James M. Joyce
This article is concerned with Bayesian epistemology. Bayesianism claims to provide a unified theory of epistemic and practical rationality based on the principle of mathematical expectation. In its epistemic guise, it requires believers to obey the laws of probability. In its practical guise, it asks agents to maximize their subjective expected utility. This article explains the five pillars of Bayesian epistemology, each of which claims and evaluates some of the justifications that have been offered for them. It also addresses some common objections to Bayesianism, in particular the “problem of old evidence” and the complaint that the view degenerates into an untenable subjectivism. It closes by painting a picture of Bayesianism as an “internalist” theory of reasons for action and belief that can be fruitfully augmented with “externalist” principles of practical and epistemic rationality.
This article finds it characteristic of orthodox Bayesians to hold that for each person and each hypothesis it comprehends, there is a precise degree of confidence that person has in the truth of that proposition, and that no person can be counted as rational unless the degree of confidence assignment it thus harbors satisfies the axioms of the probability calculus. In focusing exclusively on degrees of confidence, the Bayesian approach tells nothing about the epistemic status of the doxastic states epistemologists have traditionally been concerned about—categorical beliefs. The purpose of this article is twofold. First, it aims to show that, as powerful as many of such criticisms are against orthodox Bayesianism, there is a credible kind of Bayesianism. Second, it aims to show how this Bayesianism finds a foundation in considerations concerning rational preference.
This article focuses on naturalism. It makes one terminological distinction: between methodological naturalism and ontological naturalism. The methodological naturalist assumes there is a fairly definite set of rules, maxims, or prescriptions at work in the “natural” sciences, such as physics, chemistry, and molecular biology, this constituting “scientific method.” There is no algorithm which tells one in all cases how to apply this method; nonetheless, there is a body of workers—the scientific community—who generally agree on whether the method is applied correctly or not. Whatever the method is, exactly—such virtues as simplicity, elegance, familiarity, scope, and fecundity appear in many accounts—it centrally involves an appeal to observation and experiment. Correct applications of the method have enormously increased our knowledge, understanding, and control of the world around us to an extent which would scarcely be imaginable to generations living prior to the age of modern science.
Michael D. Resnik
This article focuses on Quine's positive views and their bearing on the philosophy of mathematics. It begins with his views concerning the relationship between scientific theories and experiential evidence (his holism), and relate these to his views on the evidence for the existence of objects (his criterion of ontological commitment, his naturalism, and his indispensability arguments). This sets the stage for discussing his theories concerning the genesis of our beliefs about objects (his postulationalism) and the nature of reference to objects (his ontological relativity). Quine's writings usually concerned theories and their objects generally, but they contain a powerful and systematic philosophy of mathematics, and the article aims to bring this into focus.
This article on rationality and game theory deals with the modeling of interaction between decision makers. Game theory aims to understand situations in which decision makers interact. Chess is an example of such interaction, as are firms competing for business, politicians competing for votes, jury members deciding on a verdict, animals fighting over prey, bidders competing in auctions, threats and punishments in long-term relationships, and so on. What all these situations have in common is that the outcome of the interaction depends on what the parties jointly do. Rationality assumptions and equilibrium play are the basic ingredients of game theory. The main focus of this article is on the relationship between rationality assumptions and equilibrium play.
This article plans to sketch the outlines of the Quinean point of departure, then to describe how Burgess and this article differ from this, and from each other, especially on logic and mathematics. Though this discussion touches on the work of only these three among the many recent “naturalists,” the moral of the story must be that “naturalism,” even restricted to its Quinean and post-Quinean incarnations, is a more complex position, with more subtle variants, than is sometimes supposed.