Those knowledgeable about the subject of Professor Suppes’ paper will appreciate that there are few contemporary philosophers who are equal to debate with him on this topic or to criticize his application of the various probability approaches to specific domains of empirical investigation and practice. In his present paper it is mainly in the appendix, in which he sketches his calculus for determining upper and lower probability approximations, as detailed in his 1974 paper on ‘The Measurement of Belief’ [1], that Suppes exhibits his special technical expertise. There he sets forth his version of Bayes’ well-known theorem as a more plausible approach than other probability techniques for purposes of applying statistical methods to situations of practical belief, decision and practice. As is to be expected, his exposition provides no opportunity for critical comment.