Hi Russell,
I got your book. Congratulation for that very nice introduction to the
subject and to your ideas. It is a very gentle and lovely book.
Probably because you are to kind to your audience, it seems to me you
have sacrifice perhaps a bit of rigor. I am still not sure about your
most basic assumption, but I see we share a big amount of the
philosophy.
I am already glad you did take into account 1/5 of my earlier remarks,
I wish you at least five next editions ;-).
To be honest I don't think you really get the comp idea, and it is a
good think your work does not really rely on it. Now I will not hide
the pleasure I have when seeing the 8 hypostases (even the sixteen
one!) sum up through their modal logic in table 71 page 129.
I will neither repeat my olds comments nor make new one, but hope our
future discussion will give opportunities to clarify the possible
misunderstandings and relationship between our approaches.
I let you know that I will be very busy from now until end of october,
so that I will be more slow for the comments' replies (or more grave
for the spelling mistakes if that is possible).
==================================
Russell wrote
>
> 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,
This can make sense only if you tell us how to interpret a string or
how you interpret the Nothing, I mean formally.
From this I infer that your nothing is an informal theory of infinite
strings.
Also I give only ontological status to object in the scope of an
arithmetical existential statement. For example I do believe in the
existence of prime numbers.
> must be inconsistent, of course.
Only a theory can be inconsistent. But I don't see a theory.
> Our
> reasoning about it need not be, and certainly I would be grateful for
> anyone pointing out inconsistencies in my writing.
That is why I would insist to be as clear as possible so that the
inconsistencies are more easy to find.
>
>>
>> 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.
The formal/informal distinguo has nothing to do with the
mathematical/non-mathematical distinguo. Nor with
rigorous/non-rigorous.
100 % of mathematics, including mathematical logic is informal. Now,
logicians studied "formal theories" or "machines" because it is what
they are studying. But they prove things about "formal systems" in an
informal way like any scientist.
In some context formal and informal are relative.
Of course a description of a formal system looks formal, but we reason
*about* those formal systems. Now, if your strings are all there is, I
wait for an explanation of what those strings does "formally", but I am
not asking to formalize your reasoning in your string-language, unless
for illustrative purpose in case you want to illustrate how a string
interprets something. Like we can explain how a brain or more simply
how a turing machine can interpret some data. To be sure, given that
your strings are infinite I have no clue how the strings can interpret
things.
>>
>>> 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.
Really? I thought only Chalmers does that. Do you know someone else?
Lee Corbin was apparently doing that, but when I insisted on the 1/3
distinction, Lee did eventually admit he could not predict its
immediate future *first person* experience: the comp 1-person
indeterminacy (casr "3)" above). OK Lee, if you are still there?
> That would certainly be eliminated by
> something like the PROJECTION postulate.
Honestly I feel it not being necessary, for the same reason the
collapse is not necessary in QM.
>
>> 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.
I hope your book will help me to figure out what you say.
>> 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.
What is 1*, is it "1111111111..." why 1/2?
Is it "1" follow by any strings. Then OK, for some measure.
> 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.
Is that a new postulate? Why "Nothing" ?
>
>> 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.
Indeed, but a theory of everything should, in some sense (by definition
of everything). If you have only infinite string in the ontology, I
guess you have to modelize the observers by an infinite string, or by
something you can derive from the set of infinite strings, and you have
to explain how you make the derivation, and how those observer will
converge on your theory, or explain why they diverge from it.
> One
> can use whatever mode of logical reasoning one is comfortable with -
Sure, but in front of unclarity or conceptual problems we should be
able to say which logic we use, even informally, like with or without
excluded-middle, or with or without some infinity axiom, etc.
> 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.
Indeed, you are saying that set (of real numbers) exists. I guess you
presuppose some set theory? It is different to say "all strings exist"
and "the set of all string exists". Again, in some informal reasoning
to make that difference explicit would be falling in the 1004 fallacy,
but if you say the strings are the fundamental object, then if you talk
on that set you have to explain in which sense that set is a string.
To my knowledge only the UD does that effectively. In a frame with
infinite objects, some non effective way has been given but it always
lead toward very difficult mathematics (ZF + axiom of anti-foundation
like Stephen appreciates, or NF + universal sets (NF = Quine's new
foundation; nobody know really if NF is consistent).
> When one shows that this
> leads to Occams razor, one is doing logic, not ontology.
Are you really saying that Occam follows from your string "theory"?
Also you could perhaps use "stream" instead of "string", to prevent
confusion with the use of string by physicist, and also because for
many computer scientist strings (of characters) are supposed to be
finite. Just a little suggestion.
>
>> 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 could elaborate a lot about the vagueness of the notion of "finding"
something in the UD* (the infinite complete running of the UD).
I could ask "finding by who?", from inside? from the terrestrial
(verifiable) view or the divine one (true but non verifiable)?, from
which x-person point of view? Etc.
Given that the UD cannot not dovetail on all the reals, there is a
sense in saying all the infinite strings are generated, but this gives
a noisy background first person machine have to live with. The UD is
not equivalent with "all infinite strings", the UD* is a static given
of all computations. Those computations can be represented by very
peculiar finite and infinite strings together with a non trivial
structure inherited from computer science/number theory.
>
>>
>> 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.
What could "UD* mean, without CT? If you don't use CT, you have to give
at least one precise universal machine (or sigma1 complete theory).
>
> 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).
Indeed.
> Either you presuppose the
> existence of some simple program,
I do! The S and K combinators for example. Or the axioms of RA, or any
Universal Diophantine Equation. I do presuppose the notion of universal
machine. That is what CT is all about.
> or you note as I do that the set of
> strings is the simplest possible object (by definition of simplicity).
An infinite set of infinite objects ? Including obviously some
structure on it, if only to give sense to your projection postulate, I
am not sure this is simple. I can miss something of course, but it
seems to me your theory, if we assume comp, will be more or less
equivalent to a simple infinite iteration of the WM duplication
experiment, on which the natural comp "projection" leads to noise. So I
guess your theory is complementary to comp instead. UD* is a far more
sophisticate mathematical structure than a real topological line. Its
sophisticateness, if I may say, comes from the non triviality of
computer science, of the Fi and the Wi, for example, through the many
incompleteness phenomena, and it is that highly structured complexity
which gives rise to highly non trivial internal n-person views (the
hypostases and their logical multiverses).
Bruno
http://iridia.ulb.ac.be/~marchal/
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Received on Tue Sep 26 2006 - 10:14:41 PDT