Post #4274088

@rzeta0@mathstodon.xyz if it's really true that whenever proposition X is true, then so is Y (which is what X→Y asserts), then it cannot possibly be that X is true without Y being true. ‘X is true only if Y is true’. It doesn't mean that X will be true if Y is true, just that it can only be that X is true if Y is true. To tie this in with your chosen example, it's obviously true that if I am a man then I am a mammal, and it's also true that I cannot be a man unless I am a mammal. Really, ‘if X then Y’ and ‘X only if Y’ are two ways of saying the same thing. I'm not sure if that makes sense.