 The proposal of the straight rule goes back to the problem of assertability of probability claims he discussed in his thesis. Reichenbach’s proposal is reminiscent of the law of large numbers, that the empirical distribution of a sequence of independent and identically distributed trials converges in probability to the true distribution. But the law of large numbers depends on independent, identically distributed trials. Reichenbach cannot resort to such assumptions if he wants to avoid circularity in his account of inductive inference. Instead he introduces “posits” that can basically be understood as leaps of (tentative) faith that the empirical distribution is representative. Posits can be “blind” or “appraised.” Posits are blind when there is no data available to justify the posit. For example, if all one has is a sequence of measurements for which the empirical frequency distribution of events is given by F, then a blind posit might state that the probabilities specified by F are within ε, for some small ε, of the true distribution P. One has no reason to justify this claim, the posit is blind. However, if one had several sequences of measurements resulting in empirical frequency distributions F1,…, Fn, then the relative frequencies found in each of these empirical distributions can, according to Reichenbach, be used to get higher order distributional information about the original posit itself, and the posit therefore becomes appraised. So, if one has sequences of measurements of the gravitational constant from the Earth, the Moon, the 7 other planets, and, say, the Cavendish balance—10 sequences in total—and in all cases except for Mercury, the gravitational constant is within some small value ε of g, then the higher order probability of the posit that the true value of the gravitational constant is within ε of g is 9/10. How sure can one be that the appraisal of the posit is accurate?—For that Reichenbach introduces again an even higher order blind posit. One thus arrives at a hierarchy of posits, of which the lower levels are appraised posits, and the highest levels are blind posits. Just how the integration of different levels is supposed to occur, remains unclear and a point of criticism by Ernest Nagel (see below). The general idea appears to be that at the “data” level one counts frequencies and integrates higher levels using Bayes rule. 