BM: But you agree there is no plenitude without an UD.
GL: No I don't agree. I don't agree that the UD is the origin of all things.
But to say that there is no plenitude without an UD does not mean that the UD is the origin of all things.
This is typical classical thinking.
But I am a classical (boolean) thinker. (and actually it was a typical confusion between A->B and B->A, don't worry it happens all the time).
"In the beginning there was the UD (eg. x=x+1).
(Technical details: the UD is a little more than x = x+1, but OK)
And the UD generated the Plenitude (eg. 0, 1, 2, 3, ...)
Be careful. I thought we agreed that the Plenitude is a first person notion.
the O, 1, 2, 3, .... could not even be used to describe a notion of 3-plenitude.
The 3-plenitude is best described by the whole arithmetical truth, which has been
proved to be not describable by any finite theory. It is not completely unifiable.
. Out of the plenitude came out different worlds.
But you *do* have understand the UDA argument (I have links!), and now you begin to talk
like Schmidhuber. With the comp hyp only one physical world exists, and it is an emerging
(from the 1-point of view) appearance. It emerges from all the comp histories.
For exemple, although newtonian worlds are generated by the UD, no consciousness
can ever stabilize on it because it is (or should be) of measure zero.
Out of some of these worlds conscious creatures emerged. We are some of these creatures."
And so this sentence has just no meaning with (classical) comp.
This is 3rd person thinking. It leads to the mind-body problem.
I resolve the mind-body problem at the outset by using the observer as a starting point. The "I" is both an observable fact and an axiom. "I" can observe that "I" am capable of logical thinking and that my thoughts are consistent. ( I will leave to you the detail regarding what kind of logic applies) My logical ability leads me to the principle of sufficient reason One way to phrase this principle is "If there is no reason for something not to be then it must be. Since I am in a particular state and there is no reason for me not to be in any other state, then I must also be in those states. This leads me to think that there are other observers beside myself, in fact, all possible observers.
I can also apply this same principle to the world that I observe. If the world is in a particular state, and there are no reasons for this world to be in this particular state, then in must be in all possible states. This leads me to the plenitude. Thus the plenitude includes all possible worlds.
The indistinguishability of which observer I am and (conjugately?) which world I occupy leads to first person indeterminacy.
I agree with all this. my point is that this is indeed the correct (with comp) discourse of the first person. I can't say more without technics.
I suppose "I" am the UD. Or maybe "I*" am the UD??? I don't know if this makes sense.If not recall me what you mean by the plenitude. Remember also that from a machine's point of view (1 or 3 whatever) the plenitude is given by the the UD, or more exactly its complete execution (UD*).
I don't think so.
It may be possible that the need to invoke a UD originates from classical 3rd person (objective or absolute) thinking in which several separate physical worlds are simulated.
I would be prudent before linking "objective" with "absolute". I could argue that
only the subjective is absolute (for example it is hard to relativize actual pain ...).
Also, I insist (I know you did got that probably subtle point), but with comp
the adjective "physical" cannot be applied to anything capable of being
emulated (because the physical is a sum on all possible emulations at once,
and that cannot be emulated).
As I said I think the UD is a remnant of 3rd person thinking.
I don' t understand why you dislike so much 3-person thinking (although I appreciate very much your respect for the 1-person). 3-person thinking is called usually "science". It is communicable falsifiable (mainly) propositions and proofs. Like a proof that 17 is a prime number.
The comp hypothesis may be better off without a UD simply because it is possible to derive the plenitude without a UD. And should you refuse to accept the observer as a starting point, you could assume the plenitude as a starting pont axiom. It is "simpler" to assume the plenitude as an axiom than an arbitrary UD. At least there is nothing arbitrary about the plenitude.
But the UD is just a machine-independent (and thus non arbitrary) description of the
comp plenitude as it can be talked about in a 3-person way by (consistent) machines.
I keep insisting that the UD is not given as an possible explanation, but it is
a *necessary problem* (once we postulate comp). I did prove that that necessary problem
is equivalent to the extraction of the physical laws from number theory/arithmetic.
It may be that using the observer as starting points will force White Rabbits to be filtered out of the observable world
And again I totally agree. It *is* what is proved in my thesis. I have done two things:
1) I have given a proof that if we are machine then physics must be redefined as a
science which isolates and exploits a (first person plural) measure on the set of all
computational histories. The proof is rigorous, I would say definitive (unless some systematic
error of course), although provably unformalizable (so that only 1 person can grasp it).
2) I provide a mathematical confirmation of comp by showing that (thanks to Godel,
Lob, Solovay ...) we can literally interview a universal machine, acting like a scientist
---by which I mean we will have only a third person discourse with her. BUT we can
interview her about the possible 1-person discourse. That is a "tour de force" in the sense
that the notion of first person is absolutely not formalizable (and so we cannot
define it in any third person way). But by using in a special way ideas
from Plato's Theaetetus + Aristotle-Kripke modal logic + Godel's incompleteness
discovery make the "tour de force" easily tractable.
Here I can only be technical or poetical, and because being technical seems
yet premature I will sum up by saying that with comp, the plenitude is just the
incredibly big "set" of universal machine's ignorance, and physics is the common
sharable border of that ignorance, and it has been confirmed because that
sharable border has been shown to obey to quantum laws.
I get recently new result: one confirm that with comp the first person can hardly know
or even just believe in comp; the other (related to an error in my thesis I talked
about in some previous post) is the apparition of a "new" quantum logic (I did
not command it!) and even (I must verify) an infinity of quantum logics between
the singular first person and the totally sharable classical discourses.
This could go along with your old theory that there could be a continuum of
person-point-of-view between the 1 and 3 person, and that would confirms that you
are rather gifted as an "introspecter" (do you remember? I thought you were silly).
But then it looks you don't like any more the 3-person discourse, why?
PS Apology for having written so many time "Thaetetus", when the correct spelling
is Theaetetus. (Got my "Myles Burnyeat" book on the "Theaetetus of Plato", a book
I recommend for those who are interested in the "tour de force").