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LOGICAL REASONING: The Conditional Logic of Break Ups

by
Overly Nice Guy

Nice Guys Finish Last

We’ve all had a friend (or even a really close friend… so close they’re just like us, same name and same height and everything) who breaks up with someone and says, “But he’s/she’s so nice! I must not want to date nice people–what’s wrong with me?”

Whenever I hear this, it strikes me as an opportunity to give a short logic lesson, which I sometimes do, to mixed results.

Recall our classic illustration of a conditional sentence: if you’re in Canada, you’re in North America. We symbolize this as:

C -> NA

From this, there are other conditional statements that may be tempting to infer but are incorrect. One is that if you’re in North America you’re in Canada (not true–you could be in Minnesota):

NA –> C (FALSE!)

The other is that if you’re not in Canada then you’re not in North America (now you’re in Mexico–Minnesota was too cold):

~C –> ~NA (FALSE!)

The one inference we can make from that first statement is that if you’re not in North America, you’re not in Canada:

~NA –> ~C (TRUE.)

How might “omigosh-I-must-only-have-crushes-on-horrible-humans-since-I-find-one-decent-human-boring” fit this model?

Pause here to think about this on your own. When you’re ready read on. (It’s more useful to practice yourself than to go straight into reading the answer.)

Ready? Okay.

While it’s true that if you aren’t interested in nice people, you won’t be interested in this nice person:

~Nice People –> ~This Nice Person

… the omigosh statement would be broken down as:

~This Nice Person –> ~Nice People

How do these compare? It’s the same as flipping Canada and North America and saying that if you’re in North America you’re in Canada. It’s false.

There are many nice fish in the sea, and not liking one of them doesn’t mean you don’t like all of them.

Note: this particular pep talk may draw yawns, eye rolls, or expressions of concern (“Jim, please stop studying for the LSAT, you’re not behaving normally”), but it’s true nonetheless. And your more logic-minded friends may appreciate it.