[jsnx]

If two logical statements are equivalent, then yes indeed, evidence that implies one of them (in classical logic) implies the other one. The solution is indeed intuitive but is not formalizable in classical logic.

Classical logic does not, in general, jibe with the intuition: consider the case of the negative antecedent:

http://www.earlham.edu/~peters/courses/log/mat-imp.htm

For example, the statement, "If unicorns have one horn, then I am the Queen of England." is logically true.

[immad]

hmm, I see the point. But isn't that just the limitations of classical logic? Just seems like a question of semantics rather than a clash between logic and intuition, but maybe I don't get it

[jsnx]

It is a clash between classical logic and intuition, which is the point -- it indicates a difficulty with applying classical logic, and encourages us to take up other avenues.