Strict Conditional - Avoiding Paradoxes

Avoiding Paradoxes

The strict conditionals may avoid paradoxes of material implication. The following statement, for example, is not correctly formalized by material implication:

If Bill Gates had graduated in Medicine, then Elvis never died.

This condition should clearly be false: the degree of Bill Gates has nothing to do with whether Elvis is still alive. However, the direct encoding of this formula in classical logic using material implication leads to:

Bill Gates graduated in Medicine Elvis never died.

This formula is true because a formula is true whenever the antecedent is false. Hence, this formula is not an adequate translation of the original sentence. An encoding using the strict conditional is:

(Bill Gates graduated in Medicine Elvis never died.)

In modal logic, this formula means (roughly) that, in every possible world in which Bill Gates graduated in Medicine, Elvis never died. Since one can easily imagine a world where Bill Gates is a Medicine graduate and Elvis is dead, this formula is false. Hence, this formula seems a correct translation of the original sentence.