5 ms·
It's not subset, but https://en.wikipedia.org/wiki/Material_conditional https://en.wikipedia.org/wiki/Material_conditional
by gwern 7y ago
It's not subset, but https://en.wikipedia.org/wiki/Material_conditional https://en.wikipedia.org/wiki/Material_conditional
- repsilat 7y agoSure, though the grandparent is kinda correct in one sense -- if one were to use a set operator to mean logical implication, you could use "is a subset of". Imagine the set universe has just one element, "truth". Every statement is a set, and that set contains "truth" or it doesn't. Now, if A implies B, then one of three things is true: - A contains "truth" and so does B, - B contains "truth" but A does not, or - Neither A not B contains "truth". So implication would mean that B is a superset of A (or A⊆B.) There are senses in which the reverse operator could make sense, though, like for logical corrolaries. Any statement provable from B is also provable from A, but not necessarily vice-versa. If each statement corresponds to the things it implies, then if B can be proven from A then A⊇B. I guess this difference is natural. Think of these logical statements as constraining the universe of possible things. More constraints means fewer possible universes. (More to the point, a subset of constraints leads to a superset of universes.) The direction of Set relationships between logical statements will depend on which you put in your sets. EDIT: I just re-read this and fixed a couple of errors, leading to maybe the opposite conclusion!?
- sn9 7y agoCould you please include a note explaining that in the text? I, too, thought it was referring to a subset relationship. Ctrl-F 'Material' also doesn't turn up anything in the page.