On 11 Jan 2014, at 08:29, Stephen Paul King wrote:

Dear Brent,

"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)."

But consistent, like provable, is theory dependent.




nom·o·log·i·cal
ˌnäməˈläjikəl/
adjective
1.
relating to or denoting certain principles, such as laws of nature, that are neither logically necessary nor theoretically explicable, but are simply taken as true.

Then arithmetical truth nomological. But once assuming it, physical truth becomes necessary and logical.



Right! It was a very crude and informal explanation. Things become, hopefully, more clear when one considers the scenario where there are many minds that are communicating/interacting while evolving. Interaction requires some level of similarity between the participants.

Sure, but you are assuming much more than comp allows. That is a form of treachery which prevent the use of the G/G* distinction, and it inheritance on the other hypostases, to be used to distinguish qualia and quanta. In fact you are doing physics again, if you *assume* interacting observers. You are ignoring comp, or the UDA, in such approaches.




For example, I I where to experience a White Rabbit, what effects would it have to have on others that I interact with so that it would not effect their 1p content. I would say that it was a hallucination, maybe... We forget that what we experience of the world is not that world itself, it is our mind/brains version of such. We have to take the capacity of hallucinations into account in our thoughts of that is a mind...
   Can we not take as "true" what we experience?

Not when assuming comp. You need Church thesis, which need "17 is prime" even when we don't experience the fact.



How can we know that it is not some controlled simulation? We need to answer Descartes question: How do I know that I am not just a brain in a vat (or a computation running in some UD)?

Comp answers this by saying that we (in the 3p sense, at the right and other levels) are emulated in the UD or arithmetic, even in some brain in a vat, itself emulated in the UD, even in some UD emulated by some brain in a vat. We are in absolutely all of them. Physical reality is a self-referential emerging pattern coming from all of those emulation infinitely distributed in UD*.

Bruno







On Sat, Jan 11, 2014 at 12:45 AM, meekerdb <meeke...@verizon.net> wrote:
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"?. 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.

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 <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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