I have no difficulties with such notions, but would like to see a more general situation discussed such as how we can have a formal model of multiple 1-person intentionalities. I see this more general stuation as being the exact analogy of the "problem of time" in physics and given my interest in that problem I am engaging in this discussion. ;-)
Third person self-reference (corresponding to Kleene, Case, ...):
p ( = Godel's beweisbar), p arithmetical proposition.
First person "self-reference without self-name):
p & p That gives through Kripke semantics an antisymmetrical
logic of "subjective time".
Note G* proves p <-> (p & p), but G does not prove it!!!!!!!!!!!
Also "p & p" is not definissable in arithmetic: the machine will hardly
confuses herself with a description, or any 3-view of herself like a
First person plural (rational plausible communicable belief)
<>p & p p arithmetical proposition
First person plural knowledge restricted to the DU accessible propositions/states:
<>p & p p \Sigma_1 arithmetical proposition.
This gives the "quantum" modal logics Z1 and Z1*. Where the atomical
propositions (here just the leaves of DU*) are persistent in the sense that
once a lobian machine got it in her "actual world", it remains true in her
neighborhood (which is sparse in UD*).
Here I gave a little sketch of the translation of UDA in a "consistent
SPK: Ok, I am not questioning whether or not there "exists" self-referential programs (plural???) or a "Univiversal program" (singular???), I am wondering about how do we go from formal existence postulation to the possibility of "maniferstation" itself. This is where I think that there is a problem if only in that the domain of explanatory power of such models only applies to a very narrow range.
BM Not with comp by hypothesis. Manifestation are indexicals. Strictly speaking this follows from the UDA + OCCAM RAZOR, or better UDA + MOVIE GRAPH. (we can come back on this latter). See Maudlin 89 for something equivalent to the movie graph. Maudlin realises the incompatibility between the "physical supervenience thesis" (sup-phys) and comp. Because he want sup-phys, he abandons comp. Because I postulate comp, I abandon sup-phys. SPK
Here we find the following: http://www.cis.udel.edu/~case/slides/krt-consc-cs-slides.ps
BM: Nice. I didn't see it! SPK:
Exactly what is the formal statement of "if she looks closely enough to its probable local implementation" or equivalently, "near its comp substitution level"? Are you assuming some kind of "delta-epsilonics" here?
BM: It means that your substitution level are the neurons and you look at the molecules which constitute the neurons. Or your substitution level is the quarks and you look at anything apparently making up the quarks, etc. It happens when you look at a so much fine grain that you face the 1-person undistinguishable stories. I am not assuming "delta-epsilonics" things, but it is an open problem if sort of "delta-epsilonics" is not dormant here. CF: the UD dovetails on the reals, oracles, ...
SPK: I still do not understand how you go from UDA to 1-uncertainty. Please point me to the definitions again. ;-)
BM: See http://www.escribe.com/science/theory/m2978.html and follow up.
SPK:BM: QM confirms that. But people have invented selecting rules, like the collapse of the wave or some guiding potential, making things look more Aristotelian. But Everett comes and said "why for?".[SPK] Hold on! The "collapse of the wave function" is introduced to try to explain the disparity between the non-distributive and non-Boolean aspect of QM and the logic implicit within individual 1-person experiences. QM has been compared by David Finkelstein to a relativity of experiments, where there does not exist an absolute universal experiment. As I re-read D. Finkelstein's essay: Finite Physics, it seems that what you and other computationalist are proposing is identical to that Prof. Finkelstein is trying to generalize: "An abolute or nonrelativistic physics ... postulates 1) a universal experimental language, 2) a universal experiment, and 3) a universal experimental subject. The universal experiment is the simultaneous determination of all the variables of the system.
BM: Does Finkelstein interprets it in that way? I doubt that. SPK:
The universal subject is the universe itself.
BM: ? SPK:
Both figure explicitly, fdor example, in Laplace's fantasy of the intelligence who knows all and does nothing." It is easy to see the analogy!
SPK:BM: And I come, if you want, and just say that if you take seriously the Everett comp then you can ask "why for?" even for the SchroedingerEquation.[SPK] I would kindly submit that neither you not I understand exactly what the SWE is, but to say that Everett's comp idea exists without SWE is absurd! It is the SWE that defines the "thereexist X" postulation of the "relative states" that are considered as "worlds" or "minds" or "histories", etc. , such that without X being assumed to exist the notion of self-aware entities of self-referential systems is meaningless noise, at best!
SPK: But that's the physicalist postulate. I show it incompatible with comp. SPK:
I do not dispuse "LOGIC + ARITHMETIC". I am just wondering how it is that you can assume that LOGIC + ARITHMETIC can be meaningfull and persistent entities without having to deal with the obvious infinite regress that is entailed.
BM: Kleene recursion theorem, or Cantor-Post-Turing Kleene sort of diagonalisation. For the natural numbers I aknowledge that I cannot define them without infinite regress. But then that is why I postulate them. Nobody can explain things informally from nothing. At least arithmetical truth justifies its own "mystery", that is that it is impossible to get them without postulating them. SPK:
> >SPK:> Your model, as I understand it, ... BM: But I'm afraid you miss the point. It is not a "model". It is not a theory. It is a "theorem", a deductive argument. If you don't understand it, you should tell me at which step of the reasoning you are stuck.[SPK] Even so, the theorem is based on an assumption!
