grammar rage volume ii: the exception that proves the rule

This time I turn my attention to the misused phrase, "the exception that proves the rule."

The phrase is often used to mean "the exception to the rule." Consider the hypothetical conversation:

"Of course colas have caffeine. But root beers don't."
"Well, Barq's root beer has caffeine."
"Yeah, well, that's the exception that proves the rule."

It kind of goes along with the (incorrect) idea that every rule has to have an exception. Of course, the logic doesn't hold. Finding an exception to a rule doesn't prove that the rule is a rule. If anything, it weakens it.

Unless...

Suppose there's no rule explicitly stated, but an exception is explicitly stated. The statement of the exception implies the existence of the rule. Because, if there were no rule, there would be no need to state the exception. And that's what "the exception that proves the rule" is all about.

Suppose, for example, there's a sign along the curb: "No parking Wednesdays 9 AM - 10 AM." Because there's a sign specifying a limited time when parking is not allowed, one can reasonably infer that parking is allowed at other time. The exception, the stated fact that you can't park during that one hour every week, proves the rule, that you can park there other times.