The exception proves the rule.
A seemingly nonsensical familiar expression is ‘The exception proves the rule.’ Those who say 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, doesn’t prove the statement “All bears are brown or black.”
The phrase’s meaning is actually quite different from its most common usage.
Some attempt to explain the seeming contradiction of ‘The exception proves the rule’ by looking at the verb ‘proves’. While we’re now most familiar with ‘proves’ as a verb meaning ‘to establish as truth,’ an older meaning is ‘to test.’ As in ‘proving grounds’. This way, ‘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’ — the fact that certain exceptions are made in a legal document or announcement confirms the rule 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. The posted exception, therefore proves (demonstrates) that at other times the rule is in effect.
snopes.com: Etymology of Exception Proves the Rule