~A, but A

I love sudoku. I loved tenth-grade geometry. I loved my GRE section on Analytical Ability. And I loved freshman year Philosophy 250: Symbolic Logic. You give me any kind of logic problem, lay out the postulates, and stand back.

I mean, it’s really interesting that I went into qualitative rather than quantitative research, because I love logical pattern. Card games, board games, probabilities… I was in a graduate statistics course of about 30 students, and finished the semester with a z-score of 2.4. (Look it up. I dare you.) Given a different upbringing—or set of postulates, if you will—I could totally have become a mathematician, or an engineer, or a card counter at blackjack.

Here’s an example. Given a perfectly circular disc of any size, a compass and a straightedge, how would you find the center of the circle? And how would you prove that your answer was correct? I love that shit.

Anyway, I completely remember how much fun I had grinding my way through these gigantic logic proofs, using the logical forms of modus ponens and modus tollens, a hundred or more steps to get to the . (I am, as you can tell, just geeking out all over again just thinking about it.)


I worked at the town dump today on our bi-annual Large Waste Day, during which people can discard ranges and sofas and garage doors and barbecue grills. I worked at our regular transfer station, handling household trash and recycling and electronics, while our regular attendant worked the large waste site, because he loves to scavenge things. Once we closed at noon, I drove down to the other site to hand over the cash box. And as we were chatting about the news of the world, one of my friends said “I don’t want to wish anybody ill, but I hope he gets sick enough to really know how much harm he’s caused.” (Oh, come on, you know what I’m talking about.) And that led me to think about a common rhetorical structure that I’ll call ~A, but A —>~~A. (or, in English, I will assert that A is not true; but then I will assert that A is true; that implies that you should understand the double negative, that I really do not believe that A is not true.) In other words, starting a conditional statement with something you don’t really believe, and are about to prove false. You’ve seen this a million times, but just haven’t thought about it in terms of logical operations. Here’s maybe the most common example:

[I’m not a racist], but [some stupidly racist thing] implies [yes, I really am racist]

That’s the form that my friend used at the dump. [I don’t want to wish anybody ill] but [I hope he gets sick enough to really know how much harm he’s caused] implies [I really do wish him ill].

You know this form. You’ve probably used it yourself.

  • I wish it weren’t true, but… (meaning It IS true, and I’m going to gloat about it)
  • I probably shouldn’t say this, but… (meaning I’m perfectly justified in saying this)
  • I know I’m not all that smart, but… (meaning I’m smarter than you…)
  • I’m just a simple guy, but… (meaning I’m more sophisticated than you give me credit for)

This is such a common rhetorical trope that I’m sure my friends who really are rhetoricians can tell me the proper term for it. It’s kind of like bug spray that we coat ourselves with before we go into the field: we hose ourselves down with “I’m not a racist” so that we can go out and say racist things with impunity. And like bug spray, it doesn’t work, but it makes us feel better.

So save us all some time, and leave that first clause off there. We can hear you just fine without it.