On 11 Oct 2010, at 00:54, Stephen Paul King wrote:
Fixing a missing part of my post
From: Stephen Paul King
Sent: Sunday, October 10, 2010 2:46 PM
To: [email protected]
Subject: Re: A paper for your Comments
Hi Bruno,
Interleaving...
From: Bruno Marchal
Sent: Sunday, October 10, 2010 11:16 AM
To: [email protected]
Subject: Re: A paper for your Comments
Hi Stephen,
The discussion has evolved enough now from my original topic as
to require that I restate my thesis and add some new ideas in a new
post with a new subject line, given some new understanding of your
ideas. I greatly appreciate your patience and comments as I have
learned a great deal from it. I believe that we agree on sufficient
points to move forward so that I will leave you comments below
stand as a reference for the future. Right now I have one question:
Are you familiar with Jaakko Hintikka's idea of game semantics for
Logic in which (crudely put) on thinks of a proof is related to the
existence of a winning strategy in a 2-person game.
What is your opinion of such, if any?
For examples please see:
http://plato.stanford.edu/entries/logic-games/
http://www.csc.villanova.edu/~japaridz/CL/gsoll.html
http://en.wikipedia.org/wiki/Game_semantics
[BM] That is very interesting, but with respect to the question I am
interested in, this is a question of implementation. The point of
mechanism is that the internal views does not depend on the choice
of the initial system.
[SPK]
My idea is that the "top-down" instantiation of proofs from
Arithmetic Realism's P.o.V. is reflected in a "bottom-up" way by an
infinite number of interactions *between many agents, thus the
relevance of the notion of proofs from semantic games and
correlations therein*. This sets up a natural symmetry of sorts
between the ONE and the MANY, where the "internal views" are within
the MANY *as 1st person PoV*.
There would be no unique "initial system" in the objective sense
for the same reason that there can be no first implementation in the
objective 3rd person sense. This has the implication for physical
systems that there is no origin for time and space in an objective
sense. The Perfect Cosmological Principle that the Universe is
homogenous and isotropic in space and time would obtain for an
average "observer"; thus a finite space and duration of the world
would obtain for any instance. This would solve the initial
conditions problem in physics.
**
I ask this because it seems that one of the key points of
divergence in our discussion is related to my use of ideas that are
implicit in game semantic based logics.
[BM] All digital parallelism can be emulated by digital sequences.
In the mind-body problem parallelism is a red herring, because IF it
plays some role for the measure problem, THEN it will be justified
by the extraction of space and time. Of course in concrete 3D-time
applications, parallelism is without doubt of upmost importance.
[SPK]
I agree and this goes straight to the root of the idea that
I am exploring. This is why I am looking at the duality between
Boolean algebras (and their generalizations) and disconnected/
scattered spaces that we see in the Stone Representation theorem.
Minds would be instances of the former and Bodies would be instances
of the latter. The trick is to see how the evolution of these works;
this is what Pratt has figured out (in basic terms).
<Emoticon1.gif> Additionally, your repeated notion that if "any
empirical difference between this arithmetical physics and the
empirical physics, would refute, not Plotinus, but the present
arithmetical interpretation" requires a means to connect or
analytically continue into physical theory; "concrete 3D-time
applications" are instances of the latter. By the way, the passages
that I quoted previously from Stephen Wolfram where relating to that
physical side and speak to limits on the content of individual
Mechanisms; those are what I am considering in the bisimulation
model of interactions.
I am not advocating physicalism except as one side of a duality.
You mean "matter". By definition physicalism excludes that the other
part as a fundamental ontology. In a sense numbers don't exist for a
physicalist. Only a dulaist can believe in number and primitive
fundamental particle.
Your quote too much in different fields to grasp what you are trying
to say.
I am against the idea that the physical (or the logical) is "all
that exists"
Make clear what are your assumption. What exist for you at the base
level.
and the proof of sorts that I point to is the epiphenomena problem
that both physical monism and mental/ideal monism have.
It is not symmetrical. If you believe in "only mind", you don't need
to make matter an epiphenomena given that uou have only "phenomena".
