What about a statement with the form, "p only if q?"
I'll stay home tomorrow only if I'm sick.
Am I saying that if I am sick I will stay home tomorrow? No--I am
saying that if I am not sick, then I will not stay home. Being
sick is the only thing that would keep me home. Think of this as
a promise I've made to you. Now suppose I am sick, but I show up
anyway. Have I broken my promise? No--but I would break the
promise if I stayed home and was not sick.
Thus, the statement, "p only if q" can be translated in either of
two equivalent ways:
1. If not-q, then not-p.
2. If p, then q.
The first translation sounds more natural in some contexts, and the second in
others. But because they are contrapositives, they are logically