On 10/21/2011 1:05 AM, Russell Standish wrote:

On Thu, Oct 20, 2011 at 08:00:55PM -0400, Stephen P. King wrote:There has to be some form of identity thesis between brain and mind that prevents the Occam catastrophe, and also prevent the full retreat into solipsism. I think it very much an open problem what that is.Hi Russell,## Advertising

Would the conjecture that the Stone duality provide a coherent version of this "identity thesis"? Minds, as per Comp, -> logical algebras and Brains -> topological spaces. Not not, how so? Onward! StephenI have to confess to not having the slightest inkling what you're saying here. I did briefly look at Stone duality on Wikipedia, but it didn't help much. I assume that you're interested in some duality between an algebra (perhaps one of Bruno's hypostases, if they're an algebra) and a topological space that could stand in for physical reality, but beyond that I'm totally lost :).

Hi Russell,

`The Stone duality was first found as an isomorphism between Boolean`

`algebras and totaly disconnected compact Hausdorff spaces.`

`Generalizations are being studied. Consider what these topological`

`spaces "look" like... What does a Cantor set look like, for example? The`

`idea is to shift from thinking of algebras and spaces as purely static`

`and consider them as evolving systems, ala Hintikka's game theoretic`

`semantics for proof theory. The idea that I am studying was first`

`proposed by Vaughan Pratt using Chu spaces. See:`

`http://boole.stanford.edu/pub/ratmech.pdf`

`If Bruno's UD is a logical algebra, then it would have a Stone`

`space as its dual. If the UD evolves, then so too does its Stone space.`

`This implies a nice identity thesis and avoids the Occam catastrophe`

`because of compactness. BTW, compactness requires a topological form of`

`finiteness, thus the measure problem is also solved. There are still`

`some open problems, such as the degenerasy into solipsistic systems,`

`that need to be addressed. I suspect that Tennenbaum's theorem might be`

`a place to start.`

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