"The riddle of induction can be put thus: What rational basis is there for any of our beliefs about the unobserved? The theory of personal probability touches on the domain of the riddle and can even be construed as giving a partial answer. The theory prescribes, presumably compellingly, exactly how a set of beliefs should change in the light of what is observed. It can help you say, "My opinions today are the rational consequence of what they were yesterday and of what I have seen since yesterday." In principle, yesterday's opinions can be traced to the day before, but even given a coherent demigod able to trace his present opinions back to those with which he was born and to what he has experienced since, the theory of personal probability does not pretend to say with what system of opinions he ought to have been born. It leaves him, just as Hume would say, without rational foundation for his beliefs of today. Can there be any such foundation? The theory as such is silent, but I am led by study of it to doubt that there is a rational basis for what we believe about the unobserved. In fact, Hume's arguments, and modern variants of them such as Goodman's discussion of 'bleen' and 'grue', appeal to me as correct and realistic. That all my beliefs are but my personal opinions, no matter how well some of them may coincide with opinions of others, seems to me not a paradox but a truism. The grandiose image of a demigod tracing his beliefs back to the cradle only to find an impasse there seems a valid metaphor. If there is rational basis for beliefs going beyond mere coherency, then there are some specific opinions that a rational baby demigod must have. Put that way, the notion of any such basis seems to me quite counterintuitive."