David Stove - Philosophy of Science, Induction and Probability

Philosophy of Science, Induction and Probability

Stove's starting point in philosophy of science was the Humean argument for inductive skepticism. Stove was a great admirer of David Hume but thought that this argument (which some contemporary Hume scholars would hesitate to attribute to Hume) was not only fallacious but harmful in its effects, and was one of the causes (though not the only one) of the "modern nervousness". Stove took it as his main task to refute Hume's inductive skepticism. There were two aspects to this task. The first was negative - to show that Hume's argument failed. The second was positive - to provide a justification of induction.

Stove's argument for the negative task was this. Consider a claim such as "All ravens are black". Hume argued that we don't know this a priori and that it cannot be entailed from necessary truths. Nor can it be deduced from our observations of ravens. We can only derive it from these observations if we add a premise to the effect that the unobserved is like the observed. But we have no a priori justification of this premise, and any attempt to derive it by empirical means would be circular. So Hume concluded that induction is unjustified.

Stove argued that Hume was presuming "deductivism" (Stove's best-known expression of this point was in a paper titled 'Hume, Probability and Induction'). This is the view, explicitly or implicitly accepted by many modern philosophers, that the only valid and sound arguments are ones that entail the arguments' conclusions. But if we accept that premises can support a conclusion to a greater (or lesser) degree without entailing it, then we have no need to add a premise to the effect that the unobserved will be like the observed - the observational premises themselves can provide strong support for the conclusion, and make it likely to be true. Stove argued that nothing in Hume's argument shows that this cannot be the case and so Hume's argument does not go through, unless one can defend deductivism. This argument wasn't entirely original with Stove but it had never been articulated so well before. Since Stove put it forward some philosophers have come to accept that it defeats Hume's argument.

The positive task was attempted by Stove in Probability and Hume's Inductive Scepticism (1973) and later in The Rationality of Induction (1986). Stove's principal positive argument for induction was presented in the latter book and was developed from an argument put forward by one of Stove's heroes, the late Donald Cary Williams (formerly Professor at Harvard University) in his book The Ground of Induction. Stove argued that it is a statistical truth that the great majority of the possible subsets of specified size (as long as this size is not too small) are similar to the larger population to which they belong. For example, the majority of the subsets which contain 3000 ravens which you can form from the raven population are similar to the population itself (and this applies no matter how large the raven population is, as long as it is not infinite). Consequently, Stove argued that if you find yourself with such a subset then the chances are that this subset is one of the ones that are similar to the population, and so you are justified in concluding that it is likely that this subset 'matches' the population reasonably closely. The situation would be analogous to drawing a ball out of a barrel of balls, 99% of which are red. In such a case you have a 99% chance of drawing a red ball. Similarly, when getting a sample of ravens the probability is very high that the sample is one of the matching or 'representative' ones. So as long as you have no reason to think that your sample is not unrepresentative you are justified in thinking that probably (although not certainly) that it is representative.

Stove also worked on falsificationism, the raven paradox, grue (color) and inductive logic.