On 1/10/2014 9:05 PM, Stephen Paul King wrote:
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.
Hmm? Steven turns into a White Rabbit is not a /*logical*/ contradiction, it's a
/*nomological*/ one. If there's a transition from (t1,x1) to (t2,x2) it seems the only
/*logical*/ contradiction would be x2="Not x1 at t1." "Logical" is a very weak condition;
as far as I know it just means being consistent=(not every sentence is a theorem).
Brent
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 <[email protected]
<mailto:[email protected]>> 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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