In Bayesian epistemology, the problem of the priors is this: How should we set our credences (or degrees of belief) in the absence of evidence? That is, how should we set our prior or initial credences, the credences with which we begin our credal life? David Lewis liked to call an agent at the beginning of her credal journey a superbaby. The problem of the priors asks for the norms that govern these superbabies. -/- The Principle of Indifference gives a (...) very restrictive answer. It demands that such an agent divide her credences equally over all possibilities. That is, according to the Principle of Indifference, only one initial credence function is permissible, namely, the uniform distribution. In this paper, we offer a novel argument for the Principle of Indifference. I call it the Argument from Accuracy. (shrink)

The idea of a probabilistic logic of inductive inference based on some form of the principle of indifference has always retained a powerful appeal. However, up to now all modifications of the principle failed. In this paper, a new formulation of such a principle is provided that avoids generating paradoxes and inconsistencies. Because of these results, the thesis that probabilities cannot be logical quantities, determined in an objective way through some form of the principle of indifference, is no longer supportable. (...) Later, the paper investigates some implications of the new principle of indifference. To conclude, a re-examination of the foundations of the so-called objective Bayesian inference is called for. (shrink)

the symmetry of our evidential situation. If our confidence is best modeled by a standard probability function this means that we are to distribute our subjective probability or credence sharply and evenly over possibilities among which our evidence does not discriminate. Once thought to be the central principle of probabilistic reasoning by great..

A central problem facing a probabilistic approach to the problem of induction is the difficulty of sufficiently constraining prior probabilities so as to yield the conclusion that induction is cogent. The Principle of Indifference, according to which alternatives are equiprobable when one has no grounds for preferring one over another, represents one way of addressing this problem; however, the Principle faces the well-known problem that multiple interpretations of it are possible, leading to incompatible conclusions. I propose a partial solution to (...) the latter problem, drawing on the notion of explanatory priority. The resulting synthesis of Bayesian and inference-to-best-explanation approaches affords a principled defense of prior probability distributions that support induction. (shrink)

The idea of a probabilistic logic of inductive inference based on some form of the principle of indifference has always retained a powerful appeal. However, up to now all modifications of the principle failed. In this paper, a new formulation of such a principle is provided that avoids generating paradoxes and inconsistencies. Because of these results, the thesis that probabilities cannot be logical quantities, determined in an objective way through some form of the principle of indifference, is no longer supportable. (...) Later, the paper investigates some implications of the new principle of indifference. To conclude, a re-examination of the foundations of the so-called objective Bayesian inference is called for. (shrink)

In a recent article, Adam Elga outlines a strategy for “Defeating Dr Evil with Self-Locating Belief”. The strategy relies on an indifference principle that is not up to the task. In general, there are two things to dislike about indifference principles: adopting one normally means confusing risk for uncertainty, and they tend to lead to incoherent views in some ‘paradoxical’ situations. I argue that both kinds of objection can be levelled against Elga’s indifference principle. There are also some difficulties with (...) the concept of evidence that Elga uses, and these create further difficulties for the principle. (shrink)

Dr. Evil learns that a duplicate of Dr. Evil has been created. Upon learning this, how seriously should he take the hypothesis that he himself is that duplicate? I answer: very seriously. I defend a principle of indifference for self-locating belief which entails that after Dr. Evil learns that a duplicate has been created, he ought to have exactly the same degree of belief that he is Dr. Evil as that he is the duplicate. More generally, the principle shows that (...) there is a sharp distinction between ordinary skeptical hypotheses, and self-locating skeptical hypotheses. (shrink)

In addition to being uncertain about what the world is like, one can also be uncertain about one’s own spatial or temporal location in the world. My aim is to pose a problem arising from the interaction between these two sorts of uncertainty, solve the problem, and draw two lessons from the solution.

This paper justifies the inference of probabilities from symmetries. I supply some examples of important and correct inferences of this variety. Two explanations of such inferences -- an explanation based on the Principle of Indifference and a proposal due to Poincaré and Reichenbach -- are considered and rejected. I conclude with my own account, in which the inferences in question are shown to be warranted a posteriori, provided that they are based on symmetries in the mechanisms of chance setups.

I hear the patter of little feet around the house, I expect Bruce. What I expect is a cat, a particular cat. If I heard such a patter in another house, I might expect a cat but no particular cat. What I expect then seems to be a Meinongian incomplete cat. I expect winter, expect stormy weather, expect to shovel snow, expect fatigue---a season, a phenomenon, an activity, a state. I expect that someday mankind will inhabit at least five planets. (...) This time what I expect is a state of affairs. If we let surface grammar be our guide, the objects of expectation seem quite a miscellany. The same goes for belief, since expectation is one kind of belief. The same goes for desire: I could want Bruce, want a cat but no particular cat, want winter, want stormy weather, want to shovel snow, want fatigue, or want that someday mankind will inhabit at least five planets. The same goes for other attitudes to the extent that they consist partly of beliefs or desires or lacks thereof. But the seeming diversity of objects might be an illusion. Perhaps the objects of attitudes are uniform in category, and it is our ways of speaking elliptically about these uniform objects that are diverse. That indeed is our consensus. We mostly think that the attitudes uniformly have propositions as their objects. That is why we speak habitually of "propositional attitudes.". (shrink)

I argue that a particular restricted version of the Principle of Indiference is a consistent, indispensible tool for guiding our probabilistic judgements.

the symmetry of our evidential situation. If our confidence is best modeled by a standard probability function this means that we are to distribute our subjective probability or credence sharply and evenly over possibilities among which our evidence does not discriminate. Once thought to be the central principle of probabilistic reasoning by great..

This paper examines the debate between permissive and impermissive forms of Bayesianism. It briefly discusses some considerations that might be offered by both sides of the debate, and then replies to some new arguments in favor of impermissivism offered by Roger White. First, it argues that White’s (Oxford studies in epistemology, vol 3. Oxford University Press, Oxford, pp 161–186, 2010) defense of Indifference Principles is unsuccessful. Second, it contends that White’s (Philos Perspect 19:445–459, 2005) arguments against permissive views do not (...) succeed. (shrink)

The epistemic probability of A given B is the degree to which B evidentially supports A, or makes A plausible. This paper is a first step in answering the question of what determines the values of epistemic probabilities. I break this question into two parts: the structural question and the substantive question. Just as an object’s weight is determined by its mass and gravitational acceleration, some probabilities are determined by other, more basic ones. The structural question asks what probabilities are (...) not determined in this way—these are the basic probabilities which determine values for all other probabilities. The substantive question asks how the values of these basic probabilities are determined. I defend an answer to the structural question on which basic probabilities are the probabilities of atomic propositions conditional on potential direct explanations. I defend this against the view, implicit in orthodox mathematical treatments of probability, that basic probabilities are the unconditional probabilities of complete worlds. I then apply my answer to the structural question to clear up common confusions in expositions of Bayesianism and shed light on the “problem of the priors.”. (shrink)

The idea of a probabilistic logic of inductive inference based on some form of the principle of indifference has always retained a powerful appeal. However, up to now all modifications of the principle failed. In this paper, a new formulation of such a principle is provided that avoids generating paradoxes and inconsistencies. Because of these results, the thesis that probabilities cannot be logical quantities, determined in an objective way through some form of the principle of indifference, is no longer supportable. (...) Later, the paper investigates some implications of the new principle of indifference. To conclude, a re-examination of the foundations of the so-called objective Bayesian inference is called for. (shrink)