6.1: Karl Popper

Karl Popper was a philosopher in Vienna during the reign of Logical Positivism, but he was not himself a Positivist. Popper is best known for his contributions to the problem of induction and the demarcation problem. In both cases his views were critical of the Logical Positivists.

Conjecture and Refutation

As you will recall, Hume argues that inductive arguments fail to provide rational support for their conclusions. His reason for taking induction to be irrational is that every inductive argument assumes that unobserved events will follow the pattern of observed events and this assumption cannot be supported either deductively or inductively. No purely deductive support can be given for this principle of induction because it is not a mere truth of logic. And any inductive argument offered in support of the inductive principle that unobserved cases will be like observed cases will be circular because it will also employ the very principle of induction it tries to support as a premise.

Popper accepted Hume’s conclusion that inductive inference is not rationally justifiable. He takes the problem of induction to have no adequate solution. But he rejects the further conclusion that science therefore yields no knowledge of the nature of the world. With Hume, Popper holds that no number of cases offered as confirmation of a scientific hypothesis yields knowledge of the truth of that hypothesis. But just one observation that disagrees with a hypothesis can refute that hypothesis. So while empirical inquiry cannot provide knowledge of the truth of hypotheses through induction, it can provide knowledge of the falsity of hypotheses through deduction.

In place of induction, Popper offers the method of conjecture and refutation. Scientific hypotheses are offered as bold conjectures (guesses) about the nature of the world. In testing these conjectures through empirical experiment, we cannot give positive inductive reasons for thinking that they are true. But we can give reasons for thinking they are false. To see how this works, let’s look at the pattern of reasoning employed in testing a scientific hypothesis using induction on the one hand, and Popper’s deductive method of conjecture and refutation on the other. First, in designing an experiment, we determine what we should expect to observe if the hypothesis is true. Using induction, if our observation agrees with our expectation, we take the hypothesis to be inductively confirmed. The pattern of reasoning looks like this:

1. If H, then O
2. O
3. Therefore, H

This pattern of reasoning is not deductively valid (generate a counterexample to see for yourself), and as an inductive argument it faces the problem of induction. So this pattern of reasoning fails to provide us with rational grounds for accepting H as true. But suppose that when we carry out our experiment, we observe “not O.” In this case our pattern of reasoning looks like this:

1. If H, then O
2. not O
3. Therefore, not H

This pattern of reasoning is deductively valid. To see this try to suppose that the premises are true and the conclusion is false. If the conclusion were false, then ‘H’ would be true. And, given this and the truth of the first premise, ‘O’ would follow. But ‘O’ contradicts ‘not O” which is asserted by the second premise. So it is not possible for the premises to be true and the conclusion false. In other words, the pattern of reasoning here is deductively valid.

The latter is the pattern of reasoning used in the method of conjecture and refutation. It is a deductively valid pattern that makes no use of inductive confirmation. It should now be clear how Popper’s method of conjecture and refutation works and how empirical inquiry making use of this method can provide us with knowledge of the world (or rather, how the world isn’t) while avoiding the problem of induction.

According to Popper, there is no rational methodology or logic for evaluating how scientists come up with hypotheses. They are just conjectures and no amount of evidence is capable of inductively confirming hypotheses in the sense of giving us positive reason for thinking our hypotheses are true. Evidence in agreement with a hypothesis never provides it with inductive confirmation. If all the evidence is in agreement with a hypothesis, we can say that it is “corroborated.” To say that a hypothesis is corroborated is just to say that it has survived our best attempts at refutation. But contrary evidence can decisively refute hypotheses.

Demarcation through Falsifiability

The demarcation problem is the problem of distinguishing science from other things, from poetry to religion to obscure metaphysics. Popper offers an alternative to the Positivist’s verificationist theory of meaning in addressing this problem. The Positivist’s solution to the demarcation problem had the downside of denying that we can assert as true that it is wrong to torture innocent babies just for fun. Popper’s view of the matter avoids this unsavory consequence.

Popper’s method of conjecture and refutation suggests his criterion for distinguishing science from non-science. For it to be possible to refute a hypothesis requires that there be possible observations that would give us grounds for rejecting the hypothesis. We can only scientifically investigate hypotheses that take observational risks, those that are exposed to the possibility of being shown false through observation. That is, we can take a hypothesis to be scientific if and only if it is falsifiable. For a hypothesis to be falsifiable we must be able to specify possible observational conditions that would be grounds for rejecting the hypothesis as false. But this does not mean that that it will be proven false or that it can be shown to be false (either of these confusions would lead to the absurd view that a claim is only scientific if it is false). Let’s look at some examples to make this clear.

