On 07 Aug 2012, at 21:03, Stephen P. King wrote:

On 8/7/2012 5:37 AM, Bruno Marchal wrote:

Hi Stephen,

On 8/6/2012 8:29 AM, Bruno Marchal wrote:
[SPK] Which is the definition I use. Any one that actually thinks that God is a person, could be a person, or is the complement (anti) of such, has truly not thought through the implications of such.
For me, and comp, it is an open problem.
? Why? It's not complicated! A person must be, at least, nameable. A person has always has a name.


   Because names are necessary for persistent distinguishability.

OK. You are using "name" in the logician sense of "definite description". With comp we always have a 3-name, but the first person have no name.

Dear Bruno,

First I must tell you that however I might get frustrated at your seeming intransigence, I do appreciate your patience and thoughtfulness! :-) I am learning a lot from these exchanges. Now to the content of your reply.

You are welcome.

(My ideas are still evolving on this and my postulate of Identity is still not well formed.)

UDA is build in a way such that we don't need to have a theory on personal identity.

Yes, I see a name as a "definite description" and I see this as harmonious with my postulate that the best possible computational simulation of an autonomous system *is* the system itself.

I remind you that this is not the computer science notion of simulation.

Thus the name of an entity (an autonomous system) is dependent on autonomy

Is not the name (program, body, definite-description) prior to the function of that name in some environment (universal number)?

and thus independence from any particular embedding,

This is functionalism, which is a consequence of comp. Comp implies functionalism at the substitution level. The independence of the physical, and the dependence of the physical from only the numbers (and their laws) is the object of the proof.

but this independence is not separateness in general and this is where we disagree on Step 8.

But you have still not address the reasoning itself.

Let us try an informal proof by contradiction. Consider the case where it is *not* necessary for a person to have a name. What means would then exist for one entity to be distinguished from another?

By the entity itself: no problem (and so this is not a problem for the personal evaluation of the measure). By some other entity?

What kind of entity might this other one be? We must show that there exist "other" similar entities and thus at least have to show (in our explanations and theories) how the "otherness" obtains.

Comp makes all entities existing "trivially" in arithmetic. Only the laws of physics are no more trivial and can't be no more be assumed, by UDA.

This is a version of the "Other minds" problem which is a corollary of the solipsism problem. Part of my reasoning is that I see the most necessary ability of consciousness is the ability to make distinctions. It is with the ability to make distinctions that allows an entity to even have beliefs. The idea of 1p indeterminacy speaks, IMHO, to this ability and you have shown in a very clever way how to make this ability vanish.


It is for this reason that you can actually make the claim that "I did provide a semi-axiomatic of God " in a resent post, but you must understand that your claim is not a universal truth. It is only a finite approximation.

We might consider the location of an entity as a proxy for the purposes of identification, but this will not work because entities can change location and a list of all of the past locations of an entity would constitute a name and such is not allowed in our consideration here.



What about the 1p content of an entity, i.e. the private name that an entity has for itself with in its self-referential beliefs?

It has no such name. "Bp & p", for example, cannot be described in arithmetic, despite being defined in arithmetical terms. It is like arithmetical truth, we can't define it in arithmetic language.

Right! and I claim (without proof at the moment) that this prohibits certain kinds of beliefs from possibly being true. In particular, it prevents absolute truth valuations from being associated with entities that cannot be named. This has profound implications! I would even go so far as to say that it even implies that phrases like "arithmetical truth" are meaningless iff they are not stated in association with a named theory.

You lost me, Stephen.

I think that John Clark's contentions about "free will" could be made coherent in this context.

? John Clark attacks only a notion of free will which makes no sense as the start. Not the high level compatibilist notion.

Since it is not communicable - as this would make the 1p aspect a non-first person concern and thus make it vanish - it cannot be a name. Names are 3p, they are public invariants that form from a consensus of many entities coming to an agreement, and thus cannot be determined strictly by 1p content. You might also note that the anti-foundation axiom is "every graph has a unique decoration". The decoration is the name! It is the name that allow for non- ambiguous identification. A number's name is its meaning invariant symbol representation class... Consider what would happen to COMP if entities had no names! Do I need to go any further for you to see the absurdity of persons (or semi-autonomous entities) not having names?

