فصل 36

chapter 36

Learning from Mistakes

Karl Popper and Thomas Kuhn

In 1666 a young scientist was sitting in a garden when an apple fell to the ground. This made him wonder why apples fall straight down, rather than going off to the side or upwards. The scientist was Isaac Newton, and the incident inspired him to come up with his theory of gravity, a theory that explained the movements of planets as well as apples. But what happened next? Do you think that Newton then gathered evidence that proved beyond all doubt that his theory was true? Not according to Karl Popper (1902–94).

Scientists, like all of us, learn from their mistakes. Science progresses when we realize that a particular way of thinking about reality is false. That, in two sentences, was Karl Popper’s view of how humanity’s best hope for knowledge about the world functions. Before he developed his ideas most people believed that scientists begin with a hunch about how the world is, and then gather evidence that shows their hunch was correct.

What scientists do, according to Popper, is try to prove their theories are false. Testing a theory involves seeing if it can be refuted (shown to be false). A typical scientist starts with a bold guess or conjecture that he or she then tries to undermine in a series of experiments or observations. Science is a creative and exciting enterprise, but it doesn’t prove anything is true – all it does is get rid of false views and – hopefully – edge towards truth in the process.

Popper was born in Vienna in 1902. Although his family had converted to Christianity, he was descended from Jews and when Hitler came to power in the 1930s Popper wisely left the country, moving first to New Zealand, and later to England where he settled, and took up a post at the London School of Economics. As a young man he had wide-ranging interests in science, psychology, politics and music, but philosophy was his real love. By the end of his life he had made important contributions both to the philosophy of science and to political philosophy.

Until Popper started writing about scientific method, many scientists and philosophers believed that the way to do science was to seek out evidence that supported your hypothesis. If you wanted to prove that all swans are white you’d make a lot of observations of white swans. If all the swans you looked at were white, it seemed reasonable to assume that your hypothesis ‘All swans are white’ was true. This style of reasoning goes from ‘All the swans I’ve seen are white’ to the conclusion ‘All swans are white.’ But clearly a swan that you haven’t observed could turn out to be black. There are black swans in Australia, for example, and in many zoos around the world. So the statement ‘All swans are white’ doesn’t follow logically from the evidence. Even if you have looked at thousands of swans and they were all white, it could still be false. The only way to prove conclusively that they are all white is to look at every single swan. If just one black swan exists, your conclusion ‘All swans are white’ will have been falsified.

This is a version of the Problem of Induction, a problem that David Hume wrote about in the eighteenth century. Induction is very different from deduction. That is the source of the problem. Deduction is a type of logical argument where if the premises (the starting assumptions) are true the conclusion must be true. So, to take a famous example, ‘All men are mortal’ and ‘Socrates is a man’ are two premises from which the logical conclusion ‘Socrates is mortal’ follows. You would contradict yourself if you agreed that ‘All men are mortal’ and that ‘Socrates is a man’, but denied the truth of the statement ‘Socrates is mortal.’ That would be like saying ‘Socrates both is and is not mortal.’ One way of thinking about this is that with deduction the truth of the conclusion is somehow contained within the premises and logic just teases it out. Here’s another example of deduction: Premise one: All fish have gills. Premise two: John is a fish. Conclusion: Therefore John has gills.

It would be absurd to say that premise one and premise two were true, but that the conclusion was false. That would be completely illogical.

Induction is very different from this. Induction usually involves arguing from a selection of observations to a general conclusion. If you notice that it rained every Tuesday for four consecutive weeks, you might generalize from this that it always rains on Tuesdays. That would be a case of Induction. It would only take one dry Tuesday to undermine the claim that it always rains on Tuesdays. Four consecutive wet Tuesdays is a small sample of all the possible Tuesdays. But even if you make numerous observations, as with the white swans, you can still be thwarted by the existence of a single case that doesn’t fit your generalization: one dry Tuesday or one non-white swan, for example. And that is the Problem of Induction, the problem of justifying relying on the method of induction when it seems so unreliable. How do you know that the next glass of water you drink won’t poison you? Answer: all the glasses of water you’ve drunk in the past were fine. So you assume that this one will be. We use this kind of reasoning all the time. Yet it seems that we aren’t completely justified in putting such faith in it. We assume patterns in nature that may or may not really be there.

If you think that science progresses by induction, as many philosophers have done, then you have to face the Problem of Induction. How can science be based on such an unreliable style of reasoning? Popper’s view of how science develops neatly avoids this problem. That’s because, according to him, science doesn’t rely on induction. Scientists start with a hypothesis, an informed guess about the nature of reality. An example might be ‘All gases expand when heated.’ This is a simple hypothesis, but real-life science involves a great deal of creativity and imagination at this stage. Scientists find their ideas in many places: the chemist August Kekulé, for example, famously dreamt of a snake biting its own tail, which gave him the idea for the hypothesis that the structure of the benzene molecule is a hexagonal ring – a hypothesis that has so far stood up to scientists’ attempts to prove it false.

