The first time I heard Carly Simon’s ‘You’re So Vain,’ I had a brain fart. This was bad, because it occured on Mopac at 70 mph. Luckily I survived, but the song’s refrain still caused a logic exception in my head every time I considered it:
You’re so vain
You probably think this song is about you
You’re so vain
I’ll bet you think this song is about you
Don’t you? Don’t you?
I even lost a little sleep thinking about it last night. The wording is odd, and combined with its vague context—Simon still refuses to say who her douchebag ex is—potentially disastrous. After a little analysis, I have reached the conclusion that Carly Simon has inhuman sluttish abilities. Work with me on this.
Until the song’s ‘you’ is defined, I am free to consider every person living in 1973 p capable of being the song’s target (set P). Naturally, I’m not saying she banged everyone on Earth in 1973. ((Probably close. Mom?)) To whittle down the size of P, apply the song logically to every potential p ∈ P. In other words, a Cinderella glass slipper-type scenario. What she is saying is ‘If your vanity is sufficiently large, you think this song is about you.’ ((I had to drop ‘probably,’ because that’s a matter of statistics: what percentage of vain people live in a self-obsessed fantasy world where Carly Simon wrote a song about them?)) Broken down even further, ‘For every p, if p’s vanity v > some arbitrary constant k, then p ∈ P.’
It doesn’t take a mathematician to see that P is a very large set. As in, untold millions of people. Carly Simon is confessing over oldies radio that she made out with entire cities, states, regions. She is either a) a boasting hussy or b) not a logician. I’ll be nice and assume the latter, in which case I’ll help her out.
Her goof is surprisingly petty and easily corrected: cause and effect are swapped. This is why I noted the song’s wording is disastrous. With a simple rearrangement of phrases, all is well. Um, until you try to sing it.
If you think this song is about you
You’re so vain
If you think this song is about you
You’re so vain
Do you? Do you?
Instead of saying every vain person in 1973 thinks they have a song dedicated to them, the lyrics simply claim that every person in 1973 who thinks the song is about them is vain. That’s a fair statement, even applied to any other song. What would you say to a person that boasted that Nine Inch Nails had him in mind when they did ‘Closer’?