I've heard the phrase, "the exception that proves the rule," but it's not clear to me what it means. It sounds self contradictory. What is a good example of "an exception that proves the rule?" Can this phrase be used effectively in formal dialog, or is it only colloquial?
The least stupid usage I have encountered for this phrase -- no real idea whether it's actually to do with its origins -- is when a rule expresses a tendency or preference rather than a hard-and-fast delineation, and the difficulty encountered in going against that tendency demonstrates the force of the rule.
A random example might be a rule that "bears do not dance". The amazing Dr. Florenheimer trains a bear to dance in his traveling circus. This forms an exception to the rule, but the years that it took Dr. Florenheimer to train the bear, along with the expense and injuries to staff, make it an exception that "proves" the rule, in some sense -- at the least, proving that it may not be violated lightly.
The phrase has its origin in the law. It means that a law written in broad terms but provided with an exceptions for some special case is properly understood broadly because the authors of the law saw fit to make a special exception for special cases.
is a very broad rule that make no allowance for special cases, and one might see fit to interpret it with some leniency, perhaps allowing ambulances, police cars and early morning deliveries to venues in the park.
On the other hand
shows that the author has explicitly considered what special cases might merit an exception, so the rule should be interpreted broadly, and delivery vehicles excluded.
The existence of the exception proves that the author meant what he or she said and that the rule applies to cases not excepted.
This is a widely misunderstood and often badly used phrase, commonly said to confirm something in the face of contradictory evidence:
When used in this way, it essentially means "I don't care about what you just said, I'm sticking to my interpretation of the facts." (Also, this is the only way I've ever actually heard it used.)
The saying originates from a now-rare use of the word 'prove': to subject to a test, experiment, comparison, analysis, or the like (dictionary.com, definition 4); the intended meaning is that "a rule is tested when you find something that appears to be an exception", not "one or two exceptions to a rule can safely be ignored." (Another example of this meaning of 'prove' is the old saying, "The proof of the pudding is in the tasting", meaning that the best way to make sure if something is good or not is to test it in its intended use.)
I don't think that the saying should be used in a formal setting because of its widely understood meaning of ignoring some contradictory data.
The version I heard is that if there is an exception to a rule, then there most likely is a rule stating the opposite of the exception in the first place.
For example if you have "Minors are not allowed to drink alcohol" then most likely drinking alcohol isn't forbidden in general. Since the exception for minors would be superfluous if nobody were allowed to drink.
Or if certain drugs is allowed for medical use, then this is the exception to the rule that those drugs are not allowed in general.