You could say "epi-ontologena", except that with "mind only" (and
mechanism) we don't need any ontology for matter, by definition.
Of course we need a neutral common ground to absorb both into but
that is taken into account in terms of "in the limit of where all
differences vanish".
This is a nice poetical description of inconsistency, the limit where
1 - 0 = 0.
Forgive me here as I am sacrificing clarity for brevity.
**
Additionally there is resent work that seems to strongly support my
crazy idea of how we might solve the measurement problem in QM
(which is my main motivation).
[BM] So you do assume QM, even QM + collapse apparently. I don't
assume anything in physics, given that the results is that physics
is derivable from arithmetic, and *has to be derived* from
arithmetic if we want obtain the qualia, and not just the quanta.
[SPK]
Yes, because I am coming from the opposite direction from
you! I assume QM
That's way too much for me. Although I believe QM is true, I estimate
we have to derive it from arithmetic. And that is the conclusion of
the UDA argument. Third person classical mechanism entails first
person plural quantum mechanism.
but not "collapse" per say as the metaphysical assumptions in
"collapse" go against the Perfect Cosmological Principle. We see
this in the preferred reference frame that any objective collapse
model generates. What we need, I believe, is a model where we obtain
what appears as a Collapse from a 1st person P.o.V. but is more like
the Everett-Dewitt idea from the outside 3rd person view all the
while understanding that there is no special "observer" that could
perceive the latter except as an abstract notion.
**
Please see: http://pages.stern.nyu.edu/~abranden/icig-05-27-08.pdf
This is very much related to the work of Jean-Yves Girard in his
"Geometry of Interaction".
[BM] ? (The relation is either trivial, or is not obvious for me.
Very technical paper(s). You should stick a bit more on the idea(s)
instead of mentioning so much papers which seems to me both a bit
1004-like with respect to the topic).
[SPK]
That paper discusses the notion of correlations in games which
is another way of looking at bisimulations between Mechanisms. From
the abstract:
"Correlations arise naturally in non-cooperative games, e.g., in the
equivalence between undominated
and optimal strategies in games with more than two players. But the
non-cooperative assumption
is that players do not coordinate their strategy choices, so where
do these correlations come from?
The epistemic view of games gives an answer. Under this view, the
players’ hierarchies of beliefs
(beliefs, beliefs about beliefs, . . . ) about the strategies played
in the game are part of the description
of a game. This gives a source of correlation: A player believes
other players’ strategy choices are
correlated, because he believes their hierarchies of beliefs are
correlated. We refer to this kind of
correlation as “intrinsic,” since it comes from variables—viz., the
hierarchies of beliefs—that are part
of the game. We compare the intrinsic route with the “extrinsic”
route taken by Aumann [2, 1974],
which adds signals to the original game."
I hoped that you might get an intuition of what I am trying to
work out by reading this paper... It seems to me that the notion of
Belief that Brandenburger et al are using would be related to your B
as in Bp&p. In my idea this manifests as simulations of simulations,
etc.
If you find a precise relation, then submit it. Well, you can think
aloud for some time, but don't expect too much understanding.
**
By the way, almost all of Girard's papers are inaccessible to me as
I am not in a university. I know of his work from my study of
Pratt's papers.
Take a look here:
http://iml.univ-mrs.fr/~girard/Articles.html
from Girard's web page:
http://iml.univ-mrs.fr/~girard/
Best,
Bruno
[SPK]
Thanks for pointing me to that, now I have 2X reasons to learn
to read French. :P I am still thinking on how to write up the
interaction idea. It takes me time to translate pictures in my head
to words on the screen. <Emoticon10.gif>
Try to write a paper, and make it readable by some experts in the
field you cross. Or for a wider audience, on a less ambitious version.
Mechanism is compatible with matter and dualism, if it is taken in
some phenomenological view.
You can assume QM, but my point is only that we can't do that, if we
assume M. (mechanism). QM has to be justified in M through machine's
self-reference intensional nuances.
Bruno
http://iridia.ulb.ac.be/~marchal/
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