PH29A Induction

Hume

The types of case Hume is particularly concerned with are two:

• prediction of a subsequent event, given a constant conjunction in past experience — the sun will rise tomorrow, given we have seen it rise each morning so far;
• prediction that constant conjunctions of features will always continue to go together — having seen many flames that are hot we expect all flames to be hot.

Put more generally, the issue is our passage from observed to unobserved cases.

Hume's arguments with respect to these moves are, firstly, that none of them are guaranteed a priori — we can always envisage that the course of nature may change. Secondly, any further claim that would provide us with a rational basis for making these moves (Hume says this would be some principle of the uniformity of nature) would itself have to be a contingent (not a priori) claim of the sort we are trying to justify. We would therefore be running around in a circle. So there is no rational justification for any of these apparent inferences; they are a matter of brute instinct, not the work of reason.

Williams' comments

Williams approaches Hume by questioning the pertinence of any sort of uniformity principle. Hume seems to suppose there might be something that could convert our bald and patently invalid (deductively invalid) inference from observed cases to unobserved into a reliable one. But Williams says that, if it is like the uniformity of nature as Hume states it, then it wouldn't be able to do that job. A general claim like the future will resemble the past or nature operates uniformly is too easy to make true because there will always be some respect or other in which things are the same tomorrow as they are today. What we need, however, is a guarantee that we have hit upon the right respects, that things will go the same with flames being hot, etc., and the general principle won't provide that.

Williams adds that this point is unaffected by any move we might make to alter the conclusion of our inference to a claim about probabilities. What is at stake is the invalidity of a move from "some X is Y" to "this X is Y".

Goodman's "new riddle" of induction

To bolster his case for saying that a Humean principle of uniformity is empty, Williams invokes a famous modern puzzle, Goodman's grue. Suppose we have the concept grue understood as "examined before now and green, or else blue". Now our observational evidence so far for the generalisation that we accept, "all emeralds are green", is equally evidence for the claim that all emeralds are grue. But we cannot accept this since the two generalisations lead us to expect very different futures in 2003. Williams says this shows how anything that can happen could be construed as nature being uniform. It also suggests that no simple formal account can be expected for inductive inference, if there is such a thing.

There has been an enormous literature on the grue problem. A common response is that there is something "unnatural" about grue, but it is not so easy to show what has gone wrong. Another common approach is to argue that green is simpler than grue, but why should we think simpler concepts are more appropriate than complex ones?

Diagnosis

Williams' diagnosis of Hume's problem is a matter of seeing it as exhibiting the standard Cartesian structure (the sort of structure Whiteley set out in his table): we divide our claims to knowledge into two distinct sets, one privileged in some way, the other to be justified by reference to the first. So we can contrast claims about the observed past with the unobserved future, the observed particular with the general, and so on. There is no deductive link from the privileged set to the other. So how can the latter be justified? As usual, Williams' response is that nothing requires us to set up a problem in these terms.

Deductivism

At this point in his discussion, Williams touches upon one of the major contentious issues in the interpretation of Hume and of Humean arguments about induction. Did Hume think that the only decent sort of argument is deductively valid? Stove was a tireless champion of this view, and claimed that many modern philosophers were also closet deductivists — they might not say that only deductively valid arguments are acceptable but that is how they operate. Stroud in his book on Hume, and more recently Okasha, have read Hume differently.

If Hume or Hume's argument requires deductivism then it seems that one obvious response to it is to claim that there are other forms of argument or inference that are not deductive but which are objectively to be endorsed. There is admittedly no deductively valid link between past and future, observed and unobserved, etc., but there may well be some genuine non-deductive link.

We will look at what non-deductive logics may be like later. For now I want to record two of Williams' points. One is that such non-deductive logic is not to be confused with statistical inference, which is a matter of deductive (mathematical) reasoning about probabilities. The second is that, given his diagnosis of the Humean problem, he is not really interested in looking for a non-deductive logic. It is an attempt to answer a question we shouldn't be asking.