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

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


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.

But describing the whole of math as the study of invariant, is either 
trivial (mathematical theorems are invariant) or it is a sin of 
geometer, perhaps even physicalist sort of geometer :-)

Invariants are important but so are the variants making those 
invariants invariant. I don't think it makes sense to try to define 
"mathematics".

Now, once you postulate comp, is it not obvious that numbers (even just 
the positive integers) will play some fundamental role?

Bruno



http://iridia.ulb.ac.be/~marchal/


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