On 9/28/2011 10:11 PM, Pierz wrote:
Not at all. That would be a physicalist revisionist definition of numbers. You need to "instantiate" 17, in some way, to talk about 17, but 17 itself does not need instantiation. With or without any physical universe, 17 remain a prime number.
With or without a mind too, I presume you believe. But this really is
a metaphysical assumption, not something that is provable. I would say
if you remove all minds, there is no 17, no primes, nothing, because
the numbers are lent existence by the mind and/or the physical
universe. My preferred ontology is idealistic (in the philosophical
sense) rather than mathematical. I tend to believe consciousness is
prior. And you've agreed consciousness can't really be defined - and
therefore dealt with explicitly in your theory. I believe there is a
pure conscious state somewhere down there (in us) that comes before
everything else, before the structure which is required to give form
to mathematics. Buddhism, the void, all that.
I would disagree with this claim. There is a difference between the existence on an entity and its properties and the definiteness thereof. Existence and the property of having a definite set of properties (as opposed to having a spectrum of possible properties) should not be conflated. My reasoning is that if the existence of an entity where to depend on whether or not a mind has the object as a subject of perception or a physical entity has some other as a effective cause of some property of its own then existence would be a property that an object could have. Is existence a property that we measure, even in principle? No. Why is this conflation so rampant in thought? I have even seen instances of this kind of language in the work of the estimable David Deutsch! How is even the question of "does the existence of an entity depend on its perception by some other entity" not seen instantly as oxymoronic?

It seems to me I can
grant 17 is prime, without granting this instantiation of everything.
Well, that solves you of a very long and not so easy work.
Haha. Well, thank god we don't have to prove everything we believe -
unless, like you, we make a living out of it! Otherwise we'd have to
prove our own arses before we could shit. But OK, this is profound
stuff, so what "seems to me" may be way off, on deeper investigation.
Could it be that the definiteness of properties of our arses, in this example, are something that is contingent on interactions but not the possibility of having properties is not?

Now, an instanciation, or emulation, can be defined from the numbers alone
I can believe that without the textbook. I'm just saying that the
instantiated emulation and the definition of the emulation aren't the
same. But I do understand what you are arguing (I think). There's
nothing intrinsically illogical about granting numbers an existence
that is prior to the physical or the mental, but are you claiming it's
To elaborate on this question by Pierz, is not "provability" a property that must be demonstrated to occur for a given abstract entity?

Recently I have updated my spectrum of Löbian machine to the octopus, and the jumping spider. I can argue that they have the cognitive ability to get UDA.
I just find that quite funny. The socratic octopus. You can argue it
in theory, but it's kind of meaningless I think, since psychology
shows abstract reasoning is confined to humans above a certain age.
Still, I like the socratic octopus so much I'll believe you anyway.
I love the way the jumping spider literally falls off its perch when
there's no spider on the other side of the mirror. :)
It would be interesting to see the experiment that would allow us to determine whether or not an octopus or spider can distinguish between a purely abstract concept and the actuality of a physical entity. How do we determine that a spider has thoughts about its percepts?

It is not a problem. It is an impossibility. You cannot prove that *I* am conscious, can you?
No of course not, that's what I meant by a "problem". A very big one!

Finally, as for obscurity, I rejected obscurity treated as a virtue,
not the necessary obscurity of certain difficult ideas - like QFT
mathematics. I suppose jumping spiders can do QFT equations too,
How could we determined If they can know that what they are doing is QFT even if they can solve QFT equations?



On Sep 29, 2:07 am, Bruno Marchal<marc...@ulb.ac.be>  wrote:
On 28 Sep 2011, at 05:44, Pierz wrote:
OK, well I think this and the other responses (notably Jason's) have
brought me a lot closer to grasping the essence of this argument. I
can see that the set of integers is also the set of all possible
information states, and that the difference between that and the UD is
the element of sequential computation. I can also see that my
objection to infinite computational resources and state memory comes
from the 1-p perspective. For me, in the "physical" universe, any
computation is restricted by the laws of matter and must be embedded
in that matter. Now one of the fascinating revelations of the
computational approach to physics is the fact that a quantity such as
position can only be defined to a certain level of precision by the
universe itself because the universe has finite informational
resources at its disposal. This was my objection to the UD. But I can
see that this restriction need not necessarily apply at the 'higher' 3-
p level of the UD's computations. What interests me is the question:
does UDA predict that the 1-p observer will see a universe with such
To be sure, this is an open problem.
To be sure, this is an open problem for physicists too.
Comp+"theatetus" will be refuted if the comp-physics will be quasi *contradicted* by some precise physical fact, not by any physical theory (unless they predicts that precise physical fact).

If it explains why the 1-p observer seems to exist in a
world where there is only a finite number of bits available, despite
existing in a machine with an infinite level of bit resolution, then
that would be a most interesting result. Otherwise, it seems to me to
remain a problem for the theory, or at least a question in need of an
answer, like dark matter in cosmology.
I am going to have to meditate further on arithmetical realism. I
don't believe in objective matter either (it seems refuted by Bell's
Theorem anyway), but a chasm seems to lie between the statement  "17
is prime" and "the UDA (Robinson arithmetic) executes all possible
Don't confuse the UD (Universal Dovetailer, a finite program) and UDA (the UD Argument = the argument that, assuming digital mechanism, physics is in principle a branch of number theory/computer science, and in which the UD plays the role of the effective definable comp ontological realm of *everything*).
Just a vocabulary remark, to avoid possible future confusion.

