I'm confused about the nature of antecedents and conditionals like: (i) "Only if A, then B".
I was told in my logic class that antecedents are always sufficient conditions and consequents are always necessary conditions. But if that's the case, then the antecedent in (i) "Only if A" is a sufficient condition. Particularly a sufficient condition for B. But saying "Only if A, then B" means that A is a necessary condition for B as well. So it appears that the antecedent in (i) is both a sufficient and necessary condition. But that doesn’t seem right, given that (i) is equivalent to (ii) If B, then A. And this means A is only a necessary but not a sufficient condition for B.
Option 1: Maybe antecedents only are sufficient conditions in simple conditionals like (iii) “If A, then B”; but they aren’t sufficient conditions in conditionals like "Only if A, then B". That might be right.
Option 2: On the other hand, we might say "Only if A" just seems to be an antecedent but isn't really. That would retain the intuitive idea that antecedents are always sufficient conditions. This might be right.
Which option do you think is right? Or is there another option I'm not seeing?
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