk through it,
however I did read the SANE and CC&Q papers, as well as a few others.

I think that SANE is enough, although some people pushes me to submit to
some more public journal. It is not yet clear if physicist or logician
will understand. Physicists asks the good questions but don't have the
logical tools. Logicians have the right tools, but are not really
interested in the applied question. By tradition modern logicians
despise their philosophical origin. Some personal contingent problems
slow me down, too. Don't want to bore you with this.

If it's sufficient, I'll just have to read the right books to better understand AUDA, as it is now, I understood some parts, but also had trouble connecting some ideas in the AUDA.

Maybe I should write a book. There is, on my url, a long version of the
thesis in french: "conscience et mécanisme", with all details, but then
it is 700 pages long, and even there, non-logician does not grasp the
logic. It is a pity but such kind of work reveals the abyssal gap
between logicians and physicists, and the Penrose misunderstanding of
Gödel's theorem has frightened the physicists to even take any look
further. To defend the thesis it took me more time to explain elementary
logic and computer science than philosophy of mind.


A book would surely appeal to a larger audience, but a paper which only mentions the required reading could also be enough, although in the latter case fewer people would be willing to spend the time to understand it.




I really hope to better understand AUDA in the future, especially the
parts about the self-referential machine.

I can explain online if you ask the questions.


I'll ask if I still don't understand it after I finish reading Boolos' books.


If one takes seriously the idea of (undefinable) truth, it might
indeed lead to ascribing some form of consciousness to Peano
Arithmetic and other such formal systems which happen to be consistent.

OK, nice. Note that arithmetical truth is not consciousness. It is
"bigger". Consciousness of a machine will be a conjunctive link between
the machine and arithmetical truth. (Bp & p). You might take a look on
the Plotinus paper, which redoes AUDA in the form of an arithmetical
interpretation of Plotinus. It was an accepted paper at the CiE 2009. I
will perhaps submit a paper at the next CiE.



What is just 'p', then?

I've read the Plotinus paper not that long ago, although I did miss some details in its second part, just like with AUDA, will re-read it again once I'm a bit more confident in my modal logic.


The only problems with this are questions about the nature of its
consciousness, it seems utterly unknowable, I'm not sure it's even
possible find an answer to this using methods one could use for
finding the answer to 'what qualia' would you experience if you added
some new sense to your (or a copies') brain (or emulation) and thus
your consciousness, or gradual structural changes to attain some
particular desired form of consciousness (this assumes a digital
mechanist substitution and that self-modifiability is possible). I'm
not even sure if one can assign such consciousness to PA without it
being embedded in some form of time, and if it would have some form of
consciousness, I would expect it to be very different from ours.

In all my current publication, I talk like if consciousness needs some
form of "time" (not necessarily physical, it could be the natural
numbers order). I have usually followed Brouwer for the intuition that
consciousness and time are deeply related, but I am less sure now.
Since I have smoked salvia divinorum, I have begun to doubt the
necessity of that association. It looks like we can be conscious, and
somehow be completely out of time. Of course I do not recommend smoking
salvia. Yet, if it is legal for you to do so, it is an interesting
experience of consciousness. Just be responsible. Note that a lot of
people reacts to salvia like they react to the comp reversal: they don't
want to know.


It seems that at least for now, some drugs are one of the very few ways one can get unusual 1p experiences (dreams would be another easily accessible way).

I have a hard time imagining what a 'timeless' 1p experience would be, but maybe one day I'll find out. The strange thing about such an experience is that it has a start and an end, so it can't really be timeless, or can it?

As for not wanting to know? Is that just fear of the unknown or preferring ignorance about certain things that scare them?



In a way, I can see how PA could contain truth to which either our
consciousness supervenes or merely /is/, but what it would be like for
PA to be consciousness itself?

I think you should more clearly distinguish PA from arithmetical truth.
PA is a little (Löbian) theory. Arithmetical truth (even from a pure 3p
view) is a non computably enumerable set of truth. It is beyond all
machines. The link between consciousness and truth makes consciousness
inherit its ineffability or non definability (like for knowledge). To be
like PA might be like to be a just born baby, or to be like you after a
strong amnesia, perhaps like after a hit of strong salvia, when you
don't remember anything, not even what time or space is. But I hardly
understand myself what I say here. Salvia is very amazing with that
respect.



Instead of PA, should have I said 'standard interpretation of arithmetic', or its standard model?


At least I have trouble imagining the
continuity or nature of that consciousness, but I'm even more curious
how PA would get to find out more about itself, self-referentially.

