Post #4038577
2026-07-18 19:52 UTC
Replies (4)
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@FishFace@ioc.exchange 2026-07-23 14:46
@rzeta0@mathstodon.xyz in casual everyday language "I am a man only if I am a mammal" sounds very similar to "I am a man if I am a mammal". The latter is clearly nonsense, but the former is true. Maybe it helps to emphasise the "only" when saying it to yourself: "I am a man ONLY if I am a mammal".
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@golemwire@social.golemwire.com 2026-07-18 20:04
@rzeta0@mathstodon.xyz p ⇒ q is the same as ~p ∨ q. So, p ⇒ q is false only when p is true and q is false. false ⇒ true is true, so it looks like "X is true only if Y is true" is wrong.
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@alexmu@social.vivaldi.net 2026-07-18 20:04
@rzeta0@mathstodon.xyz the truth of the implication tells you nothing about the truth of its converse
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@bemmesr@mathstodon.xyz 2026-07-20 18:21
@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.