Consider the hypothesis that all crows are black. We can specify observable conditions under which we would count this as false. Namely, seeing a white crow, or a green one. Being able to specify the observational conditions under which we would reject this hypothesis doesn’t mean that it false. Suppose the hypothesis is true. It is still a claim that takes risks in the face of observation because we know that some possible observations would refute it. So the hypothesis that all crows are black is falsifiable.

Now consider claims made by astrology. These are typically formulated in such a vague way that any eventuality could be interpreted as affirming the astrologer’s predictions. If there are no possible observations that could refute astrology, then it is not scientific. Some astrologers might make specific and concrete predictions. These might get to claim that they are being scientific on Popper’s view, but to the degree that astrologers do take risks of being refuted by observation, they have been refuted too often.

Political ideologies often fail to pass the falsifiability test. Popper was especially critical of Marxism which was very popular with the Viennese intellectuals he knew in his youth. Marxists seemed to have an explanation for everything. The inevitability of Marxist revolution was illustrated by its rising popularity in much of Europe. But if Americans, for instance, were not rebelling against their capitalist oppressors it was only because they had yet to see how alienating capitalism is. The conditions for revolution just weren’t yet ripe. But they will be, says the confident Marxist. Popper’s key insight was that a theory that can explain everything that might happen doesn’t really explain anything. It is empty.

Today, Popper might make the same criticism of very different political ideologies. If free markets don’t fix every problem, the libertarian can always complain that this is only because they have not been allowed to function freely enough. If government doesn’t fix every problem, the big government liberal can always complain that big government hasn’t been empowered enough (when we get around to political philosophy we will find reason to doubt that there are very many liberals that really fit this stereotype). Extreme views are only made plausible to their fans by elaborate schemes of excuses for why they don’t work out as well as they should. Popper would say that in politics as in science, we need to try things where we can honestly examine the consequences and hold ourselves accountable when they don’t go well by trying something else.

Auxiliary Hypotheses

Here we will describe an objection to Popper’s method of conjecture and refutation that will set the stage for introducing the views of Thomas Kuhn. According to Popper, we make progress in science by refuting false conjectures. We never have inductive grounds for holding that proposed scientific hypotheses and explanations are true, but we can narrow in on the truth by eliminating the falsehoods. Our hypotheses lead us to expect certain observations. If we do not observe what we expect to observe, then we have non-inductive grounds for rejecting our hypothesis. Again, the pattern of reasoning followed in eliminating false hypotheses through scientific inquiry looks like this:

1. If H, then O
2. Not O
3. Therefore, not H

This is the deductively valid pattern of reasoning known as modus tollens. However, we rarely get to test hypotheses in isolation. Typically, our expectation of a given observation is based on the hypothesis we are interested in testing in conjunction with any number of background assumptions. These background assumptions are the auxiliary hypotheses. If we take into account the auxiliary hypotheses, the pattern of reasoning used in Popper’s method of conjecture and refutation looks like this:

1. If H and AH, then O
2. Not O
3. Therefore, not H

But this argument pattern is not valid. The observation (not O) might indicate the falsity of one of the auxiliary hypotheses (AH) rather than the falsity of (H), the hypothesis we set out to test. What this tells us is that the implications of other than expected observations are always ambiguous. When our observations don’t accord with our expectations it tells us that at least one of the assumptions or hypotheses that lead us to expect a given observation is false. It may be the hypothesis we set out to test, or it may be one of our auxiliary hypotheses. But unexpected observations don’t tell us which is false.

Here’s a nice example of auxiliary hypotheses at work in everyday reasoning. Our hypothesis is that Hare is faster than Tortoise. This hypothesis leads us to expect that Hare will win a race against Tortoise. But suppose that, contrary to our expectation, we observe Tortoise winning the race. The hypothesis that Hare is faster than Tortoise is not thereby falsified because of the presence of a number of auxiliary hypotheses. Among these auxiliary hypotheses are the following: (i) Hare did not stop in the middle of the race for a snack, (ii) Hare did not get run over while crossing the road, (iii) Hare did not get eaten by Coyote during the race, (iv) Hare did not get entangled in a philosophical discussion about the rationality of scientific methods with his friend Gopher before crossing the finish line. When Tortoise crosses the finish line first, that tells us that either Tortoise is faster than Hare or one of these or many other auxiliary hypotheses is false. But Tortoise winning doesn’t tell us which. The unexpected observation thus fails to cleanly refute our hypothesis.