Claim:The exception proves the rule means "counter-examples verify the adage's claim."
TRUE (but not for the reason you think)
Origins: Native speakers of English accept without pause the many seemingly nonsensical sayings that are part and parcel of the vernacular. We blithely announce 'It's raining cats and dogs' to communicate the concept of a heavy downpour, yet spare precious little thought to the realization that neither felines nor canines play any part in the process of rainfall. Similarly, someone who is trying to say something without actually forthrightly stating it "beats about the bush" even when the topic being striven for is not shrubbery. For us, it's the saying's easy conveyance of meaning, not how it was put together, that matters.
Another seemingly nonsensical familiar expression is 'The exception proves the rule.' Those who utter it use it to convey a message that an inconsistency confirms the validity of the hypothesis, which is an absurd notion. The existence of white bears, for instance, does not elevate to truth the statement "All bears are brown or black."
The meaning of 'The exception proves the rule' is actually quite different from its most common usage even though its core concept, that an exception establishes the validity of a rule or law, is accurate.
Some who think they're in the know attempt to explain the seeming contradiction of 'The exception proves the rule' by looking at the verb used in the aphorism in a less common fashion. While we're now most familiar with 'prove' as a verb meaning 'to establish as truth,' an older meaning of that self-same word that has since almost disappeared from everyday usage defines it as meaning 'to test.' By those lights, 'The exception proves the rule' should be read as 'The exception tests the rule' — that is, the contradiction puts the claim through its paces and finds it wanting.
Yet even that is not the case. Our puzzling saying is actually a legal maxim drawn from early 17th century English law. It was then written in Latin as Exceptio probat regulam
in casibus non exceptis, which translates into English as Exception confirms the rule in the cases not excepted. More simply, 'The exception proves the rule exists' — that certain exceptions are spelled out in a legal document or announcement confirms the rule (minus the exceptions) is in force at all other times.
If that sounds a bit hard to grasp, consider this: A sign announcing 'Free parking on Sunday' should lead one to conclude that on every other day of the week there will be a charge levied for leaving one's car in that spot. The posted exception, therefore proves (demonstrates) that at other times the rule is in effect.