The exception that proves the rule
If, like me, you thought this was a nonsense phrase, then here’s an explanation. Prove is a word with several meanings. In one meaning — probably the most usual one — it is to establish, in the way that a mathematical proof establishes a claim. But that’s not the sense in which it is used in this phrase. This has been my mistake: an exception doesn’t establish a rule at all. In another meaning it is to test — as in a proving facility, or proofreading, which tests a text for errors. This is the sense it is used in the exception proves the rule. The exception tests the rule, which makes a lot more sense.