Skip to main content

In search of the quadrilemma

I've just read for review Amir Aczel's book Finding Zero. A lot of the book is concerned with his challenging attempt to track down a Cambodian inscribed stone that bears what is thought to be the oldest zero so far discovered. But along the way, he speculates on the differences between Western and Eastern approaches to thought that could have led to the invention of the mathematical zero.

Specifically he points out that traditional Western logic is very much binary - something is either true or it isn't. There are two options. But the Eastern equivalent, he suggests, which sometimes goes by the name of the quadrilemma, has four options: true, false, both and neither.

Now, on shallow observation, the 'both' and 'neither' options might seem like wishy-washy useless philosophical musings. And in some cases they are. But in fact they do sometimes make sense and are, in fact, also present in Western thinking - we just don't emphasise them as much as they might be emphasised in Eastern cultures.

So, for instance, Aristotle, when discussing infinity, described it as 'potential'. And to illustrate what his meant he used the example of the Olympic Games. If a little green man came down in a flying saucer (that bit is my addition to the illustration) and asked you 'Do the Olympic Games exist?' then I think you would say 'Yes.' But if he then asked 'Can you show me these Olympic Games of which you speak?' your answer would be 'No.' Aristotle's concept of potential is, I would suggest, pretty much identical to the third possibility in the quadrilemma - it is something which is both true and false.

How about something that is neither true nor false? Now here I would say I diverge from the Eastern approach, because while the third and fourth possibilities are distinct - so there is another, different case, which I'll illustrate in a moment - I can't say for certain which way round they are to be applied. But my final and distinct possibility is something that is imaginary (not in the mathematical sense, but literally) or fictional. Does a fictional character or an imaginary notion exist? Well, no. But on other hand, its existence isn't really false either, because we talk about them, think about them - and they make things happen. Yet this isn't the same as a potential, because a potential definitely can be, but isn't.

Who said philosophy wasn't fun?


Popular posts from this blog

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

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

Mirror, mirror

A little while ago I had the pleasure of giving a talk at the Royal Institution in London - arguably the greatest location for science communication in the UK. At one point in the talk, I put this photograph on the screen, which for some reason caused some amusement in the audience. But the photo was illustrating a serious point: the odd nature of mirror reflections. I remember back at school being puzzled by a challenge from one of our teachers - why does a mirror swap left and right, but not top and bottom? Clearly there's nothing special about the mirror itself in that direction - if there were, rotating the mirror would change the image. The most immediately obvious 'special' thing about the horizontal direction is that the observer has two eyes oriented in that direction - but it's not as if things change if you close one eye. In reality, the distinction is much more interesting - we fool ourselves into thinking that the image behind the mirror is what's on ou