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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Received on Sat Jun 24 2006 - 09:38:59 PDT