Scientists then find a way of testing this hypothesis – in this case, getting a lot of different sorts of gas and heating them. But ‘testing’ doesn’t mean finding evidence to support the hypothesis; it means trying to prove that the hypothesis can survive attempts to falsify it. Ideally the scientists will look for a gas that doesn’t fit the hypothesis. Remember that in the case of the swans it only took one black swan to undermine the generalization that all swans are white. Similarly, it would only take one gas that failed to expand when heated to undermine the hypothesis that ‘All gases expand when heated.’ If a scientist refutes a hypothesis – that is, shows that it is false – then that results in a new bit of knowledge: the knowledge that the hypothesis is false. Humanity progresses because we learn something. Observing lots of gases which do expand when heated won’t give us knowledge, except perhaps a little more confidence in our hypothesis. But a counter-example really teaches us something. For Popper a key feature of any hypothesis is that it has to be falsifiable. He used this idea to explain the difference between science and what he called ‘pseudo-science’. A scientific hypothesis is one that can be proved wrong: it makes predictions that can be shown to be false. If I say ‘There are invisible, undetectable fairies making me type this sentence’, then there is no observation that you can make that will prove my statement is false. If the fairies are invisible and don’t leave any trace, there is no way of showing that the claim that they exist is false. It is unfalsifiable and so not a scientific statement at all.

Popper thought that many statements made about psychoanalysis (see Chapter 30) were unfalsifiable in this way. He thought they were untestable. For example, if someone says that everyone is motivated by unconscious wishes, there is no test to prove this. Every bit of evidence, including people denying that they are motivated by unconscious wishes, is, according to Popper, merely taken as further proof that psychoanalysis is valid. The psychoanalyst will say, ‘The fact that you deny the unconscious demonstrates that you have a strong unconscious wish to challenge your father.’ But this statement can’t be tested because there is no imaginable evidence that could show that it was false. Consequently, Popper argued, psychoanalysis wasn’t a science. It couldn’t give us knowledge in the way a science could. Popper attacked Marxist accounts of history in the same way, arguing that every possible outcome would count as support for the view that the history of humanity is a history of class struggle. So again, it was based on unfalsifiable hypotheses.

In contrast, Albert Einstein’s theory that light would be attracted by the sun was falsifiable. That made it a scientific theory. In 1919 observations of the apparent position of stars during an eclipse of the sun failed to refute it. But they might have done. The light from the stars was not normally visible, but under the rare conditions of an eclipse scientists were able to see that the stars’ apparent positions were where Einstein’s theory predicted they would be. If they had seemed to be somewhere else, this would have undermined Einstein’s theory of how light is attracted to very heavy bodies. Popper didn’t think these observations proved that Einstein’s theory was true. But the testability of the theory, and the fact that scientists had been unable to show it to be false, counted in its favour. Einstein made predictions which could have been wrong, but they weren’t.

Many scientists and philosophers have been deeply impressed by Popper’s description of scientific method. Peter Medawar, who won the Nobel Prize for Medicine, for example, said, ‘I think Karl Popper is incomparably the greatest philosopher of science there has ever been.’ The scientists particularly liked the description of their activity as creative and imaginative; they also felt that Popper understood how they actually went about their work. The philosophers were delighted with the way that Popper got around the difficult issue of the Problem of Induction too. In 1962, however, the American historian of science and physicist Thomas Kuhn published a book called The Structure of Scientific Revolutions, which told a different story of how science progresses, one that suggested Popper had got things wrong. Kuhn believed that Popper hadn’t looked closely enough at the history of science. If he had he would have seen a pattern emerging.

Most of the time what he called ‘normal science’ goes on. Scientists work within a framework or ‘paradigm’ that the scientists of that day share. So, for example, before people realized that the earth revolves around the sun, the paradigm was that the sun goes round the earth. Astronomers would do their research within that framework and would have explanations of any evidence that didn’t seem to fit with it. Working within this paradigm, a scientist like Copernicus who came up with the idea that the earth goes round the sun would be thought to have made a mistake in his calculations. According to Kuhn, there aren’t facts out there waiting to be discovered: instead, the framework or paradigm to some extent fixes what you can think about.

Things get interesting when what Kuhn called a ‘paradigm shift’ happens. A paradigm shift is when a whole way of understanding is overturned. This can happen when scientists find things that don’t fit in with the existing paradigm – such as observations that didn’t make sense within the paradigm that the sun goes round the earth. But even then it can take a long time for people to abandon their old ways of thinking. Scientists who have spent their lives working within one paradigm don’t usually welcome a different way of looking at the world. When they do eventually switch to a new paradigm, a period of normal science can begin again, this time working within the new framework. And so it goes on. That’s what happened when the view that the earth was the centre of the universe was overturned. Once people started to think about the solar system in that way, there was a lot more normal science to do to understand the paths of the planets around the sun.

Popper, not surprisingly, didn’t agree with this account of the history of science, although he did agree that the concept of ‘normal science’ was useful. Whether he was like a scientist with an outdated paradigm himself, or had got closer to the truth about reality than Kuhn had, is an intriguing question.

Scientists use real experiments; philosophers, on the other hand, tend to invent thought experiments to make their arguments plausible. The philosophers Philippa Foot and Judith Jarvis Thomson have developed a number of carefully constructed thought experiments that reveal important features of our moral thinking.