The Law of the Excluded Middle

"The universe", says Lytton Strachey in his Eminent Victorians, "is full of laws - the Law of Gravity, the Law of the Excluded…

"The universe", says Lytton Strachey in his Eminent Victorians, "is full of laws - the Law of Gravity, the Law of the Excluded Middle, and many more besides." Now few would argue with his main contention, but how many could cite the Law of the Excluded Middle? Strangely enough, it has some relevance to meteorology.

The principle in question is a philosophical concept on a par with Russell's Paradox and Occam's Razor. The latter, as Weather Eye readers will be well aware, is Entia non sunt multi-plicanda praeter necess itatem: "No more things should be presumed to exist than are absolutely necessary" - sound advice delivered by William of Occam in the 14th century. The Paradox, on the other hand, concerns a barber. Russell's idiosyncratic barber is bewhiskered and shaves a man if, and only if, that man does not shave himself. But the question arises: who shaves the barber? If he shaves himself, then, by definition, he does not; but if he does not shave himself, then, by definition, he does. So he does and, simultaneously, he does not.

Russell's Paradox, as it happens, is an apparent violation of the Law of the Excluded Middle. Said law, apparently, is one of the three cornerstones of Aristotelian logic, devised to make us think more clearly. It states that every proposition must be either true or false, that there is no middle ground. A typical rose, for example, is either red or it is not red; it cannot be red and not red.

But some weather forecasts, it could be argued, provide another violation of the law. According to Aristotle and his friends, a forecast must be either right or it is wrong; it cannot be both right and wrong at the same time. But this may not be so.

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In fact, a complete weather forecast is seldom absolutely right, and only very rarely totally incorrect. A prediction perceived by one individual to have been "good" because it was correct in what concerned him - the wind, for example, or the temperature - may have been a failure to another who has different interests. The sailor may care little about the frost which troubles gardeners, but it may be a matter of life and death to him to get timely warning of a storm. And suppose rain is forecast for a certain spot, and just a single drop occurs; to the meteorologist, the forecast is correct - but is it right for the person who carries an umbrella needlessly to town?

As Hamlet says: "There are more things in heaven and earth, Horatio, than are dreamt of in your philosophy."