On Sun, Sep 24, 2006 at 03:23:44PM +0200, Bruno Marchal wrote:
> 
> 
> Le 23-sept.-06, ˆ 07:01, Russell Standish a Žcrit :
> 
> 
> > Anything provable by a finite set of axioms is necessarily a finite 
> > string of
> > symbols, and can be found as a subset of my Nothing.
> 
> 
> You told us that your Nothing contains all strings. So it contains all 
> formula as "theorems". But a theory which contains all formulas as 
> theorems is inconsistent.
> I am afraid you confuse some object level (the strings) and 
> theory-level (the theorems about the strings).

Actually, I was wondering if you were making this confusion, owing to
the ontological status you give mathematical statements. The
Nothing, if interpreted in its entirety, must be inconsistent, of course. Our
reasoning about it need not be, and certainly I would be grateful for
anyone pointing out inconsistencies in my writing.

> 
> Perhaps the exchange is unfair because I react as a "professional 
> logician", and you try to convey something informally. But I think that 
> at some point, in our difficult subject, we need to be entirely clear 
> on what we assume or not especially if you are using formal objects, 
> like strings.
> 

I'm not that informal. What I talk about are mathematical objects, and
one can use mathematical reasoning. However, the objects are more
familiar (to a mathematics student) than the ones you discuss (its
just standard sets, standard numbers and so on), so I suspect you read
too many nuances that aren't there...


> 
> 
> > I should note that the PROJECTION postulate is implicit in your UDA
> > when you come to speak of the 1-3 distinction. I don't think it can be
> > derived explicitly from the three "legs" of COMP.
> 
> 
> I'm afraid your are confusing the UDA, which is an informal (but 
> rigorous) argument showing that IF I am "digitalisable" machine, then 
> physics  or the "laws of Nature" emerge and are derivable from number 
> theory, and the translation of UDA in arithmetic, alias the interview 
> of a universal chatty machine. The UDA is a "reductio ad absurdo".  It 
> assumes explicitly consciousness (or folk psychology or grandma 
> psychology as I use those terms in the SANE paper) and a primitive 
> physical universe. With this, the 1-3 distinction follows from the fact 
> that if am copied at the correct level, the two copies cannot know the 
> existence of each other and their personal discourse will 
> differentiate. This is an "illusion" of projection like the wave packet 
> *reduction* is an "illusion" in Everett theory. 

Fair enough, the "Yes Doctor" is sufficiently informal that perhaps it
contains the seeds of the PROJECTION postulate. When we come to the
discussion of the W-M experiment, there are 3 possible outcomes:

1) We no longer experience anything after annihilation at Brussels
   (contradicts YD)
2) We experience being both in Moscow and Washington simulteously
   (kinda weird, and we dismiss as a reductio, but could also be seen
   as contradicting PROJECTION)
3) We experience being in one of Moscow or Washington, but not both,
   and cannot predict which.

I've noticed a few people on this list arguing that 2) is a possible outcome -
probably as devil's advocates. That would certainly be eliminated by
something like the PROJECTION postulate.

> The UDA reasoning is 
> simple and the conclusion is that there is no primitive physical 
> universe or comp is false. Physics emerges then intuitively from just 
> "immaterial dreams" with subtle overlappings. The UDA does not need to 
> be formalized to become rigorous. But having that UDA-result, we have a 
> thoroughly precise way to extract physics (and all the other 
> hypostases) from the universal interview. For *this* we need to be 
> entirely specific and formal. That is why in *all* my papers (on this 
> subject) I never separate UDA from the lobian interview. This is hard: 
> I would not have succeed without Godel, Lob and other incompleteness 
> theorems.
> I have a problem with your way of talking because you are mixing 
> informal talk with formal object (like the strings). Like when you 
> write:
> 
> 
> > The Nothing itself does not have any properties in itself to speak
> > of. Rather it is the PROJECTION postulate that means we can treat it
> > as the set of all strings, from which any conscious viewpoint must
> > correspond to a subset of strings.
> 
> 
> It looks like a mixing of UDA and the lobian UDA. It is too much fuzzy 
> for me.
> 

I'm sure you know about mathematical modelling right? Consider
modelling populations of rabbits and foxes with Lotka-Volterra
equations. The real system differs from the equations in a myriad of
ways - there are many effects like drought, the fact that these
animals breed sexually etc. that aren't represented in the
equations. Nevertheless, the two systems, formal LV equations, and
informal real fox/rabbit system will behave concordantly provided the
systems stay within certain limits.

