Discussion: what philosophical arguments should everyone know about?

One of my most-read posts of all-time is my post on Judith Jarvis Thompson’s “famous violinist” argument in defense of abortion. It’s somewhat unusual among my blogging in that I have something unambiguously positive to say about a very typical bit of contemporary philosophy (as opposed to, say, heretical x-phi stuff on free will.) I like it when lots of people read something I’ve written, so I’m thinking about trying to write more posts like it, specifically in the sense of posts that explain a bit of philosophy more people should know about. But what would I write about?

What’s remarkable about the famous violinist thought-experiment is that it’s something that seems to have a chance of improving the quality of a lot of ordinary people’s thinking about a topic they care about. Unfortunately, though, this seems pretty rare. Standard lists of “great philosophical ideas” are way too heavy on “look at this crazy-sounding thing a famous person said!” For example: “Hume said we can’t know if the sun will rise tomorrow!” Or “Kant said it’s wrong to lie to Nazis who want to know if you’re hiding any Jews!” Or “Something about Bentham and rabbits!”

Ahem. The point is that it’s unclear at best whether exposure to these ideas actually improves the quality of anyone’s thinking. In some cases, I rather suspect they damage it. The other side of this problem is that less crazy pieces of philosophy, like Gettier’s argument against the JTB analysis of knowledge, have no clear relevance for things ordinary people care about.

But maybe I’m overlooking something important? What philosophical arguments do you think everyone should know about?