In particular, this definition of a conditional statement is the only one that allows other rules about logic to be consistent.

I'll expand this comment I made previously:

A

*theorem *is supposed to be a true statement. A proof has to demonstrate that the theorem is true.

Most theorems have the form, "If (conditions), then (conclusion)."

In order to say that such a theorem is proved to be

*always *true, we want that conditional statement to be true, even when the conditions don't apply. This, ultimately, is why we

*define *a conditional statement as being true in all cases except when the conditions are true but the conclusion is not. Only that definition of the truth value of a conditional statement allows theorems to called true!

(The same can be said, more strongly, about logical arguments, which are proved valid by using formal logic to show that the conditional statement expressing the argument is a tautology.)

I find this explanation to be stronger than just declaring that truth is the default, or that a statement is innocent until proved guilty (though those are both great ways to make the idea memorable).