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 examines epistemological issues that have logical aspects. It considers the epistemology of proof with the help of the knower's paradox. One solution to this paradox is that knowledge is not closed under deduction. This article reviews the broader history of this maneuver along with the relevant-alternatives model of knowledge. This model assumes that “know” is an absolute term like “flat.” This article also argues that epistemic absolute terms differ from extensional absolute terms by virtue of their sensitivity to the completeness of the alternatives. This asymmetry undermines recent claims that there is a structural parallel between the supervaluational and epistemicist theories of vagueness. Finally, this article suggests that the ability of logical demonstration to produce knowledge has been overestimated.
The first part of this article shows some main points of Brouwer's mathematics and the philosophical doctrines that anchor it. It points out that Brouwer's special conception of human consciousness spawns his positive ontological and epistemic doctrines as well as his negative program. The second part focuses on intuitionistic logic: once again a brief picture of the technical field will precede the philosophical analyses—this time those of Heyting and Dummett—of formal intuitionistic logic and its role in intuitionism. The third part, however, aims to show that matters aren't (or needn't be) so bleak. It suggests, in particular, that putting all this in historical perspective will show intuitionism as technically less quixotic and philosophically more unified than it had initially seemed.
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.
This article provides a panoramic view of paradoxes of theoretical and practical rationality. These puzzles are organized as apparent counterexamples to attractive principles such as the principle of charity, the transitivity of preferences, and the principle that one should maximize expected utility. This article gives an account of the following paradoxes: fearing fictions, the surprise test paradox, Pascal's Wager, Pollock's Ever Better wine, Newcomb's problem, the iterated Prisoners' Dilemma, Kavka's paradoxes of deterrence, backward inductions, the bottle imp, the preface paradox, Moore's problem, Buridan's ass, Condorcet's paradox of cyclical majorities, the St. Petersburg paradox, weakness of will, the Ellsberg paradox, Allais's paradox, and Peter Cave's puzzle of self-fulfilling beliefs.
This article examines the role of picturability in mathematical demonstration in the seventeenth and eighteenth centuries and draws attention to the general question of the role that picturability places in cognitive grasp. It suggests that mathematical demonstration is particularly applicable in cognitive grasp it allows the problematic to be identified with some precision. It also discusses infinitesimal analysis and the question of direct proof and evaluates the role of picturability in the analysis of human cognitive capacities.
The state of modern mathematical practice called for a modern philosopher of mathematics to answer two interrelated questions. Given that mathematical ontology includes quantifiable empirical objects, how to explain the paradigmatic features of pure mathematical reasoning: universality, certainty, necessity. And, without giving up the special status of pure mathematical reasoning, how to explain the ability of pure mathematics to come into contact with and describe the empirically accessible natural world. The first question comes to a demand for apriority: a viable philosophical account of early modern mathematics must explain the apriority of mathematical reasoning. The second question comes to a demand for applicability: a viable philosophical account of early modern mathematics must explain the applicability of mathematical reasoning. This article begins by providing a brief account of a relevant aspect of early modern mathematical practice, in order to situate philosophers in their historical and mathematical context.
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.