On 11 Jan 2014, at 06:05, 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"?.
This solves the mind-body linkage problem of Descartes' dualism.
The paper 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.
It is a nice idea, but it does not take into account the FPI (he is
unaware of it), and so does not address the comp mind-body problem.
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!)
AR provides the neutral monism!
Comp is neutral monism. Neither mind, nor matter are taken as
primitive. Both emerge from the additive-multiplicative structure of
arithmetic (AR), and that structure provides the neutral stuff.
Bruno
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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