Saturday, December 16, 2006

At that Tower of Babel, they knew what they were after.

A friend asked me about clearer ways of thinking about arguments, and I began to write my take on this stuff, when I decided this was too much to burden one person in an e-mail with and you never know, it might be of interest to somebody.

When you first learn maths, you learn sums as bland pieces of information. You learn that one plus one is two, two plus two is four and so on. And to begin with, this doesn’t have any meaning, just as it doesn’t make much sense why words are spelt in the way they are. You are given this information, you are asked to remember this information, so that’s just the way it is.

However, at some point, you suddenly realise that this means something; that two lots of one added together is in fact exactly equal to two and that's the only inflexible thing - there are other ways of making two and there are all sorts of other things you can do with the ones. You can't go wrong so long as what is on the left hand side of the equals sign balances against what is on the right hand side of the equals sign.

I happen to have a vivid memory of this precise revelation, looking at the blackboard in my second year of primary school – which is perhaps a little late on for this to have sunk in. I could always do sums before then because I had a good memory for the sums I had learnt, but suddenly it wasn’t my memory doing the work any more. I then went through that infuriating phrase of demanding that adults give me a sum, any sum, and I could do it for them there and then.

Other forms of logic or reason or logical reasoning work in a very similar way, but people don’t tend to think about arguments which are expressed in words in this way. On the one hand, the arguments we make with don’t seem that complicated; it’s all common sense. On the other hand, to properly dismantle an idea can seem too much like hard work and it’s all relative anyway, isn’t it?

No. Logic is exact and through logic, the truth can be obtained. Sometimes. It is no coincidence that many of our greatest philosophers have also been notable scientists and mathematicians; Plato, Aristotle, through to Descartes and Alan Turing. One of our most important living philosophers is Richard Dawkins, who is first and foremost a biologist. Excuse the Western bias; I believe the same applies throughout the world.

Like mathematical calculations, arguments can have a shape to them. In fact, all deductive (sound) arguments can be written as a syllogism (a word whose pronunciation would lend support to Monty Python's assertion that Aristotle, Aristotle was a bugger for the bottle).

You would have met syllogisms at school where you had to determine what truth could be extracted from a group of facts like

All pongberry bushes bear purple and pink stripey fruit.
Some of the bushes in my garden are pongberry bushes.

[And you'd fill in] Therefore some of the bushes in my garden bear purple and pink stripey fruit.

But some of them were more tricky, when no truth could be extracted or they tried to mislead you in some way. You remember the sort of thing? The most perfect and sound argument ever written (by René Descartes) comes in the form of a syllogism:

In order to experience a thought, an entity must exist.
I am experiencing a thought.

Therefore I must exist.

In other words, I think therefore I am.

Nothing else about reality is certain. I might be the only one that exists. I may be a butterfly, merely dreaming that I am a human being and having forgotten, for this fleeting moment, that I am in fact a butterfly. I may be inside the Matrix. Who knows? Who cares? I exist! Hooray!*

Truthfully, that could be our only truth (or uh, my only truth, since you might not exist). However, almost all other arguments assume that the world is more or less as we find it, with physical objects and various energies like gravity and so on. That’s possibly because I dreamt it all up and my dreams tend to be consistent within themselves.

In all seriousness, it is certainly the case that in both science and philosophy there are lots of things which we don't know or cannot prove absolutely which we have to work with as premises. Which is part of the reason that our forefathers managed to make so very many mistakes which we can laugh at now, even though they were no less intelligent, wise or virtuous than we are.

But as well as dealing with slightly less information, there have always been and always will be a great deal of other mistakes which were more akin to errors in calculation. Which you'll be pleased to know, I will write about in another post. But not very soon because we're about to head south for Christmas.

* This also leads to the awful joke...
"I think not!" said Descartes and with that, he vanished.


Mary said...

I think I sort of get what you mean... I never got ecstatic about "sums" in primary school, but in middle school they taught us basic algebra, and I found that every time I put a complicated equation at the top of my page and then did things to both sides to make it simpler and simpler until finally at the bottom of the page I could write "x = 12" and underline it, upon which I got an intense feeling of satisfaction at a problem well solved. I got the same feeling when I understood a theory being expounded in a TV documentary, or read a good critical essay on my English Lit texts. It's nice when mud is slowly and methodically made clear.

wopa said...

Exactly the way I think about life. Nothing is certain, but if you accept some premises, everything seems to fit and then it doesn't matter whether the world you experience through these premises is correct, absolutely true or not.
But I was struck by the title. I've wondered many times what these words meant(information for other visitors: they are from Patti Smith's 'Land: Horses/Land of a Thousand Dances/La Mer'). What is the link between the text and the title?