If I believe “anyone who isn’t my enemy is my friend,” then I can evaluate Ethel for enemyhood. Do we dislike one another? Do we act against one another’s interests? No, we do not. Thus we aren’t enemies… and it follows from my belief that Ethel is my friend.
If I believe “anyone who isn’t my friend is my enemy,” then I can evaluate Ethel for friendhood. Do we like one another? Do we act in one another’s interests? No, we do not. Thus we aren’t friends… and it follows from my belief that Ethel is my enemy.
Thanks—that’s interesting.
It seems to me that this analysis only makes sense if you actually have the non-excluded middle of “neither my friend nor my enemy”. Once you’ve accepted that the world is neatly carved up into “friends” and “enemies”, it seems you’d say “I don’t know whether Ethel is my friend or my enemy”—I don’t see why the person in the first case doesn’t just as well evaluate Ethel for friendhood, and thus conclude she isn’t an enemy. Note that one who believes “anyone who isn’t my enemy is my friend” also should thus believe “anyone who isn’t my friend is my enemy” as a (logically equivalent) corollary.
Am I missing something here about the way people talk / reason? I can’t really imagine thinking that way.
Edit: In case it wasn’t clear enough that they’re logically equivalent:
Yes, I agree that if everyone in the world is either my friend or my enemy, then “anyone who isn’t my enemy is my friend” is equivalent to “anyone who isn’t my friend is my enemy.”
But there do, in fact, exist people who are neither my friend nor my enemy.
If “everyone who is not my friend is my enemy”, then there does not exist anyone who is neither my friend nor my enemy. You can therefore say that the statement is wrong, but the statements are equivalent without any extra assumptions.
ISTM that the two statements are equivalent denotationally (they both mean “each person is either my friend or my enemy”) but not connotationally (the first suggests that most people are my friends, the latter suggests that most people are my enemies).
Thanks—that’s interesting.
It seems to me that this analysis only makes sense if you actually have the non-excluded middle of “neither my friend nor my enemy”. Once you’ve accepted that the world is neatly carved up into “friends” and “enemies”, it seems you’d say “I don’t know whether Ethel is my friend or my enemy”—I don’t see why the person in the first case doesn’t just as well evaluate Ethel for friendhood, and thus conclude she isn’t an enemy. Note that one who believes “anyone who isn’t my enemy is my friend” also should thus believe “anyone who isn’t my friend is my enemy” as a (logically equivalent) corollary.
Am I missing something here about the way people talk / reason? I can’t really imagine thinking that way.
Edit: In case it wasn’t clear enough that they’re logically equivalent:
Edit: long proof was long.
¬Fx → Ex ≡ Fx ∨ Ex ≡ ¬Ex → Fx
I’m guessing that the difference in the way language is actually used is a matter of which we are being pickier about, and which happens “by default”.
Yes, I agree that if everyone in the world is either my friend or my enemy, then “anyone who isn’t my enemy is my friend” is equivalent to “anyone who isn’t my friend is my enemy.”
But there do, in fact, exist people who are neither my friend nor my enemy.
If “everyone who is not my friend is my enemy”, then there does not exist anyone who is neither my friend nor my enemy. You can therefore say that the statement is wrong, but the statements are equivalent without any extra assumptions.
ISTM that the two statements are equivalent denotationally (they both mean “each person is either my friend or my enemy”) but not connotationally (the first suggests that most people are my friends, the latter suggests that most people are my enemies).