On 20 Dec 2013, at 20:06, Stephen Paul King wrote:
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.
Truth enter in the picture in two ways:
1) by the inetnsional nuance when we add the "& p", like in the first
and second application of Theaetetus:
Bp ===> Bp & p
Bp & Dt ====> Bp & Dt & p
and
2) By the splitting between G and G* inherited by such variants, which
is a spliiting between true about the machine and what the machine can
prove.
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...
Yes, that is captured by the Theatetus "& p" nuance.
One property of Truth (at least the Platonic notion of truth) is
that it is eternal and immutable.
OK. I would say that it is not even temporal.
There is another property that can be teased out! There is no
contingency in that 2 + 2 = 4 and that 17 is prime.
OK.
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.
I don't see this. Normally the physical reality inherits the computer
science infinities.
What would happen if we considered your UD idea on finite sets of
numbers that are very large but still finite?
?
The UD generates and execute programs, which are all finite, by
definition, on all data, which are 3p-finite, but 1p-infinite.
Would we still have the permanence and non-contingency of truth for
such sets?
?
Bruno
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/
--
You received this message because you are subscribed to a topic in
the Google Groups "Everything List" group.
To unsubscribe from this topic, visit https://groups.google.com/d/topic/everything-list/1NWmK1IeadI/unsubscribe
.
To unsubscribe from this group and all its topics, send an email to everything-list+unsubscr...@googlegroups.com
.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/groups/opt_out.
--
Kindest Regards,
Stephen Paul King
Senior Researcher
Mobile: (864) 567-3099
stephe...@provensecure.com
http://www.provensecure.us/
“This message (including any attachments) is intended only for the
use of the individual or entity to which it is addressed, and may
contain information that is non-public, proprietary, privileged,
confidential and exempt from disclosure under applicable law or may
be constituted as attorney work product. If you are not the intended
recipient, you are hereby notified that any use, dissemination,
distribution, or copying of this communication is strictly
prohibited. If you have received this message in error, notify
sender immediately and delete this message immediately.”
--
You received this message because you are subscribed to the Google
Groups "Everything List" group.
To unsubscribe from this group and stop receiving emails from it,
send an email to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/groups/opt_out.
http://iridia.ulb.ac.be/~marchal/
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/groups/opt_out.
