[S02] Scientific method

§1. The hypothetical-deductive method

The hypothetical-deductive method (HD method) is a very important method for testing theories or hypotheses. It is sometimes said to be "the scientific method". This is not quite correct because surely there is not just one method being used in science. However, it is true that the HD method is of central importance, because it is one of the more basic methods common to all scientific disciplines, whether it is economics, physics, or biochemistry. Its application can be divided into four stages :

The hypothetical-deductive method

1. Identify the hypothesis to be tested.
2. Generate predications from the hypothesis.
3. Use experiments to check whether predictions are correct.
4. If the predictions are correct, then the hypothesis is confirmed. If not, then the hypothesis is disconfirmed.

§2. Example

Here is an illustration :

1. Suppose your portable music player fails to switch on. You might then consider the hypothesis that perhaps the batteries are dead. So you decide to test whether this is true.
2. Given this hypothesis, you predict that the music player should work properly if you replace the batteries with new ones.
3. So you proceed to replace the batteries, which is the "experiment" for testing the prediction.
4. If the player works again, then your hypothesis is confirmed, and so you throw away the old batteries. If the player still does not work, then the prediction is false, and the hypothesis is disconfirmed. So you might reject your original hypothesis and come up with an alternative one to test, e.g. the batteries are ok but your music player is broken.

§3. Some comments

The example above helps us illustrate a few points about science and the HD method.

1. A scientific hypothesis must be testable

The HD method tells us how to test a hypothesis, and a scientific hypothesis must be one that is capable of being tested.

If a hypothesis cannot be tested, we cannot find evidence to show that it is probable or not. In that case it cannot be part of scientific knowledge. Consider the hypothesis that there are ghosts which we cannot see and can never interact with, and which can never be detected either directly or indirectly. This hypothesis is defined in such a way to exclude the possibility of testing. It might still be true and there might be such ghosts, but we would never be in a position to know and so this cannot be a scientific hypothesis.

2. Confirmation is not truth

In general, confirming the predictions of a theory increases the probability that a theory is correct. But in itself this does not prove conclusively that the theory is correct.

To see why this is the case, we might represent our reasoning as follows :

If H then P.
P.
Therefore H.

Here H is our hypothesis "the batteries are dead", and P is the prediction "the player will function when the batteries are replaced". This pattern of reasoning is of course not valid, since there might be reasons other than H that also bring about the truth of P. For example, it might be that the original batteries are actually fine, but they were not inserted properly. Replacing the batteries would then restore the loose connection. So the fact that the prediction is true does not prove that the hypothesis is true. We need to consider alternative hypotheses and see which is more likely to be true and which provides the best explanation of the prediction. (Or we can also do more testing!)

In the next tutorial we shall talk about the criteria that help us choose between alternative hypotheses.

3. Disconfirmation need not be falsity

Very often a hypothesis generates a prediction only when given additional assumptions (auxiliary hypotheses). In such cases, when a prediction fails the theory might still be correct.

Looking back at our example again, when we predict that the player will work again when the batteries are replaced, we are assuming that there is nothing wrong with the player. But it might turn out that this assumption is wrong. In such situations the falsity of the prediction does not logically entail the falsity of the hypothesis. We might depict the situation by this argument : ( H=The batteries are dead, A=The player is not broken.)

If ( H and A ) then P.
It is not the case that P.
Therefore, it is not the case that H.

This argument here is of course not valid. When P is false, what follows is not that H is false, only that the conjunction of H and A is false. So there are three possibilities : (a) H is false but A is true, (b) H is true but A is false, or (c) both H and A are false. So we should argue instead :

If ( H and A ) then P.
It is not the case that P.
Therefore, it is not the case that H and A are both true.

Returning to our earlier example, if the player still does not work when the batteries are replaced, this does not prove conclusively that the original batteries are not dead. This tells us that when we apply the HD method, we need to examine the additional assumptions that are invoked when deriving the predictions. If we are confident that the assumptions are correct, then the falsity of the prediction would be a good reason to reject the hypothesis. On the other hand, if the theory we are testing has been extremely successful, then we need to be extremely cautious before we reject a theory on the basis of a single false prediction. These additional assumptions used in testing a theory are known as "auxiliary hypotheses".

§4. When should we reject a theory?

When a theory makes a false prediction, sometimes it can be difficult to know whether we should reject the theory or whether there is something wrong with the auxiliary hypotheses. For example, astronomers in the 19th century found that Newtonian physics could not fully explain planet Mercury's orbit. It turns out that this is because Newtonian physics is wrong, and you need relativity to give a more accurate prediction of the orbit. However, when astronomers discovered Uranus in 1781, they also found out that its orbit was different from the predictions of Newtonian physics. But then scientists realized that it could be explained if there was an additional planet which affected Uranus, and Neptune was subsequently discovered as a result.

In 2011, scientists in Italy reported that their experiment seemed to have shown that some subatomic particles could travel faster than the speed of light, which would seem to show that relativity theory is wrong. But on closer inspection, it was discovered that there was a problem with the experimental setup. So if a theory has been very successful, even when a result seems to show that theory is wrong, we need to make sure that the evidence is strong and reliable, and try to replicate the result and eliminate alternative explanations. "Extraordinary claim requires extraordinary evidence".