  Along with his attack on a subjectivist account of probability, Peirce also attacked the use of what came to be called the method of “inverse probabilities” as a way of solving the problem of induction. In the process, he also excoriated the theoretical work, in this connection, of de Morgan and Adolphe Quetelet (the Belgian criminologist and early user of statistical analysis in sociology). Induction, as we have seen, Peirce counted as an inference from sample to population. The method of inverse probabilities offers itself as a way of calculating the (conditional) probability that a population has a trait in a certain proportion given that a sample drawn from that population has the trait in that proportion. It proposes to calculate this conditional probability by applying the so-called “Bayes’s Theorem” in order to express it in terms of the (inverse conditional) probability that the sample has the trait in the crucial proportion given that the population has the trait in the crucial proportion. In the expression of the first conditional probability in terms of the second conditional probability, however, there occur certain quantities, known as the “Bayesian prior probabilities.” What Peirce pointed out is that there is no way to assign any quantities in a rational fashion to the requisite Bayesian prior probabilities. The appearance that one does have a reason for assigning particular quantities results only from an illicit substitution of subjective probabilities for the needed objectivist probabilities. What the user of the method of inverse probabilities does is to equate complete lack of information about something with the claim that all possibilities must have equal probabilities. This equation was called “the principle of insufficient reason” in the nineteenth century; John Maynard Keynes later named it “the principle of indifference.” This principle is, however, completely irrational without a dependence on a subjectivist account of probability.  What we need, however, is objective probabilities, and so we have no reason for assigning any particular values to the Bayesian prior probabilities. Only “if universes were as plenty as blackberries,” wrote Peirce, would the analysis of de Morgan and Quetelet make any sense.