Some purported solutions to the problem of induction

Falsificationism (Karl Popper)

1. Hume is right that induction cannot be justified.
2. A theory that takes the form of universal generalization (Every A is B) cannot be proven, but it can be falsified.
3. The basis of science should be falsification rather than induction. We should try to falsify our theories, and retain those theories which have survived the most rigorous falsification attempts (highly corroborated theories).

Problems

1. Is induction really irrelevant?
2. Why retain highly corroborated theories?

Strawson on induction - the ordinary language approach

• Semantic thesis: Using induction to justify empirical beliefs is part of what we mean by "rational".
• Asking whether it is rational to use induction is like asking whether the law is legal.
• No need for justification: It is impossible to provide a further justification of why it is rational to use induction. Failure of justification does not constitute a good objection to induction. The demand for justification should be rejected.

Issues

• Is the semantic thesis correct?
• Does the semantic thesis entail that it is a conceptual truth that we should use induction?

Armstrong - induction as IBE

Armstrong What is a Law of Nature

• Induction has two steps:

1. Infer from observed cases to underlying laws / theories. (Inference to the best explanation)
2. Draw conclusions about unobserved from laws / theories. (deduction)

• It is analytic that IBE is rational.

@I start from the premise that ordinary inductive inference, ordinary inference from the observed to the unobserved is, although invalid, nevertheless a rational form of inference. I add that not merely is the case that induction is rational, but it is a necessary truth that it is so...We need an explanation of the rationality of induction. My own explanation is this. The sort of observational evidence which we have makes it rational to postulate laws which underlie, and are in some sense distinct from, the observational evidence. The inference to the laws is a case of inference to the best explanation. ..the inferred laws entail conditional prediction about the unobserved (if it is an F, then it will be a G) ... To tie up the argument it is necessary to ask why inference to the best explanation is rational. But that I think is analytic in a fairly obvious way. If making such an inference is not rational, what is? It may still be asked why the inference to underlying laws is the best explanation of our inductive evidence. The only answer to that is to challenge the questioner to find a better explanation. (p53) @

How does IBE actually work? How do we identify the "best" explanation?

Further discussion

• White, F.C. (1988) Armstrong, rationality and induction. Australasian Journal of Philosophy, Volume 66, Number 4, December 1988 , pp. 533-537(5).
• van Frassan, B. (1989) Laws and symmetry. Oxford : Oxford University Press.

The pragmatic justification

Reichenbach (see http://homepages.nyu.edu/~mjr318/btk08/BTK%2014%20-%20Reichenbach.pdf)

A pragmatic justification of induction - that induction is the best method for achieving our aim.

1. Agrees with Hume that we cannot show that induction is actually reliable (giving us true conclusions most of the time).
2. But we can show that induction is reliable if any method is reliable.
3. If that's the case, then it is rational to use induction because there is no better method.

The argument for (2).

1. If nature is chaotic and no method of prediction is successful, induction will not be successful.
2. If nature is not chaotic and there is some method of prediction that that will be successful, induction will also be successful.
3. Therefore, we are justified in using induction because induction will be successful if anything is.

Compare - Doctor : "If any treatment can cure this cancer, this operation also can."

• It is possible that this cancer is not curable.
• But it would be rational to undergo the operation if the patient wants to cure the cancer.