I'm notoriously loath to match my socks. Almost everyone that knows me knows this about me. And I love fancy socks. So my socks are always calling attention to their mismatched role. Before I was married everyone told me I needed a wife to match them for me. First of all that's sexist. Why should I expect my wife to do it if I wouldn't do it myself? Secondly it's just not worth the effort because I own so many socks and most of my favourite socks have lost their partner. So it saves me money too. If I lose one sock with ducks on it it doesn't matter because those go perfectly with my purple and green argyle sock.
"Sagehen" posted several days ago on ADS-L a suggestion regarding some problematic axioms.
If "proof" is thought of as a process, a test, and not just as the completed demonstration, through testing, of the truth of something, odd-seeming expressions like..."the exception that proves the rule" become sensible. ..."the exception that tests the rule."
It might work. That phrase has puzzled me for a long time. Why would any exception prove that a rule is being applied? If the rule is that a train passes every hour on the hour why would the one hour when the train fails to go through prove the rule?
Or perhaps (and this feels like a stretch the rule is that the train passes by only on the hour and since the exception is every other part of the hour that's what creates the rule. Follow? The train flies by on the hour. So at 12:10 there's no train. At 12:23--no train. At 12:49...got the point? And at 1:00 there's a train and we now have our rule.
Well it's inelegant so I won't try to sell it.
Laurence Horn is familiar with the question and offers some insight on a follow-up post to the list. He provides an explanation by Michael Quinion who writes
It's not a false sense of 'proof' that causes the problem, but 'exception'. We think of it as meaning some case that doesn't follow the rule, whereas the original sense was of someone or something that is being granted permission not to follow a rule that otherwise applies. The true origin of the phrase lies in a medieval Latin legal principle: 'exceptio probat regulam in casibus non exceptis', which may be translated as 'the exception confirms the rule in the cases not excepted'.
Let us say that you drive down a street somewhere and find a notice which says 'Parking prohibited on Sundays'. You may reasonably infer from this that parking is allowed on the other six days of the week. A sign on a museum door which says 'Entry free today' leads logically to the implication that entry is not free on other days (unless it's a marketing ploy like the never-ending sales that some stores have, but let's not get sidetracked). H W Fowler gave an example from his wartime experience: 'Special leave is given for men to be out of barracks tonight until 11pm', which implies a rule that in other cases men must be in barracks before that time. So, in its strict sense, the principle is arguing that the existence of an allowed exception to a rule reaffirms the existence of the rule.
As I read it that's a more elegant explanation of my little train story. An easier sell.
How else might this phrase work?
People have trouble believing me when I tell them that I don't purposefully mis-match my socks. I just don't match them once they're out of the wash and when I grab them from the drawer (or the basket that they're almost always still sitting in) I put on the first two that I pick up. It's completely random.
"Yeah but if it was a matching pair wouldn't you put one of them down?" they ask.
"No" I say. "If they match that's the exception that proves the rule."