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 <[email protected]>
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 <[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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Kindest Regards,
Stephen Paul King
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Mobile: (864) 567-3099
[email protected]
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