On 12/7/2012 1:57 PM, Bruno Marchal wrote:

On 06 Dec 2012, at 01:51, Stephen P. King wrote:

On 12/5/2012 1:01 PM, Richard Ruquist wrote:
L's monads have perception.
They sense the entire universe.

On Wed, Dec 5, 2012 at 12:45 PM, Roger Clough<rclo...@verizon.net>  wrote:
>Hi Stephen P. King
>
>
>God isn't artificially inserted into L's metaphysics,
>it's a necessary part, because everything else (the monads)
>afre blind and passive. Just as necessary as the One is to Plato's
>metaphysics.
>
>
>
>
Hi Richard,

Yes, the monads have an entire universe as its perception. What distinguishes monads from each other is their 'point of view' of a universe. One has to consider the idea of closure for a monad, my conjecture is that the content of perception of a monad must be representable as an complete atomic Boolean algebra <http://ncatlab.org/nlab/show/complete+Boolean+algebra>.


A diagonal one. The Boolean algebra with a Löbian transformation. A Magari Algebra. With the CTM.

Bruno



Dear Bruno,

The Magari Algebras ( http://www.encyclopediaofmath.org/index.php/Magari_algebra) are beautiful and capture the duality relation to Stone Compacta very elegantly! But do they retain the property that a CABA has, as discussed by Pratt, that they are "fragile' in the sense that if any of their propositions are changed they collapse into a singleton - so that they can be rebuilt with different propositions? If not this would seem to make them immune to forcing, which becomes an obstruction to my proposal. I need to have a way to use Martin's axiom (and maybe its extension, the proper forcing axiom) to define relative differences between the logical algebras.

I am looking for something like a 'calculus of distinctioning' for the logical algebras which seems to be necessary for them to represent 'minds'. The motivation for this is that there has to be something meaningful to the idea: "I changed my mind". A mind that is fixed cannot know novelty or evolve.


--
Onward!

Stephen

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