To: Hakeem G.
From: Geoffrey Klempner
Subject: Descartes: being deceived about 2+3=5
Date: 20 November 2006 12:48

Dear Hakeem,

Thank you for your email of 14 November, with your essay in response to the University of London 2004 Introduction to Philosophy question, ''For whether I am awake or asleep, two and three added together are five, and a square cannot have more than four sides. It seems impossible that such transparent truths should incur any suspicion of being false.' How does this claim contribute to the argument of Descartes' First Meditation?'

Your answer is rather short, but correct as far as it goes. In an examination, you have an hour to write your essay. To get a good mark, you should aim to say more. What you have written would probably score in the low 50's - in other words it would scrape a pass.

You correctly point out that Descartes' aim in Meditation 1 is to show that every proposition can be doubted. Having cast doubt on beliefs derived from sense perception, he has to consider propositions like those of arithmetic or geometry which it seems to us that we cannot be wrong about.

How does he do this? Interestingly, he doesn't use the dreaming argument. Why not? We do find ourselves believing all sorts of absurd things in dreams, so even though I might be quite convinced in my dream that seven plus five is fourteen I can still be wrong. OK, but what about one plus one is two - is it possible that even in a dream I could think that the answer is three and not two?

Instead, Descartes considers the possibility that God might still deceive me. Here, is an opportunity for you to look in more detail at the argument Descartes uses.

We do sometimes get arithmetical sums wrong. That shows that God does 'allow' to be wrong sometimes. Is it not conceivable that God might, if he wished, make us wrong all the time? This is an opportunity for you to say whether you think that is a good argument. Is it the always case that, 'If X happens sometimes, then it is logically possible that X might happen all the time'? Think of examples.

Descartes then elaborates on his argument. Someone might argue that it would be against God's 'goodness' to allow us to be wrong about arithmetic all the time. In that case, Descartes says, it doesn't matter whether you say God makes us go wrong, or simply that our error is a result of 'fate or chance or a continuous chain of events'. In other words, it is not necessary to assume any particular cause for our being wrong.

Again, here you might try to think of some examples. When people consent to be guinea pigs of stage show hypnotists, for example, they can be easily 'persuaded' to believe the most absurd things, maybe even that one and one is three.

Have a look again at the very useful commentary that goes with the passage from Descartes in Chapter 1 of 'Reading Philosophy'. You will find plenty of examples there of ways of questioning the text, finding arguments to discuss which are not apparent at a first reading.

This is what this question is asking you to do. There is a short answer to the question: 'Descartes considers necessary truths because he wants to put all beliefs into doubt.' But then you need to go on and ask why he does this? how does he do it? how good are the arguments he uses? are there any good arguments he might have used but didn't?

It would also be relevant to answering this question to consider the phenomenon of 'being wrong' about an arithmetical or geometrical truth. If I told you to add 39305950 plus 393959092, there is a significant possibility that you would get the addition wrong. On the other hand, if I ask you to add 1 plus 1, it seems impossible to imagine how you could be wrong. Then what about 2 plus 1? 5 plus 7? 31 plus 45? At some point what seems unimaginable becomes imaginable - but what point is that? It is absurd to think that there might be a 'cut-off' point where mistakes become possible, yet if there isn't a cut off point, then what?

Although I said above that you gave a 'correct' answer to the question, you need to be aware that there is no single 'correct' response. The examiner wants to see you grappling with the problems and questions raised by Descartes' argument. Anything that you can say that is RELEVANT to the question - even if you are struggling to express yourself or have to admit that you don't fully understand - will make your essay better and earn more marks.

However, I am glad that you have made a start. Well done!

All the best,

Geoffrey