So I would guess you don’t understand why people make the mistake that “if not Q, then also not P”. Do you have another hypothesis for the origin of this mistake? (Perhaps there is more than one cause, ha ha.)
Later edit: The first sentence had an obvious error. In the quotes, I meant to write, “if Q, then P”—or, more symmetrically, “if not P, then also not Q” as the mistake that is often made from “if p then q”.
I’m actually in large agreement with you about what “p implies q” means in ordinary English, but can wobble back and forth with some effort. Let me try a little harder to convince you of the interpretation I’ve been arguing.
Let’s suppose you are told, “if P then Q”. In everyday life, you can usually take this to mean that if Q then P because P would have caused Q. If Q could instead have been caused by R and R was likely, then why didn’t the person say so? Why didn’t the person say “if R or P then Q”?
why people make the mistake that “if not Q, then also not P”.
Um… I don’t think that’s a mistake. Given “If P, then Q”, the non-existence or falsehood of Q requires that P also not exist / be false. It leads to contradiction, otherwise.
Do you have another hypothesis for the origin of this mistake?
Perhaps people are just not good at processing asymmetrical relations. They may naturally assume, for any relation R, that aRb has the same meaning as bRa. They may not notice that conclusions they make from the mistake at this level of abstraction contradicts their correct understanding at a lower level of abstraction that includes the actual definition of implication.
Interesting, but this doesn’t seem true true in general. People are pretty good at not confusing aRb and bRa when R is something like “has more status than”, for example.
I wouldn’t be surprised if the easiest relations for us to imagine between two variables were simply degrees of “bidirectional implication” or “mutual exclusivity”.
So I would guess you don’t understand why people make the mistake that “if not Q, then also not P”. Do you have another hypothesis for the origin of this mistake? (Perhaps there is more than one cause, ha ha.)
Later edit: The first sentence had an obvious error. In the quotes, I meant to write, “if Q, then P”—or, more symmetrically, “if not P, then also not Q” as the mistake that is often made from “if p then q”.
I’m actually in large agreement with you about what “p implies q” means in ordinary English, but can wobble back and forth with some effort. Let me try a little harder to convince you of the interpretation I’ve been arguing.
Let’s suppose you are told, “if P then Q”. In everyday life, you can usually take this to mean that if Q then P because P would have caused Q. If Q could instead have been caused by R and R was likely, then why didn’t the person say so? Why didn’t the person say “if R or P then Q”?
Um… I don’t think that’s a mistake. Given “If P, then Q”, the non-existence or falsehood of Q requires that P also not exist / be false. It leads to contradiction, otherwise.
Seriously? P→Q ⊢ ¬Q→¬P.
Perhaps people are just not good at processing asymmetrical relations. They may naturally assume, for any relation R, that aRb has the same meaning as bRa. They may not notice that conclusions they make from the mistake at this level of abstraction contradicts their correct understanding at a lower level of abstraction that includes the actual definition of implication.
Interesting, but this doesn’t seem true true in general. People are pretty good at not confusing aRb and bRa when R is something like “has more status than”, for example.
Good point. When the relation is obviously antisymmetric, where aRb implies not bRa, this is enough to make people realize it is not symmetric.
I wouldn’t be surprised if the easiest relations for us to imagine between two variables were simply degrees of “bidirectional implication” or “mutual exclusivity”.
Bing bing bing!
The real issue, of course, is why they’re the easiest for us to represent.
That’s coming up next.