Bruno Marchal wrote:
Le 23-juin-06, à 07:29, George Levy a écrit :

In Bruno's calculus what are the invariances? (Comment on Tom Caylor's 

Logicians, traditionally, are interested in deduction invariant with 
respect of the interpretation. A typical piece of logic is that: from 
"p & q" you can infer "p". And the intended meaning of this, is that 
that deduction is always valid: it does not depend of the 
interpretations of "p" and "q".

Those who remember the Kripke semantics of the modal logical systems 
remember perhaps that a logical theory is an invariant for the trip 
from world to world when accessible, making the theorems true in all 
(locally and currently perhaps) accessible worlds.

I suggest the following invariances which are possibly identical to the above statement about Kripke semantic, but have a more "physical" point of view. They may also be related to Church's thesis:
1) Invariance in the perception of one's own consciousness with changes in the substrate implementation : "Yes doctor" I agree that a prosthesis of part of my brain will not affect my consciousness.
2) Invariance in the perception of one's own consciousness with the MW branching: Bruno in Washington will feel just like Bruno in Moscow except for his perception of the  environment.
3) Invariance in the laws of physics with substrate implementation: simulation performed on different computers are indistinguishable if they perform the same algorithms or functions. (Note that Invariance in the laws of physics is a general relativity postulate.)
4) Invariance in the laws of physics with MW branching: This invariance may be grounded in the requirement that consciousness must require physics with consistent histories and the absence of white rabbits....

Notice the parallel between consciousness and the laws of physics.


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