Hi Stephen P. King
Pratt does not seem to understand that there is an ontological firewall between
extended (body)
and inextended (mind) entities. As far as I know, only monadology can wipe out
that problem.
Roger Clough, rclo...@verizon.net
8/23/2012
Leibniz would say, If there's no God, we'd have to invent him so everything
could function.
- Receiving the following content -
From: Stephen P. King
Receiver: everything-list
Time: 2012-08-22, 16:29:22
Subject: Re: Pratt theory
Hi Richard!
Wonderful! Another pair of eyes looking at Pratt's work. This is progress!
There are a couple open problems, such as how to model large networks of
bisimulations but from my toy model study I think I have a solution to that
one. The only technical problems are the formulation of a tensor product rule
for arbitrary Monads (whose bodies/minds are the logical algebra and
topological space couples that Pratt models using Chu_k spaces) and the
forgetful version of residuation. I have some ideas on those too...
By the way, the entire question of particles/strings/etc. is reduced to a
phenomenology/epistemology question that can be addressed using computational
simulation modeling and considerations of observational bases. We only need to
recover/derive the data not the stuff. The mereology of monads would follow
the entanglement scheme of QM (for Chu_k ; k = complex number field) and allow
us to use the pseudo-telepathy idea from quantum game theory to model
bisimulation networks in a different basis. What I like about this the most is
that it offers a completely new paradigm for investigations into physics and
philosophy. See http://boole.stanford.edu/pub/ph94.pdf for even more
discussions.
On 8/22/2012 4:04 PM, Richard Ruquist wrote:
Stephan,
Many thanks for this wonderful paper by Vaugh Pratt
http://boole.stanford.edu/pub/ratmech.pdf
Pratt theory appears to replace Godellian theory.
But Godellian theory manifests consciousness, so some think.
And Pratt theory seems to apply to the interaction of physical particles
with each other and with the monads
Its axioms seem reasonable- but who am I to say.
1.A physical event a in the body A impresses its occurrence on a mental state x
of the mind X, written a=|x.
2.Dually, in state x the mind infers the prior occurrence of event a, written x
|= a.
3.States may be understood as corresponding more or less to the possible worlds
of a Kripke structure,
and events to propositions that may or may not hold in di erent worlds of that
structure.
4.With regard to orientation, impression is causal and its direction is that of
time.
5.Inference is logical, and logic swims upstream against time.
Prolog’s backward-chaining strategy dualizes this by viewing logic as primary
and time as swimming upstream against logic,
but this amounts to the same thing. The basic idea is that time and logic ow
in opposite directions.
6.The general nature of these inferences depends on the set K of values that
events can impress on states.
7.Our rst distinction between body and mind will be the trivial one of using
di erent variables to range over these sets: A, B over bodies, X, Y over minds.
8.The second distinction will be in how the two kinds of sets transform into
each other.
9.Later we make a third distinction within the objects themselves by realizing
the two kinds as Chu spaces with dual form factors: sets tall and thin,
antisets short and wide.
10.We regard each point of the interval as a weighted sum of the endpoints,
assuming nonnegative weights p, q normalized via p + q = 1, making each point
the quantity p q.
11.We shall arrange for Cartesian dualism to enjoy the same two basic
connections and the two associated properties, with mind and body in place of
1 and 1 respectively.
12.Minds transform with antifunctions or antisets, and sets are physical.
13.Mental antifunctions/sets copy and delete, whereas physical functions
'identify and adjoin'.
14. For K the set (not eld) of complex numbers, right and left residuation
are naturally taken to be the respective products ...
corresponding to respectively inner product and its dual outer product in a
Hilbert space
That The numbers ±1 are connected in two ways, algebraic and geometric
suggests how the spatial separation of the monads is equivalent to an algebra.
This also sounds much like a straight line with points along the line having
the properties P,Q such that P+Q=1
Now this is interesting: Points have necessary existence, all being present
simultaneously in the physical object A.
15.States are possible, making a Chu space a kind of a Kripke structure
[Gup93]:
only one state at a time may be chosen from the menu X of alternatives.
Seems that divine intervention may be an assumption. I wonder who does the
choosing. May I suggest Godellian consciousness?
16. the spaces A and B play the interaction game A B, their tensor product.
17. The