Say that it is X. There is something that is not that person and that something must therefore have a different name: not-X. What is God's name? ... It cannot be named because there is nothing that it is not! Therefore God cannot be a person. Transcendence eliminates nameability. The Abrahamist think that Satan is the anti-God, but that would be a denial of God's transcendence. There are reasons why Abrahamists do not tolerate logic, this is one of them.

With comp if God exists it has no name, but I don't see why it would make it a non person. God is unique, it does not need a name.

God is unique because there is no complement nor alternative to it. Ambiguously stated: God is the totality of what is necessarily possible.

That is not bad in a first approximation. With comp, you can make it precise through the set of Gödel numbers of the true arithmetical sentences.

Yes, but only up to isomorphisms within nameable classes! Gödel numberings in general prevent exact naming even to the point of possibly only locating them as members of some coarse grained class (as we see in the level of substitution idea). This has implications with regard to the Axiom of Choice but I am not sure how to proceed further on this question.

You make things artificially more complex. You make remark far more vague and difficult than what we are talking about. And you never prove your proposition.

Obviously this is not a computable set, and it is not nameable by the machine (with comp), making set theory somehow too rich for comp.

Can COMP be extended so that we can at least define a meta- theory of sets?

This does not make sense. Comp is the theory that we survive with a digital brain, and UDA shows from that, and only that, that Robinson arithmetic has to be a theory of everything, and that physics and theology have to be retrieved from only that. So, no, comp cannot be extended, it does not even make sense. Either you do survive (perfectly) with a digital brain, or you don't. The rest is a logical consequence, including the fact that the realm is given by 0, 1, 2, ... For the internal epistemology, or truth, we can of course extend the the theory, ad infinitum, as it is irremediably incomplete. There we need an infinity of new arithmetical axioms.

Of course, arithmetic contains or emulates a lot of entities believing in set theory, but we should not reify those beliefs in the ontology. It is better to keep them only in the machine epistemology.

    I agree with you here, but this is wild speculation...

? No this is proved. It is obvious, actually. So this remark makes me think that you just don't know about theoretical computer science. Arithmetic, even the tiny Robinsonian one, emulates rich theories like ZF, despite they can prove only a tiny fragment of what ZF can prove. RA can prove that PA or ZF can prove RA's consistency, despite RA cannot prove its consistency.

On 8/6/2012 10:37 AM, Bruno Marchal wrote:
Is the translation or encoding a unique mapping? How many possible ways are available to encode B?

There is an infinity of way to encode "B". Some can be just intensionally equivalent (different codes but same logic), or extensionally equivalent but not intensionally equivalent, like Bp and Bp & Dt. They prove the same arithmetical proposition, but obeys different logic.

OK, do you not see that the infinity of ways that "B" can be encoded makes the name of "B" ambiguous?

I don't see that at all.

If we cannot achieve a "definite description" then there is no unambiguous name.


To deal with this we could use Gödel Incompleteness result to prove the existence of a meta-theory within which sentences about the ambiguously named entity are true, but doing this is equivalent to a coarse graining. We are effectively defining truth values as embedded invariants of logical theories. My question to you is whether or not there is an algebra that captures this kind of logical theory? I apologize that my wording is very bad, but does this make any sense to you? It sounds a lot like your G* idea, but I am not sure.

G* is not my discovery. It is the discovery of Gödel, Löb, ... Solovay. It is the correct logic of self-reference of a vast class of self-referential entity, among them the correct machines, once they have enough coginitive ability, like PA, ZF, etc..

The name of "B" is at most 1p; a private name and thus subject to Wittgenstein's criticism.