BM: Yes. Comp.
SPK:I am not so interested in knowing if the hypotheses are true. I am enough glad for showing them refutable. When a computationalist practitioners accepts an artificial digital brain, he does not ask for a model in its head. He asks and hope for the real thing.[SPK] There is no clear evidence that a digital emulation of brain activity will have an analogous digital 1-person associated. The strong AI hypothesis is merely that, a hypothesis. I am remined of the discussion that some have made regarding a book within which a complete description is written of Einstein's brain. Is it assumed that the mere enumeration, assuming enumerability, of the states of Einstein's brain is enough to give us a 1-person existence of Einsten? This is silly at best!
BM: Silly? But still a consequence of COMP. I guess you allude to the "conversation with Einstein brain" by Hofstadter. It is not the simple enumerability of Einstein's brain states which plays a role here, it is the relative (to you) emulability of the working of its brain. (I hope you don't give credits to Searle-like sort of "refutation of mechanism".)
SPK:In case he survives (= COMP) he can bet he is immaterial. He can choose is body and travel on the nets, without any stable body. The UDA result is that this imateriality is contagious, in some sense, the environment cannot be more material than himself. Descartes, Hume, and Kant have partially describe this.[SPK] What I am pointing out is that you are assuming at least the possibility of an "embodiment", even if there does not exist a single stable "body".
BM: I don't assume it. Only locally for some argument. See http://www.escribe.com/science/theory/m1726.html where I make also "silly hypotheses" (like existence of embodiements) and eliminate them eventually. You must understand that a proof is a connected line of arguments. I don't assume anything material or physical in the whole proof. Neither time, space, energy, equations, etc. Just (sigma1) arithmetical truth, *in fine*. Physics appears as an internal modality like those described above. SPK:
We can extend the Einstein book to a data base that is continuously circulated between servers on the internet, but the question remains, unless the possibility of a physical server with some non-zero persistence of "being" is assumed, even the notion of an Einstein data base becomes impossible.
BM: By the physicalist assumption, only.
This exposes a problem deeper than that of the causal non-efficasy of "matter" within a immaterial monist theory! It boils down to saying that you can not postulate your cake and eat it too!
SPK: >would seem to make the "mirror/ sketch >pad" to be a derivative or "epiphenomenona" of the UD, BM: Why epiphenomena? They are phenomenal appearances, stable patterns in consistent machines memories. Dreams if you want, but stable dreams in which they have partial control ...[SPK] What does the word "stable" mean in your thinking here?
BM: That if a Sigma_1 proposition is true then it is provable, and in some sense, forever true.
SPK:And thanks to the G/G* difference we get communicable and incommunicable truth. Thanks to the Z/Z* difference we get room for both physical measure and physical sensations, as uncommunicable physical result of (self)measurement. SPK: >e.g. that physicality >itself is merely derived from the intetionality of arithmetic statements, BM: Yes.[SPK] Ok, well how do we go from intesionality to persistence such that a 3-person view is even possible?
BM: See above.
SPK: >what x implies about y. My argument is that if physicality is mere >epiphenomenona, is it sufficient to merely have a "belief" by S that x >implies y to have a causal consequence on the possible behavior of S,such>that if x did not imply y behavior would be 3-person distinguishable? BM: ... would be 1-person plural distinguishable (for the technical reason that the quantum, seems to appear at the star level. I am not yet sure).[SPK] I hope that you can explain this further soon!
BM: The basic reason is that the quantum modal formula (p-> <>p) appears only at the star level. It is a theorem of Z1* and not of Z1. This means that the quantum like the whole George Levy sort of plenitude is more a 1-person plural construction than a truly 3-person objective communicable truth. It means QM belongs to "society of machines" psychology.
SPK:But you are right. That is, if that is believable and consistent. It is not that mind acts on matter, but it is more like the arithmetical border of mind defines matter. Roughly speaking.[SPK] How is this "arithmetical border of mind" any different from the Cartesian cut, the distiction between subject and object?
BM Perhaps it is not. Nice, you realize I provide a *phenomenology* of dualism, in a purely monistic context.
Don't hesitate to send a readable description of Pratt's "headway" for us all, anyway. Explain perhaps enough for explaining the subtle point which, if I understand you, would make comp inconsistent, or perhapstrivial.[SPK] Ok, it seems that this is inevitable, but you realize that if a person that is familiar with computer science, such as yourself, is having difficulties understanding Pratt's paper, imagine the mere amateur such as myself! I find this incredible! Is there nothing in his paper that gives you a "toehold" on what he is talking about? BTW, you are not the first to not understand his idea! I have tried to engage Pratt directly in a discussion of his paper and so has Peter Wegner, but he seems to not be willing to do so for some reason. Since so much of my own idea depends on Pratt's notions, I will try to produce a "readable description", but it will take some time and effort.
BM: Both Wegner and Pratt's paper are interesting for their own sake but, imo, lack philosophical rigor. Wegner's idea to use SIM, ... for getting the quantum is refuted by the kochen-Specker theorem, for example. But thank you for the effort in writing a post on Pratt and your views. My current feeling is that you are physicalist, but you want keep comp. But that's just impossible. (Unless there is a flaw in my reasoning, of course). Best Regards, Bruno