Le 21-sept.-07, à 02:30, Russell Standish a écrit :
> I do take the reversal, but not as granted. It is essentially a
> consequence of any ensemble theory of everything with a 1-3
> distinction. This is most clearly enunciated from within a
> computationalist position, which is why I think your UDA is so
> important, (to convince the doubters) but in fact the result is much
> more general, and computationalism per se is not needed.
I agree. I do propose this as subject research, but it is full of
>> I do consider that the discovery (by Babbage, Post, Church, Turing,
>> ...) of the Universal Machine is a major discovery of our time which
>> changes almost all what has been thought about machine up to then.
>> is reflected in the computability theory, and I exploit those
>> theoretical consequences.
> Of course. But I also put Darwinian evolution up there with that
> (variation/selection is a powerful theory).
This to vague for me. I have no (big) conceptual problem with Darwinian
Evolution, but this is not something fundamental at all. This has to be
derived from a more fundamental theory, as even today's Darwinist would
say (thinking about physics but we know that is wrong).
> As is stated in "Why Occams Razor", and made more explicit in
> "Importance of the Observer" and "Theory of Nothing", what is the U
> used in computing the universal prior? It can be nothing other than
> the observer. U needn't even be a machine, any partition of the
> strings into measurable subsets suffices.
> And this identification turns an essentially 3rd person account into a
> 1st person account. To talk about ASSA or RSSA one has to introduce
> some notion of time, or at least successor states.
Which we have without ay physical time notion, nor subjective time
notion with comp. Successor states are definable by use of numbers and
successor of numbers. This can be important given that everybody agrees
on numbers (except ultrafinitist, but I know only one in Russia), but
nobody agrees on what "time" could be (even the third person physical
one, or first person plural).
> As I have said, I have been taking David Deutsch's idea seriously, of
> combining a many universes ontology, with information theory and
> Darwinian evolution. (David also suggests Popperian epistemology as a
> fourth strand, but I consider this to be a special case of evolution).
... like I consider "evolution" as a special case of distributed
> In order to do this, I need to assume whatever is needed to even make
> sense of these concepts. At a minimum it would seem to include some of
> set theory, of measure theory and classical logic, but maybe it can
> pared down to a more spartan set of axioms. The point is I
> don't really care what is involved, but someone else will bother
> with these details. That is why I say I'm acting like a physicist.
Yes. A problem (at least for communicating) in a non necessarily
> One way of connecting with what you do is to say that I assume the
> existence of UD*, without concerning myself about the existence of the
This does not make sense at all for me, given that the UD is
interesting only through the UD*. UD is just a rigorous definition
(logical name) of the UD*.
> The CT thesis comes into play to justify the use of information
Why? Actually information theory use CT only when it becomes
"Algorithmic Information Theory". CT is needed to give "scientific"
meaning to expression like "computable" and above all expression like
"NON computable". And with comp this is important given that comp makes
reality, whatver it is, partially but fundamentally NOT computable.
> Regardless of what is really out there, all that we can know
> about it must come to us in the form of strings, and so we can just
> start with considering sets of strings.
This reminds me the particular case of the iterated Washington-Moscow
self-duplication. But in this case comp predicts random noise (even no
And this is completely different from the guy who is in front of a
universal dovetailer (running in his reality to makes things straight).
This leads to a infinitely subtle prediction. CT is a strong postulate,
despite or because it admits deep weakening.
> Hence computationalism is not
> assumed, but your universal dovetailer provides a computationalist
> model. It remains to be seen whether computationalism is the only
> possible model (I suspect not, but I don't know).
I have proved and I have insisted that if COMP is true then COMP is
either refutable, or unprovable, in which case comp justifies (and even
more: comp classifies) all other possible model. The point here is that
the logic G and G* (on which physics and theology eventually reduce)
still apply. Only the big unnameable can be thought as escaping the
laws of G and G*.
> Guardian angel would seem to fit into this latter
> category. I have no problem with the use of colourful rhetoric like
> this, but I have enough mathematical training to know that it simply
> refers to that which is true but not provable, and not something of
> greater significance.
G* \ G refers indeed, for any ieally correct machine, to what is true
about that machine, but that the machine cannot prove, but can still
infer, anticipate, bet on, gamble on, hope, pray, etc.
This gives machine's theology. Something of greater significance, imo.
Physics has to be part of it. And it explains better qualia than
anything suggested up to now (imo).