In this case, I would say the "Nothing" is an informal concept, and
the set of all strings (U say) is a formal concept that models it. I
would go further and say that whatever we observe, whatever we
construct, corresponds to that subset of U whose elements mean (or
describe) what we observe etc. This is the PROJECTION postulate. It is
also an act of faith that this model is the best we can possibly do as
conscious observers, so that this model is a candidate for a Theory of
Everything (or Theory of Nothing). Ultimately, one hopes for testable
predictions, and indeed there do appear to be predictions of sorts,
although whether these are empirically verifiable is another
matter. Obviously, there are a number of other seemingly reasonable
assumptions (which I have tried with utmost care to extract as
postulates) needed to connect the dots. So empirical falsification
will not necessarily bring down the entire ediface, but would
certainly lead to some interesting insights.

> 
> >
> >> But it is neither "nothing". It is the natural numbers without 
> >> addition
> >> and multiplication, the countable order, + non standard models.
> >
> > I disagree - it is more like the real numbers without order, addition
> > and multiplication group structures, but perhaps with the standard
> > topology, since I want to derive a measure.
> 
> 
> Are you saying that your Nothing is the topological line? Again it is 
> not nothing (or it is very confusing to call it nothing), and what you 
> intend will depend on your axiomatization of it. 

It is the set of all infinite length strings (in some alphabet). There
is a probability measure defined on infinite subsets - this would be
enough to show that the measure of the subset 1* (for binary strings)
is 0.5 and so on. Looks like a topological line, but would need to
check the axioms.

It is "Nothing", because of the modelling relation, and the insistence
that all we can know of anything comes in the form of strings.

> If you stay in first 
> order logic, this will give an even weaker theory than the theory of 
> finite strings: you will no more be able to prove the existence of any 
> integer, or if you take a second order logic presentation of it, then 
> your "nothing" will contain much more than what the ontic comp toes 
> needs, and this is still much more than "nothing". 

This comment sounds like it is coming from arithmetic
realism. Theories about something, don't have to be the something. One
can use whatever mode of logical reasoning one is comfortable with -
the onotological status is simply given by the modelling
relation. When I say "The set of all strings (or descriptions)
exists", I am making an ontological statement. When one shows that this
leads to Occams razor, one is doing logic, not ontology.

> To be franc I am 
> astonished you want already infinite objects at the ontological level. 
> If *all* infinite strings are in the ontology, that could be a 
> departure from comp (and that would be interesting because, by UDA, 
> that would make your theory predicting a different physics and then we 
> could test it (at least in principle), and only when your theory will 
> be precise enough.
> 

I'm not convinced it is a departure from COMP, but as you say it would
be interesting if true. Can you elaborate further on your reasons,
perhaps saying which infinite strings cannot be found in UD* for example?

> 
> I though your ontic TOE (the strings) was similar to RA, but I guess I 
> was wrong, so I am less sure I understand what you try to do.
> 

I would say it is more like assuming that UD* exists, whilst remaining
silent on the topic of whether a universal dovetailer exists, or even
on the prerequisites such as AR or the CT thesis.

Of course, a certain amount of this is taste - assuming that UD* is
identical to the set of all infinite length strings (which your
previous comments have given doubt). Either you presuppose the
existence of some simple program, or you note as I do that the set of
strings is the simplest possible object (by definition of simplicity).

Cheers

-- 
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