Re: ... cosmology? KNIGHT & KNAVE

From: Jesse Mazer <lasermazer.domain.name.hidden>
Date: Fri, 23 Jul 2004 16:58:14 -0400

Bruno Marchal wrote:

>All right. But modal logic are (traditionaly) extension of classical logic,
>so that causal implication, or >natural language entailment, when study
>mathematically are generally defined through modalities + >"material
>implication".
>
>So in a sense, you confuse yourself by premature anticipation.

Well, I guess "in every possible world where X is true, Y is true also" can
only be false if there's a possible world where the classical logical
statement "X -> Y" is false (because in that possible world, X is true but Y
is false). So perhaps the possible-world statement would be equivalent to
the modal-logic statement "it is necessarily true that X->Y"--would this be
an example of modal logics "extending" classical logic? In any case, in
classical logic X -> Y can only be false if X is true in *our* world,
whereas the possible-world version of "if X then Y" does not require that X
is true in our world, although it must be true in some possible world. And
like I said, I think the possible-world statement more accurately captures
the meaning of the natural-language statement.

Jesse
Received on Fri Jul 23 2004 - 17:04:43 PDT