The exception that proves the rule

How's this for a nice paradox: the exception that proves the rule? Shouldn't an exception be seen as something that contradicts or invalidates the rule, rather than something that proves it?

It isn't true what some people claim about this saying, namely that prove is used here in the sense of 'test'. Rather, the expression goes back to maxim in Roman law, which stated that making an exception proves that the rule exists and is valid in those cases in which you're not making an exception ('Exceptio probat (or firmat) regulam in casibus non exceptis'). Well, that's perhaps rather trivial: an exception does not invalidate the rule, because if it did, we wouldn't call it an exception to that rule. It's because the rule, as formulated, is still seen as generally valid that we can speak of an exception, and by speaking of an exception, we acknowledge the 'otherwise validity' of the rule.

What's less trivial, and considerably more problematic, is that there's a notion in linguistic theory which compels us to accept cases which are at the same time exceptions to the rule but still actually follow the rule, in the sense of being an application of that rule. The notion I'm referring to is that of partial productivity. A rule is partially productive if you can't just apply it generally. Its scope is limited, not open-ended, which means that you have to kind of learn and know the cases which fall under it. Yet, a partially productive rule is not unproductive. New items do on occasion appear, but these are then
1) exceptions to the rule-as-a-list-of-learned-instance: they're not in the list of known cases, hence 'exceptional', special, one-offs.
2) applications of the rule-as-pattern: they are in accordance with the regularity that the rule attempts to capture.

For example, most instances of the Adj as N pattern, described by the linguist Paul Kay, are lexically listed (fit as a fiddle, cool as a cucumber, happy as a lark, dumb as an ox, etc.). You can't just compare anything to anything else, which means that if you do create a new simile, for example dull as a butter knife (which, to be fair, is not exactly new, as I found it in a corpus), this new application of the rule is, actually, a kind of exception at the same time! We're making an exception in order to apply the rule. Paradox...