^{page 333 note 1} Recently John Kemeny has developed a more general theory on the criteria for judging the simplicity of a quantitative hypothesis (see his “The Use of Simplicity in Induction”, Philosophical Review, 57,1953, pp. 391–408).Google Scholar

^{page 336 note 1} This is so because the proof on pp. 380–1 of theorem (1) essentially depends on the assumption that any possible combination of n atomic facts is equally likely- which is true only under Wittgenstein's probability metric.

^{page 336 note 2} Jeffreys's proof is based on the fact that the set of all possible, essentially different, quantitative hypotheses is a denumerable set; therefore it can be arranged in a linear order; and we can assign the probabilities 1/2, 1/4,1/8, to the successive members of the set. Under this arrangement each hypothesis will have a non-zero a prior probability and the sum of all probabilities will be unity as required.

^{page 337 note 1} I am indebted for this example to Professor John Pass more.

^{page 338 note 1} Popper uses this principle only to discourage the introduction of unjustified auxiliary hypotheses (see p. 145). But it seems to me it has a much wider application and indeed is one of the most fundamental principles of scientific method.

^{page 340 note 1} But of course these hypotheses in turn will leave their own basic assumptions without explanation.