> Let's consider a non-Brunotheological case. Your hypostases for
> instance. I don't understand what makes some of them 1st person, and
> others 3rd person.
Good questions. It seems to me I have answered them, but don't hesitate
to ask, or wait that I am going through again, and again ...
Here the real answer has to be long, so I will just say the key idea.
In science, we never know and we always believe. That gives the third
person objective frame. It is because it is objective that it can be
shown to be wrong. But knowledge, by definition, is always directly in
touch with the (already unameable truth): it is incorrigible. To go
from third person scientific opinion, to knowledge, Godel's theorem
shows that the only way to do that (this is proved in detail in
"conscience et mecanisme") consists in using the Theatetical definition
of knowledge (By prove p and p is (serendipitously perhaps) true (the
Bp & p). Confirmation is provided by the fact that that doing this
gives an unameable (by itself) self quite similar to Brouwer's theory
of consciousness (which has given birth to intutionnist math and
philo). Much much more can be said here.
Another good question nobody seems to ask is: what is the relation
between this theatetical definition of knowledge/first person and the
definition of first person used in the UDA? (I let this as exercice or
subject of reflexion for now).
> As I understand it, they're axioms for systems of
> logical statements. The axioms proscribe what can and can't be stated
> for the given system.
Careful. Those are "axioms" of some modal logic. But those modal logic
describe the discourse of self-observing machine. But this is a
theorem. nobody has choose those axioms. The main axiom of G is Lob
formula, for example. But the arithmetical interpretation of Lob
formula is a theorem (Lob's theorem), capable of being proved by PA (as
Lob shows). All precise correspondance are given in most of may papers
(but the complete proof are in the theses).
> But what does any of that have to do with experience?
Experiences are the roots of incorrigible knowledge.
> What is the
> connection with the dovetailer of the UDA?
Again a very good question. Please wait I explain this again when I
will be convinced most people grasp what is needed to go through this
without leaving the list in hurry for reason of math anxiety. Actually,
I was close to make this point as clear as possible until I realize I
need to use Church Thesis, but also the seven first step of UDA, etc.
> I understand that some of
> the systems admit a representation in terms of Kripke frames, but
> again what does that have to do with time?
The cute reason is that the knower extract from the lobian interview
gives a temporal logic of evolving states of knowledge (S4Grz). Indeed
the Kripke frame is a temporal structure. This gives an arithmetical
transparent interpretation of the theory of time by Bergson/Brouwer
(and it clarifies the misunderstanding between "scientist" and Bergson
(or even the one between Brouwer and Cantor, and the one between Goethe
and Newton, and the one between Parmenides and Heraclite. That is the
optimistic view of the lobian machine. The pessimist will say that it
just show that lobian machine will develop the similar
misunderstanding. They are true, for a while. But in the limit (= some
day) lobian machine got the root of that misunderstanding too).
(The knower is, again, the one defined by the logic of "Bp and p" like
in Plato's Theatetus), B is the arithmetical Beweisbar of Godel, p is
for arbitrary arithmetical proposition, (or other for those who does
not like the numbers, but my attempt to use the combinators instead, in
this list, has failed: this is another reason why I keep the numbers:
people know them).
> I can understand that some
> of the systems might also be used to model a multiverse of observer
What you say here corresponds to my old idea (in this list) to model
the OM by the Kripke worlds. But as you know (I think), the fourth and
fifth hypostases have no Kripke semantics (or quite deformed one). And
also, OMs can vary themselves as you change the hypostases. So that you
can have first person OM, third person OM, first person plural OM, etc.
(for all the 8 hypostases).
That is why I have proposed to model the OM by the Sigma_1 sentence,
and this is the subject of the current "Observer Moment =
Sigma1-Sentences" thread (or the same with some amount of "Rép : Rép :"
in front. I will come back on this. The importance of the Sigma_1
sentences stems from the importance of Church thesis (even if we weaken
the comp hyp). Roughly speaking the Sigma_1 sentences will classify the
histories generated by the UD.
> but I don't see the connection between logical statement and
> observer moments.
This is just because I interview a machine which makes (logical, and
arithmetical) statements, and then I interview her on the OMs. More
exactly, for getting physics I restrict the interview of the machine
(which gives the 8 hypostases) on the sigma_1 sentences. (cf: you refer
to this in your book page 128-129, if we have the same edition ;)
We will come back on this.
Must go. Will be rather more busy now. No time to reread (could this
entails less spelling mistakes ...
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