All the names of "B" are third person notion, even if "B" itself cannot recognize its body or code. It is only "self-ambiguous", which is partially relevant for the measure problem. This is why I use modal logic to handle that situation, besides the fact that incompleteness leaves no real choice in the matter.

OK, but exactly how is this third person defined? Who is it? What is their name?

By a machine description or by its Gödel number. Come one, "B" is defined in arithmetic in Gödel's original paper.

The experiences are strictly 1p even if they are the intersection of an infinity of computations, but this is what makes then have a zero measure!


What is the cardinality of the infinity of computations that is implied by a 1p?


A finite and semi-closed consensus of 1p's allows for the construction of diaries and thus for the meaningfulness of "shared" experiences. But this is exactly what a non-primitive material world is in my thinking and nothing more. A material world is merely a synchronized collection of interfaces (aka synchronized or 'aligned' bisimulations) between the experiences of the computations. I use the concept of simulations (as discussed by David Deutsch in his book "The Fabric of Reality") to quantify the experiences of computations. You use the modal logical equivalent. I think that we are only having a semantical disagreement here.


The problem that I see in COMP is that if we make numbers (or any other named yet irreducible entity) as an ontological primitive makes the measure problem unsolvable because it is not possible to uniquely name relational schemata of numbers. The anti-foundation axiom of Azcel - every graph has a unique decoration - is not possible in your scheme because of the ambiguity of naming that Godel numbering causes. One always has to jump to a meta-theory to uniquely name the entities within a given theory (defined as in Godel's scheme) such that there is a bivalent truth value for the names. Interestingly, this action looks almost exactly like what happens in a forcing! So my claim is, now, that at best your step 8 is true in a forced extension.


Sorry, bad wording. I will try harder to make myself clear on this.

On 8/6/2012 10:37 AM, Bruno Marchal wrote:
[SPK] At what level (relative) is the material hypostases?
This is ambiguous. The material hypostases (Bp & Dt) defines the (high) level where machines (the person incarnated by the machine) can make the observations. But it is preferable to extracts all those answer by yourself, for all what I say here needs to be extracted to get the UDA step by step.

Dear Bruno,

OK, we seem to be in agreement on this. At the "high level" there is a meaningful notion of observations (and naming as I have discussed in previous posts) but never at the primitive level.


My point is that this meaningfulness vanished anywhere outside of this high level.

I agree.

We cannot pull back the meaning of a term when and if we pull back the term to the primitive level, because doing so, as you discuss in step 8,


    I will write a separate post on this.

severs the connection that carries the relations that define the unique name that occurs at the high level. This is the problem of epiphenomena of immaterialism.


I would like to point you to this blog article http://www.scifiwright.com/2007/12/immaterialism-the-long-answer/ It addresses many of my concerns!

Then use it to make your concern clear.

On 8/6/2012 10:37 AM, Bruno Marchal wrote:

We cannot use the Godel numbering because they are not unique,

If the names (description) were unique, there would be no first person indeterminacy. A enumerable infinity , non mechanically enumerable though, of explicit description of Stephen King exists in arithmetic, if comp is true.

Dear Bruno,

   But it does not exist uniquely as a singleton in arithmetic


and that is the problem.

The interesting problem, yes. That is the point.

OK, but could you comment on the implications of this that you see?


Well, the main point is that physics is a branch of the theology of numbers, or arithmetic/computer science, or intensional arithmetic.

It does exist as the equivalence relation on a infinite class of computations, but these equivalence classes do not have a power- set of which they are a uniquely defined.


Names are only meaningful when and if they are 3p.

You must clearly define what 3p is in your theory! My definition of 3p is "a consensus of many distinct 1p".

That consensus is not 3p. It is only first person plural. Like physics will be. "3p" means at first "belongs to the diary of an observer of a teleportation or duplication", like in the protocol of the first UDA steps. 3p means that it is independent of 1p. Eventually 3p will mean, after UDA, arithmetical.

Many question that you ask are answered all along the reasoning. So, I am not sure you really do the reasoning, to be franc.



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