But we can't tell which of these arguments is sound and which is not. Hence neither argument is very persuasive . In general, when you're engaging in philosophical debate, you don't just want valid arguments from premises that happen to be true. You want valid arguments from premises that are recognizable as true, or already accepted as true, by all parties to your debate. These are the sorts of arguments you should try to offer.
P is called the antecedent of the conditional, and Q is called the consequent of the conditional.
It's only the case that P if it's also the case that Q P only if Q Note the terms sufficient condition and necessary condition . To say that one fact is a sufficient condition for a second fact means that, so long as the first fact obtains, that's enough to guarantee that the second fact obtains, too. For example, if you have ten children, that is sufficient for you to be a parent. To say that one fact is a necessary condition for a second fact means that, in order for the second fact to be true, it's required that the first fact also be true. For example, in order for you to be a father, it's necessary that you be male.