Skip to main content

What is a paradox? It's paradoxical

Is the definition of a paradox paradoxical? Before we get into a philosophical spiral, this thought was inspired by a complaint I received when I published a review of a book about the Fermi paradox. Mark Hogarth remarked 'They'll call anything a paradox these days.' When I pointed out the name Fermi paradox dates back to the 50s, he responded 'Yes, I know, but you gotta agree that the word 'paradox' is rarely used properly... here it's just a puzzle, like the twin 'paradox'. Now Russell's paradox - that IS a paradox.'

So was Mark right? Have many of us (me included) been using the term incorrectly? So you don't have to, I delved into the trusty source of all things wordilicious*, the Oxford English Dictionary. And got quite a surprise.

Apart from an obsolete usage, the dictionary's first definition is the one that I use - a statement that appears to contradict itself or be ridiculous, but which turns out to be well founded or true. Rather confusingly, the second definition is an almost opposite version which I know some people use, making a paradox a not-so-obvious fallacy. And the third definition is the logician's version, which makes a paradox an argument that appears to be sensible and based on logical principles, but which leads to a conclusion that is, as the OED coyly puts it 'against sense.' Like Russell's paradox** or the rather crude example I've used as an illustration above.

However, what is really interesting is that (apart from the obsolete meaning) my definition has the oldest citation, going back to 1569, the negative definition is almost as old, with the first example dating from 1570 - but the logician's definition has no evidence before the 20th century (in fact Bertrand Russell himself in 1903 is the first  usage they know of).

So, interestingly, Mark's complaint was back to front. It's not that they'll call anything a paradox these days, but rather that logicians have taken a word with a long established meaning and (relatively) recently given it a different one. Don't you just love words?


* Sadly, 'wordilicious' isn't in the OED. But it ought to be.

** Very crudely, Russell's paradox, which requires some basic set theory goes something like this. Imagine we've got the set of all sets that are members of themselves (lets call it the SELF set). So, for instance, the set 'dogs' is not in the SELF set, as the set 'dogs' is not a dog. But the set 'things that aren't dog's is in the SELF set, because it isn't a dog.

The paradox arises when we consider the set of things that aren't in the SELF set. Is that set in the SELF set? If it is in the SELF set, then it isn't in the SELF set - which doesn't make sense. But if it isn't in the SELF set, then it's not a member of itself, so it is in the SELF set - which also doesn't make sense. But it does make your head spin.

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