This chapter is concerned with an aspect of the problem of describing or specifying those inductive practices we take to be rational.
At the level of description, there is no doubt that one common inductive practice we take to be rational is to project common properties from samples to populations, to argue from certain Fs being G to certain other Fs being G. There are many ways we can try to spell out this practice in semi-formal terms: by saying ‘Fa & Ga’ confirms ‘(x)(Fx⊃Gx)’, or ‘All examined As are B’ supports ‘All unexamined As are B’, or ‘Fa1 &…& Fan’ gives a good reason for ‘Fan+1’, and so on. The precise way chosen will not particularly concern us, and I will simply refer to the kind of inductive argument pattern reflected in the various formalisations as the straight rule (SR). The discussion will be restricted to the simplest case where everything in a sample, not merely a percentage, has the property we are concerned with.
To say that the SR is one common inductive argument pattern we all acknowledge as rational is not to say that it is the most fundamental inductive argument pattern, or the most important in science, or the pattern that must be justified if induction is to be justified; it is simply to say what is undeniable—that we all use it on occasion and take it as rational to do so. This chapter is not concerned with how important or fundamental the SR is—for example, vis-à-vis hypothetico-deduction—it is concerned with the description of those applications of the SR which we regard as rational.
Since Nelson Goodman’s 1946 paper and the development of it in Fact, Fiction, and Forecast,1 it has been very widely supposed that the rough description of the SR given above—as certain Fs