Thanks to all the commenters who responded to my plea in yesterday's post about what the phrase "the exception that proves the rule" means.
The issue has been explained to me, and my confusion about what the phrase means has abated. It seems that, revised for accuracy, it would read: "The exception that tests the rule for the likelihood but not the certainty of its own existence."
Now, though, I am baffled by another issue. Why the hell is there a popular phrase which means that?
First, let's resolve the original quandary.
It seems that the issue that I had with "The exception that proves the rule" was two-fold. The first issue is that the phrase, an old one, employs a now-defunct meaning of the word "prove," which meaning is "test".
So now we have "the exception which tests the rule." That's a bit better but still somewhat odd and unnecessary.
To explain the other issue, I will defer to my very brilliant friend Brady Manning, who posts:
"The phrase "the exception that proves the rule" is actually a bastardization of a different phrase "the exception proves the existence of a rule in cases not excepted." This was a legal argument used by Cicero in his defense of Lucius Cornelius Balbus. His point, as I'm sure you can see, is that if an exception exists then there must be some rule to to which the case is an exception. Ergo, the simple existence of an exception proves the existence of a general rule.
The phrase was actually never intended to be a form of inductive or deductive reasoning, but rather a legal defense. You make the point in your post that this is not logically sound, and you are correct. To use the swan example, Cicero is saying that the fact that a black swan is an exception to the rule "all swans are white" shows that, in cases not excepted, the rule exists. I'm not sure if this legal defense worked out for Cicero, but I kind of doubt it if the Romans knew much about logic.
So, why do people continue to use the phrase incorrectly, even when the original one was not logically sound? Beats me, probably because it sounds fancy and has helped many people to win arguments against people who do not understand logic. But regardless, there is no such thing as an exception proving a rule, that would be wholly contradictory."
I neglected the obvious answer to the question of why there exists a useless, contrived, poorly phrased cliche which does not meet good principles of reasoning and serves only to cloud issues.
It's the lawyers!