"It would be interesting to see how the world would be different if Dick Cheney really listened to Radiohead’s OK Computer. I think the world would probably improve. That album is fucking brilliant. It changed my life, so why wouldn’t it change his?"
Chris Martin of Coldplay, Guardian Weekend 28 May 2005

Our ability to predict what will happen and detect order in the world depends upon a type of argument which is strictly speaking illogical. Induction is a form of reasoning which allows us to infer general principles from particular experiences. Sometimes we have many particulars to work on: countless observations have shown water to be H2O, so the hypothesis that all water is so composed seems pretty secure. However, we often generalise on the basis of very few observations. If you have a new gadget, you press a button and something happens, and you assume the same thing will happen if you press the button again. This is because your reasoning is informed by many other similar experiences which create a general assumption about regularity in the function of buttons.

But as philosophers have long recognised, induction is a logical embarrassment. That is because, whether we base our generalisations on many instances or just one or two, we are still concluding that something is always the case on the basis of only a limited set of observations. Most fundamentally, we are also assuming that the future will be like the past, when we have no experience at all of what the future will be like.

Given the need to reason to inductively, and the great difficulty philosophers have had justifying inductive reasoning and setting out principles for its correct use, it is perhaps unsurprising that it is very easy to do it badly. The temptation to over-generalise on the basis of a potentially misleading particular experience can be almost irresistible.

Crass Chris Martin’s comments about Dick Cheney and Radiohead is an especially egregious example of the mistake. It is hard to believe that Martin really thinks listening to an album which is lyrically opaque and far short of a coherent political treatise would change the mind of someone who has spent a whole life developing a political outlook. Of course, it might, but it seems very unlikely it would. Yet Martin seems to be convinced of the album’s transformative power because “It changed my life, so why wouldn’t it change his?”

What Martin has ignored is that people’s reactions to music are extremely variable. So the fact that OK Computer changed his life is no guarantee at all it will change the lives of others. In fact, the evidence that it often won’t is staring him in the face, since Martin must know full well that some people hate that album.

When people over-generalise from a limited number of specific instances they are said to be reading too much into merely “anecdotal evidence”. But this phrase is a little misleading, since sometimes one or two instances are enough to form an at least tentative general hypothesis. It is not strictly the number of cases you base your reasoning on that counts, but on whether they are of the right kind.

It may be hard to specify precisely what the “right kind” is, but the typical features of the wrong kind are clear enough. As in the example of Martin, you cannot generalise from situations where there are known to be considerable variations in how people or things respond.

But there is another problem with Martin’s generalisation which is more typical of arguments from anecdotal evidence. People tend to assume that the examples they are generalising from have characteristics which they may not in fact have. Did OK Computer really change Martin’s life? Perhaps, but I am pretty sure it didn’t change him from a Cheneyite neo-con to an anti-capitalist. So it is not just that the album wouldn’t have the effect claimed for it on all people; it didn’t even have that effect on Martin.

This is why anecdotal evidence is inadequate to demonstrate the efficacy of medicines. If you take a tablet and feel better, it is natural to say “it worked for me”. But you don’t know that. You cannot know whether the tablet made you feel better, taking the tablet merely coincided with the start of your recovery, or whether the believing that you would start to feel better led you to do so.

So it is not only untrue that if something works for me it will work for you: often we are just jumping to conclusions when we say it worked for me in the first place. But, as I said, this kind of mistake is natural, because even justified generalisations are not logically justified. Induction is a strange but essential beast, and one it is hard to domesticate.

Julian Baggini’s new book, The Pig That Wants to Be Eaten: And Ninety Nine Other Thought Experiments, is published 7 July by Granta.