[1] You have a crystal ball. Unfortunately, it’s defective. Rather than predicting the future, it gives you the chances of future events. Is it then of any use? It certainly seems so. You may not know for sure whether the stock market will crash next week; but if you know for sure that it has an 80% chance of crashing, then you should be 80% confident that it will—and you should plan accordingly. More generally, given that the chance of a (...) proposition A is x%, your conditional credence in A should be x%. This is a chance-credence principle: a principle relating chance (objective probability) with credence (subjective probability, degree of belief). Let’s call it the Minimal Principle (MP). (shrink)

You are, I am sure, just as aware as I am that the operational nodes of a complex problem, the points at which it can be split open to yield nuggets of new insight or achieve lasting advances, often lie in tediously technical details perhaps incomprehensible to all but specialists in the matter and anyways totally lacking in the romance and easy excitement which attract the topic's dilettantes. I would like you to hold fast to this appreciation, for the concerns (...) I shall raise here are technical indeed. They are, however,seminaltechnicalities which, as we seek to fathom them, should fundamentally reshape our comprehension of the logic of confirmation, causal connectedness, and the foundations of statistical inference. In brief, it will be seen that certain powerful everyday intuitions concerning which propositions are confirmationally irrelevant to which others are exceedingly difficult to justify. (shrink)

David Lewis (1980) proposed the Principal Principle (PP) and a “reformulation” which later on he called ‘OP’(Old Principle). Reacting to his belief that these principles run into trouble, Lewis (1994) concluded that they should be replaced with the New Principle (NP). This conclusion left Lewis uneasy, because he thought that an inverse form of NP is “quite messy”, whereas an inverse form of OP, namely the simple and intuitive PP, is “the key to our concept of chance”. I argue that, (...) even if OP should be discarded, PP need not be. Moreover, far from being messy, an inverse form of NP is a simple and intuitive Conditional Principle (CP). Finally, both PP and CP are special cases of a General Principle (GP); it follows that so are PP and NP, which are thus compatible rather than competing. (shrink)