The problem is one of instantiation. I can conceive of a
universe - a singularity perhaps, with only one bit of information -
in which the statement "17 is prime" can never be made.
Don't confuse the sociological statement "some machine asserts "17 is prime"", and the true fact that 17 is prime, which does not rely on physical universes at all, a priori.

To formulate,
ie instantiate, 17, requires a certain amount of information.
In some physical theory, but this is not an assumption in the theory. You cannot refute an argument by adding new assumptions.

To say
that a program executes, as opposed to saying it merely is implied by
a set of theoretical axioms, requires the instantiation of that
In Aristotelian metaphysics.
Also, even in platonia, a computation is described by a big number (possibly infinite) of implications.

I suppose this is a restatement of the problem above.
Arithemetical realism then would be the postulate that everything
implied in arithmetic is actually instantiated.
Not at all. That would be a physicalist revisionist definition of numbers. You need to "instantiate" 17, in some way, to talk about 17, but 17 itself does not need instantiation. With or without any physical universe, 17 remain a prime number.

Now, an instanciation, or emulation, can be defined from the numbers alone. Some numbers are universal (a relative arithmetical property) and we can say that a universal numbers instantiates 17 (say) if 17 appears in some of its purely arithmetical register.

To understand the detail of this, I can only refer you to some good textbook in computer science. The main theorem for this is the proof that all partial recursive functions can be represented in Robinson arithmetic (Boolos and Jeffrey's book do this very well, Epstein and carnielli also. ref in my theses).

It seems to me I can
grant 17 is prime, without granting this instantiation of everything.
Well, that solves you of a very long and not so easy work.

I'm also troubled by the statement that you have proved in the AUDA
that any Lobian machine can apprehend the UDA. Is not a three-year-old
child and a cat a Lobian machine? Or indeed my senile father. How can
you assert they could comprehend such an abstraction? Either they
aren't Lobian machines, or there's hole in the proof somewhere,
Recently I have updated my spectrum of Löbian machine to the octopus, and the jumping spider. I can argue that they have the cognitive ability to get UDA. But they don't have a sufficiently big brain to exploit this, and they don't have the motivation to use diaries and books, and language to generate their infinite "turing tape memory" like we do. Symptoms of Löbianity are believe in repetition and notice them (like believing in a notion of anniversary), or having empathy for an other creature, etc. This needs some form of the induction axiom. Robinson arithmetic (and Universal machines in general) are not Löbian. Peano Arithmetic is Löbian (it is reallu just Robinson arithmetic + the induction axiom for the first order describable formula).
But this is not important for the reasoning.

Jason mentions the anthropic principle (which of course I'm well
acquainted with) and the idea of the computations which contain
observers. I have read, without following, some of your propositions
involving the Beweisbar predicate and self-referential relations and
what have you. Is that the formalism that is supposed to define which
computations are conscious?
Not really. This is a subtle point. Notion like truth and consciousness are not definable by any machine. But, like with God (or Plotnus' one) we, the machines, can talk in indirect way, by taking some precaution.

Is there a summary somewhere?
It is explained in the second part of the sane04 paper. AUDA is "the interview of the Lôbian universal machine"

I am
wondering how consciousness can possibly be an attribute of some
computations and not others,
Let me be precise; consciousness is not an attribute of a computation, but is an attribute of a person. Now a person can manifest itself relatively to other person, once "enough" similar computations are going through the states of the two person, in some sufficiently cohesive way. The self-reference logics are used to single out the conditions of cohesion (unlike in linear logic, or Girard geometry of interaction, which extract such condition from symmetry intuition and proof theory).

and why, if it's a matter of some certain
mathematical properties of the computations, we could not fairly
easily write a conscious algorithm?
It is easy. I tend to think, since recently, that all universal algorithm are conscious. But their consciousness is disconnected, a bit like if they were born ... in salvialand! And, yes, before doing salvia I would have imposed Löbianity for consciousness, but I am much less sure about that. Now Löbianity is more than consciousness, it is self-consciousness. Peano arithmetic is self-conscious, I think. That is why we can discuss Plotinian theology with them, even without making their soul falling on earth, that is without implementing them and sharing our long story. Current computers have not yet long term memory, nor long term goal. But I think that PA, the octopus, and the jumping spider (but not worms, and most usual spider) are as conscious as you and me.

For the fun here is video illustrating that a jumping spider can do some inductive inference requiring some implicit beliefs in arithmetical induction (look hw she reacts when she looks behind the mirror).


As opposed, here is a typical non Löbian behavior, or a non jumping spider (yet jumping, note):


If not finding food on a top of a plant, she is programmed to jump randomly on other plant, and, in case she get the ground, to climb on a nearest plant. Here there is only a pen, perpendicularly installed on a flat ground table. She seems to repeat in cycle that behavior, except for taking some rest.

But the bigger reason why I think jumping spiders are Löbian, is that like cat and dog, they can bond with you, star at you, and perhaps even recognize you. But this can be judged only by real interaction with real spiders, not by looking at videoas, of course. Stiil, here is a very cute one:


Surely complexity can't be the
defining feature (at what arbitrary level of complexity does the light
come on?), so it should be a simple matter.
I agree. You don't need more than 10 lines instruction code for them, well, in a high logical language like prolog, for example.

(Though the proof of
having created consciousness in the program would be a problem!)
It is not a problem. It is an impossibility. You cannot prove that *I* am conscious, can you?

we have to define consciousness (not necessarily self-awareness, or
the awareness of being aware) as a property of numbers per se?
A quasi-definition is the ability by some universal numbers to discover some non communicable truth by introspection. Consciousness is not much more than the state of believing in ...

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