Online research in philosophy

In this paper I show that David Armstrong is wrong to claim that the regularity theorist must be an inductive sceptic by demonstrating that even those who support worldly ontologies devoid of metaphysical glue (or as Hume might say, necessary connections ‘in the objects’) can justifiably make many inductive inferences. As well as branding the regularity theorist an inductive sceptic, Armstrong also claims that regularity theory (RT) laws have no explanatory value whatsoever. I try to show that Armstrong is also wrong in this respect, and that as a matter of fact, observed regularities are best explained by laws of this kind, or at least something like them.

Stove attempts to undermine Hume's argument on induction by denying Hume the claim that induction presupposes the uniformity of nature. I argue that Stove's attack on Hume's argument fails. *A paper from which the present piece was derived was read at the Hume Symposium. Flinders Medical Centre, South Australia, in July 1990, where George Couvalis and David Gauthier made helpful criticisms of my argument.

Until recently, philosophical scholarship has not been kind to Hume’s arguments in “Of scepticism with regard to reason” (A Treatise of Human Nature, 1.4.1). [1] Reid gives the negative arguments a pretty rough ride, though in the end he agrees with Hume’s conclusion that reason cannot be defended by reason.[2] Stove’s comment that the argument is “not merely defective, but one of the worst arguments ever to impose itself on a man of genius” (Stove 1973), while extreme, is not untypical. Many important books on Hume (e.g. Stroud 1977) simply ignore it, though this may be because it is difficult to find any trace of the arguments in the Enquiry Concerning the Human Understanding.[3] Furthermore, when attention was paid to the arguments, it was devoted mainly to the second of the two negative arguments Hume puts forward, and that argument was held to contain an elementary mistake concerning beliefs about beliefs (McNabb 1951).

In The Rationality of Induction, David Stove presents an argument against scepticism about inductive inference—where, for Stove, inductive inference is inference from the observed to the unobserved. Let U be a finite collection of n particulars such that each member of U either has property F-ness or does not. If s is a natural number less than n, define an s-fold sample of U as s observations of distinct members of U each either having F-ness or not having F-ness. Let pU denote the proportion of members of U that are Fs and, if S is an s-fold sample of U, let pS denote the proportion of members of S that are Fs. Call S representative if and only if |pS – pU|<0.01. Stove‘s argument against inductive scepticism is built on the following statistical fact:

As s gets larger the proportion of all possible s-fold samples of U that are representative gets closer to 1 (regardless of the size of U or of the value of pU).

In this essay I subject Stove‘s argument to thorough scrutiny. I show that the argument – as it stands – is incomplete, and I illuminate the issues involved in trying to fill the gaps. Along the way I demonstrate that one of the commonest objects to Stove‘s argument misses the point.