# Conditionals

By basic symbolic logic, A->B is true if A is false. This is quite
paradoxical. I hadn't really understood why this is true. Creatio
ex nihilo?

The most understandable answer was that A->B is equivalent to
"Not-A or B". So if A is false, the proposition is true. But why
the two propositions are the same? I have felt that it is arbitrarily
defined.

I have realised that this becomes ridiculously simple if I use
possible worlds semantics. I have known possible worlds semantics
and modal logic for a long time. I don't know why I couldn't come
up.

A->B means for every possible world in which A is true, B is true.
So it is about whether there is a possible world in which A is true
but B is false. If A is false, the class of every possible world
in which A is true is the empty class. Therefore the proposition
is true.