In Defense of IP: A Response to Pettigrew[Note 1. I owe a very special thanks to Richard Pettigrew ...]

Back in 2008 I argued that Lewis misstated his own Principal Principle when he formalized it. His verbal statement said simply that if one knows what the chance of e is then one should (barring magical information from the future) adopt it as one’s credence. There was nothing in that statement about conditionalization on the truth of ur-chance functions. And I pointed out that ur-chance functions of the kind one finds in physics do not come with assignments of probability to propositions asserting the truth of ur-chance functions. Nor does anything in their epistemic use require that they be extended to deliver such assignments. Then I introduced IP as a natural generalization of PP that said that if you don’t know what the correct ur-chance function is, you obtain your credences from a weighted mixture of the chances assigned by epistemically possible ur-chance functions.2 My response to Pettigrew’s criticism of my proposal can be quick, since he has acknowledged that the problems that he adduces for IP don’t arise unless ur-chance functions are extended to assign probabilities to propositions of the form [Cch]. I will give a brief defense of the epistemology implicit in IP, motivate the restriction against extending ur-chance functions, and point out a mistake in his argument that a reductionist about chance must reject the restriction. First a bit of terminology: