Popper writes: ‘I think that I have solved a major philosophical problem: the problem of induction.’ Discuss whether this claim is warranted.

Popper writes: 'I think that I have solved a major philosophical problem: the problem of induction.' Discuss whether this claim is warranted.

Popper approaches, and ostensibly 'solves' the problem of induction through Hume.[1] In essence, the problem lies in making any logically valid inference from instances of experience to non-experience; from observational data to some general hypothesis. Two logical points - Hume's logical criticism of induction and Popper's criterion of demarcation - are important to consider when evaluating the cogency of Popper's solution[2] and I will therefore mention these briefly to begin with. In what subsequently follows, I will outline Popper's falsificationism and argue that critical logical and pragmatic failures of Popper's 'solution', raised by Duhem and Worrall, render the above bold claim entirely unwarranted.

First then, is the problem of induction. Hume's formulation begins with an analysis of causal relations. A appears to cause B, but there is nothing discoverable within the 'idea' of A that implies the occurrence of B - there exists no logical connection between the two events. Any observation of such a connection, Hume argues, is attributable to our experience of their constant conjunction, a conjunction which we have no grounds for believing will hold in the future.[3] Any deductive argument to justify induction will rest pivotal on an inductive premise (i.e. that the future will resemble the past); and any inductive argument is question begging. The major criterion for a solution to the problem is thus made resoundingly clear: avoid induction.

Secondly, it is important to discuss Popper's criterion of demarcation prior to his related 'solution' of the problem in question. According to Popper, science is demarked from pseudo science by its method of criticism - that is, attempted falsifications as opposed to ad hoc modifications: A hypothesis is first postulated and observable predictions are deduced from this. What follows are several attempts at refutation.[4] Popper gives a more extensive definition[5], but the fundamental idea is that this demarcation criterion is, at least as Popper views it, radically different from the generally accepted inductive demarcation of science from pseudo science, and the basis for a solution to the problem of induction.[6] From his demarcation criterion, Popper concludes that induction is simply a myth[7], with no place in science or ordinary life. The real scientific method behind the smokescreen of faulty inductive demarcation amounts to constant conjecture and refutation. This forms the basis of Popper's solution.

After reformulating the problem, Popper argues that there is no clash between the problem of induction (that it is impossible to justify a law by experiment or observation), the fact that science repeatedly uses and proposes laws, and the principle of empiricism (that in science, only observation and experiment may decide on the acceptance or rejection of scientific laws and theories)[8], since any hypothesis accepted by science is 'tentative [provisional] only', conditional on the results of empirical tests.[9] There is only deduction, and thus no problem of induction exists, or, as Popper holds unshakably, the problem of induction is solved.

Of course, many (good and bad) conjectures may be put forward for a single observation statement or as Popper calls it, a problem-situation[10]. The further problem is then to decide which one to use. A process of elimination by deduction is obviously the first place to turn, but that rests on the assumption that all but one conjecture will be falsified. If a number of conjectures, say A and B, remain unfalsified at time t, Popper states that theory A will be preferable to B if it is better corroborated - that is, if, on its past performance, A is better tested than B (taking into account the severity of the tests and the ability of the conjecture to stand up to the tests).[11] According to Popper, preferring some theories to others says nothing whatever about future performance, or about the reliability of a theory. There can be no 'absolute reliance' on a theory, and yet it is rational to choose the best tested theory.[12] By rational, Popper does not mean rational in the sense that it is based upon good reasons for expecting the future to resemble the past.

The question, then, is what does Popper mean? The answer, unfortunately, is hardly clear. There are indeed problems with Popper's demarcation criterion, which I have as yet left unaddressed in order to strengthen Popper's case, but there is also evident confusion at the very point of deciding to use one scientific theory over another. I will now evaluate both of these problems with reference to Duhem and Worrall respectively.

