Online research in philosophy

Timothy Williamson's epistemology leads to a fairly radical version of scepticism. According to him, all knowledge is evidence. It follows that if S knows p, the evidential probability for S that p is 1. I explain Williamson's infallibilist account of perceptual knowledge, contrasting it with Peter Klein's, and argue that Klein's account leads to a certain problem which Williamson's can avoid. Williamson can allow that perceptual knowledge is possible and that all knowledge is evidence, while at the same time avoiding Klein's problem. But while Williamson can allow that we know some things through experience, there are very many things he must say we cannot know. Given just how very many these are, he should be considered a sceptic.

This paper is a comparison of how first-order Kyburgian Evidential Probability (EP), second-order EP, and objective Bayesian epistemology compare as to the KLM system-P rules for consequence relations and the monotonic / non-monotonic divide.

We provide a solution to the well-known “Shooting-Room” paradox, developed by John Leslie in connection with his Doomsday Argument. In the “Shooting-Room” paradox, the death of an individual is contingent upon an event that has a 1/36 chance of occurring, yet the relative frequency of death in the relevant population is 0.9. There are two intuitively plausible arguments, one concluding that the appropriate subjective probability of death is 1/36, the other that this probability is 0.9. How are these two values to be reconciled? We show that only the first argument is valid for a standard, countably additive probability distribution. However, both lines of reasoning are legitimate if probabilities are non-standard. The subjective probability of death rises from 1/36 to 0.9 by conditionalizing on an event that is not measurable, or whose probability is zero. Thus we can sometimes meaningfully ascribe conditional probabilities even when the event conditionalized upon is not of positive finite (or even infinitesimal) measure.

In this chapter we draw connections between two seemingly opposing approaches to probability and statistics: evidential probability on the one hand and objective Bayesian epistemology on the other.

Epistemological probability is the kind of probability relative to a body of evidence. Many philosophers, including Henry Kyburg and Roderick Chisholm, hold that all epistemological probabilities reflect a relation between an evidential body of propositions and other propositions. But this article argues that some epistemological probabilities for empirical propositions must be relative to non-propositional evidence, specifically the contents of non-propositional perceptual states. In doing so, the article distinguishes between internalism and externalism regarding epistemological probability, and argues for a version of awareness internalism. The article draws three main concluding lessons. First, epistemological probability is not to be identified with the sort of objective, experience-independent probability that is familiar from statistical and propensity interpretations of probability. Second, it is doubtful that epistemological probability is measurable, in any useful way, by real numbers, even if it admits of comparative assessments. Third, contrary to the familiar claim of C. I. Lewis, epistemological probability should not be viewed as requiring a basis of certainty.

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..

“Probability logic” might seem like an oxymoron. Logic traditionally concerns matters immutable, necessary and certain, while probability concerns the uncertain, the random, the capricious. Yet our subject has a distinguished pedigree. Ramsey begins his classic “Truth and Probability” [44] with the words: “In this essay the Theory of Probability is taken as a branch of logic...”. De Finetti [7] speaks of “the logic of the probable”. And more recently, Jeffrey [25] regards probabilities as estimates of truth values, and thus probability theory as a natural outgrowth of two-valued logic—what he calls “probability logic”. However we put the point, probability theory and logic are clearly intimately related. This chapter explores some of the multifarious connections between probability and logic, and focuses on various philosophical issues in the foundations of probability theory. Our survey begins in §2 with the probability calculus, what Adams [1, p. 34] calls “pure probability logic”. As we will see, there is a sense in which the axiomatization of probability presupposes deductive logic. Moreover, some authors see probability theory as the proper framework for inductive logic—a formal apparatus for codifying the degree of..

According to a standard account of evidence, one piece of information is stronger evidence for an hypothesis than is another iff the probability of the hypothesis on the one is greater than it is on the other. This condition, I argue, is neither necessary nor sufficient because various factors can strengthen the evidence for an hypothesis without increasing (and even decreasing) its probability. Contrary to what probabilists claim, I show that this obtains even if a probability function can take these evidential factors into account in ways they suggest and yield a unique probability value. Nor will the problem be solved by appealing to second-order probabilities.

This is an introduction to a collected volume. It distinguishes between evidential, statistical, and physical probability, and between objective and subjective understandings of evidential probability, in the use of Bayes’s theorem. If Bayes’s theorem is to be used to assess an objective evidential probability, a priori criteria--mainly the criterion of simplicity--are required to determine prior probability. The five main contributors to the volume discuss the use of Bayes’s theorem to assess the evidential probability of scientific theories, statistical hypotheses, criminal guilt, and miracles; and also its value for assessing physical probability.