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.

I know the "material" implication needs some time to be familiarized with.

Bruno


At 15:45 23/07/04 -0400, Jesse Mazer wrote:
Bruno Marchal wrote:

Let us suppose the native is knave. Then what he said was false. But he said "if I am a knight then >Santa Claus exists". That proposition can only be false in the case he is a knight and Santa Claus >does not exists.

This only works if you assume his "if-then" statement was shorthand for the "logical conditional", ->, in formal logic (see http://en.wikipedia.org/wiki/Logical_conditional )...if you interpret it some other way, like that it was shorthand for a modal logic idea like "in every possible world where it is true that I am a knight, it is true that Santa Claus exists", I don't think it can only be false if he is a knight. For example, there might be a possible world where he is a knight and Santa Claus does *not* exist, in which case the statement "in every possible world where it is true that I am a knight, it is true that Santa Claus exists" is false.


I think this is why the problem is confusing--for me, possible-world statements more accurately capture the meaning of "if-then" statements in ordinary language than the logical conditional.

Jesse


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



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