Editing Strict conditional (section)

==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 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 whenever the antecedent ''A'' is false, a formula ''A'' → ''B'' is true. Hence, this formula is not an adequate translation of the original sentence. An encoding using the strict conditional is:

: <math>\Box</math> (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 to be a correct translation of the original sentence.