On 17 Sep 2017, at 01:47, Russell Standish wrote:

On Fri, Sep 15, 2017 at 04:42:56PM +0200, Bruno Marchal wrote:

The universal machine put some mess in the arithmetical Heaven, and
its soul is teared apart by its eight (4 + 4*infinity actually)
points of view possible.

What the infinity doing here?

The povs implied by incompleteness are the four

p
Bp (splits in two)
Bp & p

and the 4*infinity:

Bp & Dt
Bp & Dt & p   (which both splits in two again, along G/G*)

but also the weakening (with B^n p = BBBBBp with n Bs).

B^n p & D^m t
B^n p & D^m t & p

(when n is less or equal than m, those variants still obeys a quantum logic, and that gives a graded modal logics for the quantum).

Best,

Bruno




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Dr Russell Standish                    Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Senior Research Fellow        [email protected]
Economics, Kingston University         http://www.hpcoders.com.au
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http://iridia.ulb.ac.be/~marchal/



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