The first is a logical problem that lies at the heart of Popper's demarcation criterion and falsificationist method. The method Popper puts forward is just too simple, and in reality a single conjecture cannot be tested in isolation but rather with many auxiliary assumptions, including other hypotheses and conjectures.[13] As Duhem says, 'Physics is not a machine which lets itself be taken apart'[14]. If the prediction made by the conjecture fails, then all it is possible to say is that either the hypothesis in question is false, or the other auxiliary assumptions are false, or both. Just as there is no reason to accept induction, nor is there any reason to accept falsificationism, since in reality, its ability to falsify is severely limited. Take, for example, the (obviously mistaken) conjecture that sun-cream causes sunshine. One testable observation could state that whenever there is sun-cream, there is also sun-shine. However, suppose a situation arises in which many people wear sun-cream and, in fact, get soaked with rain.  Our observation statement is false, but does this demand we drop the conjecture? Not necessarily, since perhaps the volume of sun-cream was insufficient, or the temporal relation between sun-cream and sun-shine is more disparate than we assumed. Similarly, as Duhem points out, any hypothesis can be immunised against falsification by adding extra assumptions. Taking again the sun-cream - sun-shine example, it is possible to add an assumption like 'the volume of sun-cream must be sufficient' to the hypothesis, and it is immunised from falsification. Popper's attempt at demarking science from pseudo science began by noting that pseudo-scientific claims are unfalsifiable - but because of auxiliary assumptions and the possibility of immunising hypotheses, it is unclear that real science escapes this accusation either. Moreover, it is unclear that the falsificationist demarcation criterion really captures the essence of the scientific method.[15]

Even if these criticisms are overcome, there is a second, pragmatic difficulty with Popper's 'solution' in that it simply cannot overcome Hume's logical problem of induction. As mentioned earlier, the solution must avoid induction and, as Worrall points out, Popper's does not. The advice Popper gives is to prefer the predictions of the best corroborated theory, and act as though it were true. There are no reasons for supposing it is true, but, because it is the best tested, we have least reason to suppose it is false.[16] The problem though, is that ultimately there is an inference from past experience (the theory has best stood up to tests in the past) to the future (we should act as though it is true) - and this is induction. The moment any preferred future course of action is inferred from past experience is the moment an inductive leap must be made. Popper could just call such an inductive leap 'rational' but his solution then becomes trivial, akin to Russell's view that we should just expand our definition of rationality.   

The solution therefore seems entirely unwarranted, but that is not to say Popper has not touched upon something important. Hempel, who also advocated the falsificationist method, was not at bold as Popper, and perhaps saw the advantage of a more cautious approach. Whilst scientific inquiry is certainly not inductive in the narrow sense, he says, it may be inductive in the wider sense in as much as the hypotheses it accepts are accepted because of the inductive support of data.[17] Popper's claim is unwarranted because it claims too much, but falsificationism is certainly a major part of the scientific method - albeit an insufficient response to the a-rationality of scientific induction.

I have briefly summarised Hume's logical problem of induction, and considered Popper's 'solution' - that is, that induction is not a problem because it does not, in fact, exist. The 'myth' of induction is a result of a faulty demarcation, a demarcation that Popper apparently puts right by characterising the scientific method as entirely deductive. I have argued, like Duhem, that this characterisation oversimplifies matters by ignoring the presence of auxiliary assumptions and the possibility of immunising hypotheses. I then showed that a second and fatal problem, that is, the ultimate use of induction in Poppers falsificationism, renders his solution unwarranted.

[1]K.Popper (1963) 'Science: Conjectures and Refutations'

[2] Ibid.                                                                                                          

[3] B. Russell, History of Western Philosophy, Hume, Chapter XVII, pp664-671

[4] K.Popper (1963) 'Science: Conjectures and Refutations'

[5]From K.Popper (1963) 'Science: Conjectures and Refutations'

1) It is easy to obtain confirmations or verifications for every theory - if we look for confirmations.

2) Confirmations should only count if they are the result of risky predictions

3) Every good scientific theory is a prohibition, and the more it prohibits, the better it is.

4) A theory that is not refutable by any conceivable event is not scientific

5) Every genuine test of a theory is an attempt to falsify it

6) Confirming evidence should only count when they are the result of an attempt to falsify the theory in question

7) Some genuinely testable theories, when found to be false, are 'saved' by introducing auxiliary assumptions, etc. This is always possible, but it lowers the theory's scientific status.

[6] K.Popper (1963) 'Science: Conjectures and Refutations'

[7] Ibid.

[8] Ibid.

[9] Ibid.

[10] Ibid.

[11] K. Popper 'Conjectural Knowledge: My Solution to the Problem of Induction'

[12] Ibid.

[13] P. Duhem. Selections from 'The aims and structures of physical theory' (1906)

[14] Ibid.

[15] Most scientists hold unshakably to Darwinian evolution, despite controversy surrounding its falsifiability. 

[16] J. Worrall 'Why Both Popper and Watkins Fail to Solve the Problem of Induction.'

[17] C.Hempel (1966): Philosophy of Natural Science, Chapter 2, Prentice Hall