Skip to main content

Can language trump logic?

In his book Professor Stewart's Horde of Mathematical Treasures, Ian Stewart describes a number of incidents of mathematicians struggling with ordinary life. In one we find Abraham Fraenkel, a mathematics professor 'of German origin' getting on a bus in Tel Aviv that was still in the bus station 5 minutes after it should have left. According to Stewart, Fraenkel waved a timetable at the driver, who replied 'What are you - a German or a professor?' to which, he tells us Fraenkel replied 'Do you mean the inclusive or, or the exclusive or?'

Interestingly, in English at least (this may not apply in other languages), the professor's snippy logic was beaten by linguistics, as his question was not necessary.

Fraenkel's question distinguished the exclusive or (where something has to be one thing or the other but can't be both) from the inclusive (where it can be either or both). And had he received the question from the bus driver in writing, with a slightly different wording, he would have been justified in asking the question. 'Are you a German or a professor?' written down could be inclusive or exclusive. However there was that opening word. It would have been clearer had the driver said 'Which are you' - this would force the exclusive. But even 'What are you' implies the exclusive.

However, the question wasn't written down - and interestingly, in spoken English we distinguish the inclusive and exclusive or by inflection. So had the driver said 'Are you a German or a professor?' and meant it to be inclusive he would have kept the word 'professor' at a fairly balanced or a rising pitch. If he had meant it to be exclusive, he would have said 'professor' with a falling pitch.

It's not really language trumping logic, as I asked in the title, but rather the interesting point that a phrase, particularly a spoken phrase, can contain more information than that of the basic interpretation applied by Abraham Fraenkel.

Comments

Popular posts from this blog

Why I hate opera

If I'm honest, the title of this post is an exaggeration to make a point. I don't really hate opera. There are a couple of operas - notably Monteverdi's Incoranazione di Poppea and Purcell's Dido & Aeneas - that I quite like. But what I do find truly sickening is the reverence with which opera is treated, as if it were some particularly great art form. Nowhere was this more obvious than in ITV's recent gut-wrenchingly awful series Pop Star to Opera Star , where the likes of Alan Tichmarsh treated the real opera singers as if they were fragile pieces on Antiques Roadshow, and the music as if it were a gift of the gods. In my opinion - and I know not everyone agrees - opera is: Mediocre music Melodramatic plots Amateurishly hammy acting A forced and unpleasant singing style Ridiculously over-supported by public funds I won't even bother to go into any detail on the plots and the acting - this is just self-evident. But the other aspects need some ex

Is 5x3 the same as 3x5?

The Internet has gone mildly bonkers over a child in America who was marked down in a test because when asked to work out 5x3 by repeated addition he/she used 5+5+5 instead of 3+3+3+3+3. Those who support the teacher say that 5x3 means 'five lots of 3' where the complainants say that 'times' is commutative (reversible) so the distinction is meaningless as 5x3 and 3x5 are indistinguishable. It's certainly true that not all mathematical operations are commutative. I think we are all comfortable that 5-3 is not the same as 3-5.  However. This not true of multiplication (of numbers). And so if there is to be any distinction, it has to be in the use of English to interpret the 'x' sign. Unfortunately, even here there is no logical way of coming up with a definitive answer. I suspect most primary school teachers would expands 'times' as 'lots of' as mentioned above. So we get 5 x 3 as '5 lots of 3'. Unfortunately that only wor

Which idiot came up with percentage-based gradient signs

Rant warning: the contents of this post could sound like something produced by UKIP. I wish to make it clear that I do not in any way support or endorse that political party. In fact it gives me the creeps. Once upon a time, the signs for a steep hill on British roads displayed the gradient in a simple, easy-to-understand form. If the hill went up, say, one yard for every three yards forward it said '1 in 3'. Then some bureaucrat came along and decided that it would be a good idea to state the slope as a percentage. So now the sign for (say) a 1 in 10 slope says 10% (I think). That 'I think' is because the percentage-based slope is so unnatural. There are two ways we conventionally measure slopes. Either on X/Y coordiates (as in 1 in 4) or using degrees - say at a 15° angle. We don't measure them in percentages. It's easy to visualize a 1 in 3 slope, or a 30 degree angle. Much less obvious what a 33.333 recurring percent slope is. And what's a 100% slope