Hard Tweets Explained: Contraposition

Contraposition is a logic term that I’m guessing most people don’t know. Here is a simple example.

Me: Did you brush your teeth?

7: Yes!

Me: (checks toothbrush, it is dry)

7: Oh! You mean today?

We start with a conditional implication that if she brushed her teeth, then the toothbrush would be wet.

Brushed —implies—> Wet

We don’t know whether she brushed her teeth, but we do know that the toothbrush is not wet. The logical principle of contraposition (also called modus ponens) says that if you are certain that P->Q, then you can be certain that (not Q)->(not P). If brushed implies wet, then not-wet implies not-brushed.

Note that wet does not imply brushed. Now that 7 is 8, I suspect that she may choose to wet her toothbrush instead of brushing her teeth. So you can’t just flip an implication around. That’s called confirmation of the consequent fallacy. (I’m not kidding, that’s really what that’s called.) But if you flip it around and also invert the two statements, then that is guaranteed to still be true.

OK, so now that we all understand contraposition, let’s go back to the tweet.

It says that nudity implies getting some. But that I found that through contraposition.

Observation: not getting some implies not nude.

Contraposition: nude implies getting some.

Hence the joke: I’m talking about getting some, but I know this through years of research on not getting some. This is funny because men tweeting that they are not having sex is funny. I’m actually not sure why that is. However, there are plenty of examples of men joking about how much sex they are having, and they are not at all funny. And I think we can get there through contraposition. Maybe.

Homework: Try getting some in a contraposition for a change. Just be careful not to pull a muscle.


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