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Exceptions, proofs, rules and puddings

The English language is a tricksy thing, replete with sayings that can, on the face of it, appear odd, or that get mangled after many repetitions. I recently heard something about one of these on the excellent The Studies Show podcast, hosted by Stuart Ritchie and Tom Chivers, that made me raise an eyebrow, because they claimed my interpretation of a saying was a myth.

The saying in question was 'the exception proves the rule'. I want to come back to that after a brief excursion into another saying that involves puddings.

One of the most cringe-making things for me is when I hear someone on the TV or radio say 'The proof is in the pudding.' This is a totally meaningless statement resulting from mangling the saying 'The proof of the pudding is in the eating'. Anyone using the first version needs to be sent to an English Language re-education camp immediately. But the real version itself can look distinctly confusing. We can prove a mathematical theorem, or that black swans exist... but how do you prove a pudding?

The saying depends on being aware that 'prove' has a less familiar meaning of 'test'. In fact, if you look up 'prove' in the Oxford English Dictionary, the very first definition is 'to make a trial of; to try, to test'. With this in mind, we can see that what's being said here is you can test how good a pudding is by eating it. It's not exactly great wisdom, but it makes sense.

So we move onto that disputed saying 'the exception proves the rule'. This feels weird because you might think that an exception disproves a rule. If a rule is, for example, if we posit a rule that 'all prime numbers are odd' and we point out that 2 is a prime number, this is an exception to that rule, which disproves it. Disproving theories and rules is a central part of doing science or maths.

However, if we use the same meaning of 'test' for 'prove' as we did with the pudding, it makes total sense. We are 'making a trial' of that rule with an exception and breaking it. Yet Chivers and Ritchie (sound like an upmarket jam manufacturer) say that this is a myth.

The basis for this suggestion, I suspect, is that there was a Latin legal phrase 'exceptio probat regulam in casibus non exceptis', which translates as 'the exception proves the rule in cases without exceptions' - which, to be honest, doesn't make much sense except as an indirect way of saying that rules need to exclude situations where the rules don't apply - a total truism. But these aren't the same words, and there is always a danger of deriving English constructs from Latin - this is what led to the bizarre idea that split infinitives should be allowed in English because you can't do them in Latin.

I don't doubt that the Latin phrase may have been the original inspiration of the English phrase. Emphasis on the 'may' - I am not aware of good evidence for the direct link. However, equally there is no doubt that the pudding-style 'proof' here is a valid interpretation of the phrase that frankly is more effective than the Latin use (and the OED supports it as a possible meaning), so it feels wrong to call it a myth.

While we're in the world of puddings, incidentally, I'll finish by briefly mentioning Rutherford's 'plum pudding' model of the atom, where there definitely is a myth involved. I've seen many popular science titles say that in this model the electrons are represented by plums. Unfortunately, plum pudding is an archaic name for a Christmas pudding (see illustration), where 'plum' was as a generic term for dried fruit. Christmas puddings don't contain plums and Rutherford had grape-derived dried fruit such as raisins in mind.

Image from Unsplash by Matt Seymour

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