Dear Stephen,
On 18 Feb 2012, at 20:09, Stephen P. King wrote:
On 2/17/2012 2:37 PM, Bruno Marchal wrote:
On 17 Feb 2012, at 14:23, Stephen P. King wrote:
I agree with this but I would like to pull back a bit from the
infinite limit without going to the ultrafinitist idea. What we
observe must always be subject to the A or ~A rule or we could not
have consistent plural 1p, but is this absolute?
I am not sure what we observe should always be subject to A or ~A
rule. I don't think that's true in QM, nor in COMP.
Dear Bruno,
Think about it, what would be the consequence of allowing A ^ ~A
to occur in sharable 1p?
I thought we were discussing A V ~A.
If we start out with the assumption that all logics exist as possible
I have no referent for all logics. I can't assume this.
and then consider which logics allow for sharable 1p, then only the
logics that include the law of bivalence would have sharable 1p that
have arbitrarily long continuations.
?
We could get contradictions in the physics at least! This would
disallow for any kind of derivation of physical laws. My thinking is
motivated by J.A. Wheeler's comments, re: It from Bit and Law
without Law. We are considering that our physical laws derive from
the sharable aspects of first person content, after all... This is a
natural implication of UDA, no? So either we are assuming that
physical laws are given ab initio or that they emerge from sharable
1p.
UDA shows them to have to emerge from sharable 1p. OK.
Either way, the logic of observables in any sharable 1p must be A or
~A.
?
This is part of my reasoning that observer logic is restricted to
Boolean algebras (or Boolean Free Algebras generally).
This refuted in the material hypostases. You might elaborate on the
proof above, but the premise is fuzzy, for the experession "all
logics" does not make sense for me.
My question is looking at how we extend the absolute space and
time of Newton to the Relativistic case such that observers always
see physical laws as invariant to their motions, for the COMP case
this would be similar except that observer will see arithmetic
rules as invariant with respect to their computations. (I am
equating computations with motions here.)
OK.
So do you understand my question about the Standard-ness of
arithmetic models? I am assuming that each 1p continuation has to
implement a model of arithmetic that would seem to be standard so
that it always is countable and recursive, if only to allow for
continuation. Is this OK so far?
Not really, because the model of the intensional variants of the self-
reference logics don't need to be defined in term of model of
arithmetic. An 1p continuation does not necessarily corresponds to a
standard/non-standard choice.
I do not know where the arithmetic model would be implemented.
What do mean by a model being implemented. Computations are
implemented in the arithmetical true and provable (sigma_1) relations.
Would it be in the Loebian Machine or a sublogic of it?
In arithmetic.
The idea is that every observer thinks that it's arithmetic is
countable and recursive even though from the "point of view of
god" (a 3p abstraction) every observers model is non-standard.
Proof, or argument needed. The contrary occurs? For God everything is
simple (arithmetical truth), but for the machine inside in the
transfinite non computable unnameable mess.
The alternate option to COMP being false is usually some form
of infinitely complex matter and infinitely low subst. level.
Either way, one option allows copying(COMP), even if at worst
indirect or just accidentally correct, while the other just
assumes that there is no subst. level.
No, this is only the "primitive matter" assumption that you
are presenting. I have been arguing that, among other things,
the idea of primitive matter is nonsense. It might help if you
wanted to discuss ideas and not straw men with me.
This contradicts your refutation based on the need of having a
physical reality to communicate about numbers.
OK, I will try to not debate that but it goes completely
against my intuition of what is required to solve the concurrency
problem. Do you have any comment on the idea that the Tennenbaum
theorem seems to indicate that "standardness" in the sense of the
standard model of arithmetic might be an invariant for observers
in the same way that the speed of light is an invariant of motions
in physics?
My motivation for this is that the identity - the center of
one's sense of self "being in the world" - that the 1p captures is
always excluded from one's experience. Could the finiteness of the
integers result from the constant (that would make one's model of
arithmetic non-standard) being hidden in that identity? This
wording is terrible, but I need to write it for now and hope to
clean it up as I learn better.
The feeling that + and * are computable, which most people have
when coming back from school, can be used with Tennenbaum theorem
to defend the idea that we share the standard model, in some way. I
would not dare saying more than that. Do you know if Tennenbaum
theorem extends to non countable models?
All this is a bit technical, and perhaps out of topic, I think.
No, it is important because we cannot just assume a shared
standard model of arithmetic because that would collapse all the
plural 1p Loebian Universal Machines into a single solipsistic
Machine.
The distinction between G and G* and the other hypostases prevent this
to occur.
Where has to be a reason for the separateness of the individual LUM
and what I am proposing might accomplish that and also give us a
reasoning why physics is relativistic as opposed to absolute, i.e.
why GR is possible.
Best wishes in your endeavor,
Bruno
http://iridia.ulb.ac.be/~marchal/
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