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 > > -- > 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/TBc_y2MZV5c/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 email@example.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. 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