Dear Brent,
I will try a crude summary and hope to not be misunderstood... It starts
with the Stone duality, a well known isomorphism between Boolean algebras
and totally disconnected compact Hausdorff spaces. The former are
identified with minds (logical, computational, numerical, etc) and the
latter with physical objects (what is more "physical" that a space that
looks exactly like Democritus' "atoms in a
void"<http://www.scottaaronson.com/democritus/lec1.html>
?.
This solves the mind-body linkage problem of Descartes' dualism. The
paper <http://boole.stanford.edu/pub/ratmech.pdf> then discusses how
interactions between pairs of minds (generalizations of Boolean algebras
identified as "states") is mediated via pairs of bodies (generalizations of
Stone spaces to include mass, spin, charge, potentials,... physics
identified as "events"). A crude diagram of this relation for the evolution
of a single entity is:
... -> Body -> Body' -> ...
| |
... <- Mind <- Mind' <- ...
where the "|" symbol is the Stone isomorphism, "->" is the physical
evolution of one event to the next and "<-" is the logical arrow of
implication.
Mathematics as considered my most people usually ignores evolution of
logical structures, such as Boolean algebras, and so the difference between
mind and mind' is not considered. Now that computers are commonplace, the
idea that logical structures evolve makes a lot more sense! A computation
is the transformation of information and since logical structures capture
the relations of the information, it is natural to consider this theory.
In this theory, minds and bodies (including brains!) are not separable
substances but are isomorphs that have "dynamics" whose "arrows" point in
opposite directions. Physical process moves forward from event to event' in
sequences of time according to thermodynamics, etc. and logic "looks"
backward to ensure that any new state is consistent with previous states.
This implies an elegant solution to the measurement problem of QM!
Differences between states and parameters of time can be subdivided as
finely as one wishes; even to the smoothness of continua.
It is what the logical 'side of the coin" does to select physical events
that won me over to Pratt's theory: a physical transition from event x at
time t to event x' at time t' is allowed if and only if the state x'* at t'
does not imply information that would contradict prior states at t^-1,
t^-2, etc. Basically, events will occur iff they do not imply a
contradiction of previously allowed events. This automatically solves the
White Rabbit problem by disallowing events that imply logical
contradictions.
It also gives a slightly different take on computational universality:
individual logical structures are associated with equivalence classes of
physical functions and physical systems are associated with equivalence
classes of logical structures. The equivalences are, respectively:
equivalent function and semantical equivalence. Thus computations and the
physical processes are not ontologically isolated from each other, but
universality obtains because there is no a priori bijective map between the
set of particular physical systems and the set of particular Turing
universal computations.
It seems that Pratt abandoned the theory because of a lack of interest in
the community but still hosts the papers on his website. Maybe in hope that
some one might come along, like me, that can make sense of it and develop
it further. It does not consider SR at all, which bothers me a little bit,
but that can be fixed using ideas such as those of Kevin Knuth, IMHO.
Its main prediction is that neither ghosts (logics that cannot be
associated with any physical structure) nor zombies (bodies that cannot be
represented by an internal self-referencing logical structure) exist. This
argues against both material and mental monism. (Thus my conflict with
Bruno's AR!)
On Fri, Jan 10, 2014 at 9:02 PM, meekerdb <meeke...@verizon.net> wrote:
> On 1/10/2014 2:23 PM, Stephen Paul King wrote:
>
> Dear Brent,
>
> Vaughn Pratt's dualist theory is consistent with QM and does show a
> mechanism that prohibits White Rabbits. It is intelligible to anyone that
> puts forth the effort to comprehend it.
>
>
> Can you summarize it?
>
> Brent
>
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Kindest Regards,
Stephen Paul King
Senior Researcher
Mobile: (864) 567-3099
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