Alan Hajek

Bayesianism tells a story about the epistemic trajectory of an ideally rational agent. The agent begins with a ‘prior’ probability function; thereafter, it conditionalizes on its evidence as it comes in. Consider, then, such an agent at the very beginning of its trajectory. It is ideally rational, but completely ignorant of which world is actual. Let us call this agent ‘superbaby’. We show that superbaby is committed to sincerely asserting propositions of the form [p and I am not justified in believing that p].

Probability and Statistics: 5 Questions is a collection of short interviews based on 5 questions presented to some of the most influential and prominent scholars in probability and statistics. We hear their views on the fields, aims, scopes, the future direction of research and how their work fits in these respects. Interviews with Nick Bingham, Luc Bovens, Terrence L. Fine, Haim Gaifman, Donald Gillies, James Hawthorne, Carl Hoefer, James M. Joyce, Joseph B. Kadane Isaac Levi, D.H. Mellor, Patrick Suppes, Jan von Plato, Carl Wagner, Sandy Zabell.

David Lewis introduced a new kind of reductio ad absurdum style of argument: while the claims, suitably formalized, do not lead to outright contradiction, he showed they are tenable only in trivial ways. Lewis proved what are known as triviality results against the claims. The claims are "Probabilities of conditionals are conditional probabilities." "Desires are beliefs about what is good." The author argues that the tenuous connections between the claims go considerably further still: the claims give rise to debates that display a remarkably parallel structure. He brings out their many similarities to illuminate both of them, and to point the way to some promising avenues for future research. He displays structural similarities between the fluctuating fortunes of Stalnaker's Thesis, and those of Desire‐as‐Belief. Lewis concludes telegraphically by saying that Desire by Necessity is "a form of anti‐Humeanism, sure enough, but not the right form of anti‐Humeanism"; and that's it.

Very roughly, the conditional construal of conditional probability is the hypothesis that the conditional probability P equals the probability of the conditional 'if A, then B'. My main purposes are to hone this rough statement down to various precise versions of the Hypothesis, as I call it, and to argue that virtually none of them is tenable. ;In S 1, I distinguish four versions of the Hypothesis. The subsequent four sections are largely an opinionated historical survey, tracing the motivations for and origins of the Hypothesis, and its fluctuating fortunes. By the end of S 5, the first version has been shown to be refuted, and the second version moribund. ;My own negative results against the Hypothesis begin in S 6. I first generalize Lewis' so-called 'second triviality result', adding insult to injury as far as the second version is concerned. S 7 refutes the third version of the Hypothesis, and casts serious doubt on the fourth, or so I argue. I then consider four ways in which the Hypothesis could be resurrected. In S 8, I refute the first of these ways, and strengthen some old results; and in S 9 I argue against the other three ways. ;In S 10, I contend that philosophers have been in the grip of a dogma: that conditional probability is to be univocally analyzed by the usual ratio formula. I offer a positive proposal, which I call 'the ambiguity thesis': so-called 'conditional probability' is ambiguous between the usual ratio formula, and the probability of a conditional. The demise of the Hypothesis shows that these two disambiguations cannot be identified