Dear Bruno,

  Could it be that the physical world that is associated with an observer
(using your definition of an observer) is the "truth" of that observer? I
apologize for the weirdness of this question, but consider that nothing is
more "true" than the 1st person experience that an observer has. An
observer could doubt that what it experiences is "real" and even have a
sophisticated argument for how it could not possibly be real, but
nonetheless the illusion of a physical world persist...

  One property of Truth (at least the Platonic notion of truth) is that it
is eternal and immutable. There is another property that can be teased out!
There is no contingency in that 2 + 2 = 4 and that 17 is prime. Could it be
that this 'non-contingency' is the result of the fact that at least a
countable infinity of observers (numbers!) can verify to themselves that
they are numbers (they cannot know which number they are) and thus are
members of the set of numbers.
  This leads me to guess that maybe a physical world is a finite truth of
sorts in the way that a arithmetic fact is an infinite truth.

  What would happen if we considered your UD idea on finite sets of numbers
that are very large but still finite? Would we still have the permanence
and non-contingency of truth for such sets?

  I like to see you speculating out loud so that I can add my own
speculation. It could all be nonsense... :-)



On Fri, Dec 20, 2013 at 4:51 AM, Bruno Marchal <marc...@ulb.ac.be> wrote:

>
> On 19 Dec 2013, at 22:46, Jason Resch wrote:
>
>
>
>>
>> > 8. There is no need to build the computer in step 7, since the
>>> executions of all programs exist within the relations between large numbers.
>>>
>>
>> That would only be true if everything that could exist does exist, and
>> maybe that's the way things are but it is not obviously true.
>>
>
> It doesn't require that everything to exist, it requires only one
> particular program to exist: the universal dovetailer.  This program and
> its execution exist within mathematics.
>
>
> Yes, even in arithmetic, and under different important forms. Its many
> descriptions exist, and the computation are "truly" emulated in the truth
> referred by the theorems concerning those description. That is a point
> which met some difficulties for non-logician, as it is impossible to ever
> point a computation, without mentioning a description of it. The
> computation itself is captured by the truth of certain arithmetical
> statements, not by the existence of a description of those computations.
> The nuance is subtle, because we infer the existence of the computation by
> looking at the existence of some description of them, and to show that this
> is equivalent is by no means a trivial affair, linking the syntax of the
> theory and its intended meaning (and that is why we need AR). There is a
> need to really study how simple theories (like RA) can represent in some
> strong sense the partial recursive function. It is well done in Boolos and
> Jeffrey, or in Epstein & Carnielli.
> The whole difficulty of step 8 is in this paragraph. Those who believe
> that a filmed boolean graph can be thinking commit a confusion between use
> and mention (like I have just described).
>
>
> For example, it is a true statement that the state of this program after
> the 10^100th step of its computation has some particular value X, and it is
> also a true statement that the 10^100 + 1 step has some other particular
> value Y. It is also a true statement that the program corresponding to the
> emulation of the wave function for the Milky Way Galaxy contains John Clark
> and this particular John Clark believes he is conscious and alive and
> sitting in front of a computer in a physical universe.
>
>
> OK.
>
>
>
>
>>
>> > Hence, arithmetical realism is a candidate TOE.
>>>
>>
>> A candidate certainly, but is it the real deal? Maybe but it's not
>> obvious.
>>
>
> Right, but it is a scientific question. It will not be easy but we can
> refute or confirm the theory by seeing what the UD implies for the physics
> that observers see. Everett's theory was a great confirmation, for without
> it, conventional QM with collapse (and a single universe) would have ruled
> it out. As it stands, there are several physical concepts that provide
> support for the UD being a valid TOE:
>
> Quantum uncertainty
> Non clonability of matter
> Determinism in physical laws
>
>
> Actually, this one is the problem. There might still be a too big FPI,
> like with the "white rabbits".
>
>
>
>
> Information as a fundamental "physical" quantity
>
>
> Yes, and even obeying different "information laws" above and below the
> substitution level. And this is confirmed by the difference between quantum
> information and classical (Shannon) information theory.
>
>
> (I think there is something I am forgetting, but Bruno can fill in the
> gaps)
>
>
> May be after more coffee :)
>
> What we need to do, or at least what mathematicians should do is to
> compare the empiric quantum logics with the quantum logics provided (by
> Goldblatt's result) on the (three) arithmetical quantum logic provided by
> the arithmetical quantizations (S4Grz1, Z1*, X1*). It fits up to now, but
> the program I wrote to test this should be optimized.
> We can come back on this.
>
> Bruno
>
>
>
>
> http://iridia.ulb.ac.be/~marchal/
>
>
>
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