On 26 Feb 2012, at 20:37, Stephen P. King wrote:

On 2/26/2012 12:27 PM, Bruno Marchal wrote:

On 25 Feb 2012, at 20:01, Stephen P. King wrote:


Likewize Bp & Dt, and Bp & Dt & p, are other important variants. I will say more when I get more time, but by searching 'S4Grz' or 'hypostase' in the archive you might find the many explanations I already give. See my papers and the reference therein. Ask precise question when you don't understand, so I can help.

Thank you for this brief set of remarks. I would like to see an elaboration of the Löbian entity such that we can see the means by which the 1p content is encoded.

The first person content are not encoded, they are just true belief, or correct inference with respect to plausible local universal numbers. A brain does not create a person, it helps a person to manifest herself with respect to other universal numbers (some being person themselves, and others might be less clear).

Can, for example, we include a free or atomic boolean algebra in a Löbian entity?

Algebraically Löbian machines can be handled by diagonalizable algebra (that is boolean algebra endowed with a transformation operator verifying the Löbian axioms, the fixed point property.

But what the machine can observe is non boolean, and cannot, I presume be extended in a Boolean reality. It is an open problem if all coherent dreams could define a unique physical reality. I doubt it.

I would also appreciate your comments on this paper by Barry Cooper: http://www1.maths.leeds.ac.uk/~pmt6sbc/preprints/rome.paper.pdf

Here is its Abstract:

"Amongst the huge literature concerning emergence, reductionism and mech- anism, there is a role for analysis of the underlying mathematical constraints. Much of the speculation, confusion, controversy and descriptive verbiage might be clari fied via suitable modelling and theory. The key ingredients we bring to this project are the mathematical notions of defi nability and invariance, a computability theoretic framework in a real-world context, and within that, the modelling of basic causal environments via Turing's 1939 notion of interac- tive computation over a structure described in terms of reals. Useful outcomes are: a re finement of what one understands to be a causal relationship, includ- ing non-mechanistic, irreversible causal relationships; an appreciation of how the mathematically simple origins of incomputability in defi nable hierarchies are materialized in the real world; and an understanding of the powerful ex-
planatory role of current computability theoretic developments."

Interesting, but still not taking into account the comp mind-body problem, or the comp first person indeterminacy. Might say more on this later. It would have been nice I (re)discovered that paper soon, but many thanks :)

Please also see http://homepages.inf.ed.ac.uk/jrl/Research/laplace1.pdf which contains many of the same questions that I have been asking but expressed in a more formal and erudite manner.

You cannot ask to read 50 pages long technical pages at each paragraph, and guess what are your non understing of the UDA is from that. It looks like not too bad material though, but does not really address the question we are discussing here.

I am still not seeing how you define the philosophical terms that you are using, as the way that you are using words, such as "dualism" and "monism" are inconsistent with their usage by others in philosophy.

I use them in the sense of the wiki you did provide to me.

Neutral monism, in the "philosophy of mind" consists in explaining mind and matter, and the relation between, in term of something else.

Yes, but I see numbers as belonging to the category of mental content and thus not capable of forming a neutral "something else".

But this is basically, with all my respect, a mistake. You confuse the theory of numbers, with the meta and psychological theory (which assumes much more things) of how humans mentally handle the numbers. Unless you make clear your ontology, and what is your theory, or initial theory, you might just beg the question.

It is not a question of true or false, but understanding a reasoning. You have to go through the thought experiment until you have the aha!

OTOH, if we stick to your consideration that minds are only the 1p

associated with true beliefs.

then your argument that COMP is a neutral monism is consistent modulo finite considerations. I think that considerations of 3p spoils this neutrality (the Laplace draft paper above touches on this), but let us see what happens in our discussions.


If your theory is scientific, the something else must be clearly specifiable, that is itself described by a reasonable theory, so that the explanation of mind and body from it makes (sharable) sense.

With comp, in short, a TOE is given by RA (ontological), and its epistemological laws is given by the variants of relative self- reference of all the (Löbian) numbers. Physics consists in some of those variants (hypostases).

Some believe that the numbers belongs to the mind, but with comp it is more natural to define the mind, in a large sense, by the universal numbers imagination.

This is my prejudice and I am working hard to overcome it. My resent comment that we have computations (as abstract logical machines) and physical processes as orthogonal intersections on 1p is an attempt in this direction. I am trying to remain consistent with Pratt's idea of state transitions via chained residuation.

The mind is, notably, what computer can explore, quasi by definition with comp.

Local computers, like the one you are using right now, are universal number written in physical universal sublanguage of physics. And normally UDA should help you to convince yourself that physics becomes necessarily a sort of projective limit of the mind, with comp.

I see physics, in the sense of groups and other relations, as the mutually consistent sharable content of 1p, but this does not alone cover us to solve the problem of time. The only solution that I have seen that is semi-congruent with COMP is Hitoshi Kitada's proposal (http://arxiv.org/abs/physics/0212092 ).

No problem. I don't try to solve a problem, just to formulate it, in a way such that humans, but also machine, can understand. AUDA is machine's answer, somehow.

With comp, the only way to singularize you or your neighborhood consists in layering down the substitution level in the transfinite. Why not? The study of comp can help to build rigorous non comp theory. Sets and hypersets can be helpful for this, indeed. For comp too, probably.

Ben Goertzel has a very nice paper discussing the use of hypersets and consciousness here. Craig's discussion of it is here.

Yes. It is not bad, but I use combinators or lambda terms to handle the non foundations, or the second recursion theorem, or the modal logic (based on the use of those diagonalizations), which is natural in the comp meta-theory. Ben was a participant of this list years ago. We had good discussions. It is also a not too bad material. But polishing too much tools for solving a problem can distract from solving the problem, or even from formulating it (or a subproblem of it). I already told I am skeptical on the notion of sets in general. I like very much ZF, which I have studied in deep, but I see it just as a sort of very imaginative Löbian machine. Jean-Louis Krivine, Jech, and recently Smullyan and Fitting wrote very nice books on set theory. They explain the Cohen forcing technic with a nice modal construction in S4.



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