This should not be too much difficult. PA has deep (even maximal in some
sense) introspective abilities. Remember that the notion of proof,
definable in or by PA, does use a notion of time, through the steps of a
proof. PA can assert statements on the length of proofs, compare them, etc.



Very interesting way to consider time. What about those unreachable truths (due to incompleteness theorem, or that it might take an infinite amount of "steps" to reach them)? In a way those would be p, but not Bp&p, if I understand your terminology right, so would that mean that PA would never be 'conscious' of the unreachable truths? What if they seem verifiable (such as tests keep confirming them, but we can never know for sure because the number of steps to confirm all of them would be infinite; would COMP be one such example, or something like a variant of Riemann's hypothesis (of course, if one assumes a stronger formal system, they might be able to assert more truth, but they increase their risk of becoming inconsistent))?


It
seems rather hard to fathom, especially given that PA's set of truth
sentences is infinite and I find the notion of infinite and unchanging
mind rather troublesome (seems rather much like a certain theological
idea of ``God'''s mind, for certain definitions of theology),

Again, PA is a little formal machine. It can, like all machine, only
scratch the surface of arithmetical truth. In the arithmetical
interpretation of Plotinus, Arithmetical truth plays the role of "God"
(or the ONE), and I have no clue if that God is conscious or not. It is
not a Löbian entity.



I think I understand my error here (as with my response to the previous part): I should not consider PA equivalent with arithmetical truth or the standard model of arithmetic. Regarding the not a Lobian entity part? Is that because it is already 'complete' and thus it need not talk about the provability of its sentences?

On another note, what about non-standard models?

but I
like the idea of PA having the potential to be conscious (of course,
any history of ours is unchangeable in Platonia, but from the 1p there
is always indeterminacy and consciousness and continuity).

In a sense, you might be PA yourself, except that you are more full of
supplementary contingent memories. You might get the consciousness of PA
in dreams, or in slow (non REM) sleep every night. It might even be the
consciousness of RA (PA without the induction axioms), that is the
consciousness common to all (Turing) universal entities. I am not sure.
Open and hard problem.


I can follow proofs in made in PA, and I suppose most people should be able to. I'm not entirely sure what PA's consciousness be like, probably because anything that I can talk about has to be in my memories, and (non REM) sleep doesn't seem to give me any memories (unlike REM sleep dreams which can be quite memorable).


Offtopic:

Does anyone have a complete downloadable archive of this mailing list,
besides the web-accessible google groups or nabble one?
Google groups seems to badly group posts together and generates some
duplicates for older posts.

I agree. Google groups are not practical. The first old archive were
very nice (Escribe); but like with all software, archiving get worst
with time. nabble is already better, and I don't know if there are other
one. Note also that the everything list, maintained by Wei Dai, is a
list lasting since a long time, so that the total archive must be rather
huge. Thanks to Wei Dai to maintain the list, despite the ASSA people
(Hal Finney, Wei Dai in some post, Schmidhuber, ...) seems to have quit
after losing the argument with the RSSA people. Well, to be sure Russell
Standish still use ASSA, it seems to me, and I have always defended the
idea that ASSA is indeed not completely non sensical, although it
concerns more the geography than the physics, in the comp frame.

If someone from those early times still has the posts, it might be nice if they decided to post an archive (such as a mailer spool). For large Usenet groups, it's not unusual for people to have personal archives, even from 1980's and earlier.

I had no idea that was the reason I don't seem them post anymore(when I was looking at older posts, I saw they used to post here).

As for losing the "RSSA vs ASSA" debate, what was the conclusive argument that tilts the favor toward RSSA (if it's too long, linking to the thread will do)? In my personal opinion, I used to initially consider ASSA as generally true, because assuming continuity of consciousness is a stronger hypothesis, despite being 'felt' from the inside, but then I realized that if I'm assuming consciousness/mind, I might as well assume continuity as well (from the perspective of the observer), otherwise I can't reason about my future expectations.

I will give you some references in case you want pursue the study of
AUDA. Like some books by Smullyan, Boolos, Franzen. The Davis book
"undecidability", now published by Dover is the bible. It has the basic
original paper by Gödel, Church, Turing, Rosser, and Emil Post (the
deepest guy, imo). Emil Post has anticipated in the 1920s the whole
thing, from Church thesis, Gödel to the ontological reversal. To be
sure, he changed his mind on that last one after a discussion with
Turing, who was naturalist.


Sure, I welcome names of good books on the topic, although I'll have to finish my current backlog for now.

More comments next week.

Bruno


http://iridia.ulb.ac.be/~marchal/

Looking forward to it.

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