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/ --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~----------~----~----~----~------~----~------~--~---
