Then there's the other version: "Just because they're after you don't mean you're not paranoid." I've thought of this as being an important addendum,* but it just hit me—are they saying exactly the same thing?
I enjoyed in 10th-grade Geometry, when we were learning about proofs, the business about... well, hell, I don't remember the terminology. Logic. If the statement "If A, then B" is true, then only its contrapositive(?) follows: "If not B, then A"; other versions, such as "If B, then A" (inverse?) or "If not A, then not B" (converse?), are not evident from the original statement. So, like, if it's true that If you're Ke Huy Quan, then you're a human being, it follows that if you're not a human being, you're not Ke Huy Quan, but it does not follow that if you're a human being you're Ke Huy Quan, or that if you're not Ke Huy Quan, you're not a human being.
These "Just because you're..." statements about paranoia are not if-thens. Really all the first one is saying, if you sort of take it apart or untangle it, is that paranoia and persecution are not mutually exclusive. "Just because you're paranoid don't mean they're not after you" ≠ "If you're paranoid, they might be after you"**: really it's more the negation of an if-then, a statement that it is not true that "If you are paranoid, then they are not after you"—and all that means is that paranoia and their being after you can coexist (but not that they must). And once the statement is just that two things can coexist, it doesn't matter what order you say it in, and indeed the second version adds nothing.
And—hey!—now I see that the second version kind of is a corollary (see footnote): it isn't if you see them as saying different things, but once you see that they're saying the same thing... Actually, I don't really know what I'm talking about. I'd summon Dr. Math but I don't want to overuse the Math Signal.
This entry was brought to you by the letter Not Enough Sleep.***
(stolen from this web site, via Google)
* I want to say corollary, even though I'm pretty sure it's wrong, but how would I ever face Dr. Math after that?
** Did the not-equal sign come through? One can hope.
*** Not a letter.
3 comments:
Sorry I'm late; there was a math emergency at the old warehouse downtown.
To answer the question, yes, the statements "Just because you're not paranoid don't [sic] mean they're not after you" and "Just because they're after you don't [sic] mean you're not paranoid" are substantively different. Let's break it down, logic-style:
According to the rules of logic, the negation of the statement "If A, then B" is the statement "A and not B". Thinking of it pictorially, "If A, then B" means that the set of "A" events is contained entirely in the set of "B" events; A is a small circle inside the larger circle, B. To say that this statement is false is just to say that some part of A overlaps with the outside of B. But we don't know yet if A is contained entirely in the set outside of B or whether it maybe straddles both "B" and "not B". And that's where your second statement comes into play.
If we let "P" be the event "You are paranoid" and "A" be the event "They're after you", then statement 1 is "not (P implies (not A))", which is equivalent to "P and not(not A)", i.e., "P and A". In words, there have to be some instances of you being paranoid and them actually being after you.
However, statement 2, "not (A implies (not P))" is the same as "(not A) and P", i.e., there are some instances of you being paranoid and them not being after you.
That's not so Earth-shattering, since the definition of "paranoia" is "unjustified or excessive sense of fear." I guess what Kurt et al. were getting at here is that it's possible to be irrationally afraid of things that you should still actually be afraid of.
Reminds me of that story about Hemingway, who was convinced in his later years that the FBI was following him. People dismissed him as paranoid, but after his death the FBI revealed that they had, in fact, been following him that whole time.
-DrM
So wait...
"Just because you're paranoid don't mean they're not after you" means that sometimes both are true, sometimes one is true and not the other...right?
Doesn't "Just because they're after you don't meant you're not paranoid" also mean that sometimes both are true and sometimes one is true and not the other?
I.e., if #1 is "P and not(not A)" (where actually I'd assume "not(not A)" ≠ "definitely A"), then #2 is "A and not(not P)." No?
Seems to me that the only substantive difference is that #1 assumes P and #2 assumes A, but in both cases they're hypotheticals, so... Well, I still don't see it.
Help!
So, I got a little sloppy with the parentheses and the nots there. What can I say? I was wasted.
Let me try again now that I've sobered up (somewhat):
Statement #1, "Just because you're paranoid don't mean they're not after you", is represented as "not(P implies not(A))", which is equivalent to "P and not(not(A))", which is the same as "P and A". In words, "Sometimes you're paranoid and they are after you."
Statement #2, "Just because they're after you don't mean you're not paranoid", is represented as "not(A implies not(P))", which is equivalent to "A and not(not(P))", which is the same as "A and P". In words, "Sometimes they're after you and you're paranoid."
So the two statements are, in fact, the same. I'm so embarrassed.
-DrM
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