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 o…

Read moreIn 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.