“The exception proves the rule” is repeated often enough that most people have probably heard it. On the face of it, it seems to mean that finding an exception to a rule provides proof that the rule is correct. Or maybe that the rule is in effect. Or something. Maybe it doesn’t make any sense at all. Or does it? Does it really mean that if you find a purple cow, that helps prove that as a rule, cows are not purple?
If you investigate the phrase you’ll find some suggestion that the word “prove” is being used in the phrase to mean a “test” — something like the way “prove” is used in “proving grounds.” The idea is that you use an exception to TEST the rule. This doesn’t agree with what seems to be the source of the phrase, though.
The expression comes from a Latin phrase: “exceptio probat regulam in casibus non exceptis.” The Latin version means “the exception confirms the rule in the cases not excepted.” That is, the exception proves that there IS a rule, because by pointing out an exception, you’re demonstrating that it’s an exception from something — namely, a rule.
There are examples all over the place. If a street restricts parking on most days, but it’s allowed on, say, Sunday, there are two ways to express this. One is to post a sign with a complicated message explaining that parking is restricted Monday through Saturday, but OK on Sunday. Or you could make the message simpler: “Parking on Sunday only.” The simpler message suggests that because you’ve singled out Sunday — made it an exception — it means Sunday is different. It’s an exception that “proves” (or “shows” or “demonstrates”) that there’s a rule in place.
It’s not really that complicated, but it’s still true that the phrase is often confusing. Most common phrases are used because they’re so simple, as a rule. This one is just an exception.