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/
Received on Fri Jul 23 2004 - 16:18:27 PDT