Games such as the St. Petersburg game present serious problems for decision theory.1 The St. Petersburg game invokes an unbounded utility function to produce an infinite expectation for playing the game. The problem is usually presented as a clash between decision theory and intuition: most people are not prepared to pay a large finite sum to buy into this game, yet this is precisely what decision theory suggests we ought to do. But there is another problem associated with the St. (...) Petersburg game. The problem is that standard decision theory counsels us to be indifferent between any two actions that have infinite expected utility. So, for example, consider the decision problem of whether to play the St. Petersburg game or a game where every payoff is $1 higher. Let’s call this second game the Petrograd game (it’s the same as St. Petersburg but with a bit of twentieth century inflation). Standard decision theory is indifferent between these two options. Indeed, it might be argued that any intuition that the Petrograd game is better than the St. Petersburg game is a result of misguided and na¨ıve intuitions about infinity.2 But this argument against the intuition in question is misguided. The Petrograd game is clearly better than the St. Petersburg game. And what is more, there is no confusion about infinity involved in thinking this. When the series of coin tosses comes to an end (and it comes to an end with probability 1), no matter how many tails precede the first head, the payoff for the Petrograd game is one dollar higher than the St. Petersburg game. Whatever the outcome, you are better off playing the Petrograd game. Infinity has nothing to do with it. Indeed, a straightforward application of dominance reasoning backs up this line of reasoning.3 Standard decision theory. (shrink)

This book defends the view that any adequate account of rational decision making must take a decision maker's beliefs about causal relations into account. The early chapters of the book introduce the non-specialist to the rudiments of expected utility theory. The major technical advance offered by the book is a 'representation theorem' that shows that both causal decision theory and its main rival, Richard Jeffrey's logic of decision, are both instances of a more general conditional decision theory. The book solves (...) a long-standing problem for Jeffrey's theory by showing for the first time how to obtain a unique utility and probability representation for preferences and judgements of comparative likelihood. The book also contains a major new discussion of what it means to suppose that some event occurs or that some proposition is true. The most complete and robust defence of causal decision theory available. (shrink)

The eminent philosopher of science Carl G. Hempel, Stuart Professor of Philosophy at Princeton University and a Past President of the American Philosophical Association, has had a long and distinguished academic career in the course of which he has been professorial mentor to some of America's most distinguished philosophers. This volume gathers together twelve original papers by Hempel's students and associates into a volume intended to do homage to Hempel on the occasion of his 65th year in 1970. The papers (...) are grouped around the unifying topic of Hempel's own interests in logic and philosophy of science, the great majority dealing with issues on inductive logic and the theory of scientific explanatio- problems to which Hempel has devoted the bulk of his outstandingly fruitful efforts. With the approach of 'Peter' Hempel's 65th birthday, an editorial committee sprang into being by an uncannily spontaneous process to prepare to commemorate this event with an appropriate Festschrift. The editors were pleased to receive unfailingly prompt and efficient coopera tion on the part of all contributors. The responsibility of seeing the work through the press was assumed by Nicholas Rescher. The editors are grateful to all concerned for their collaboration. ALAN ROSS ANDERSON PAUL BENACERRAF ADOLF GRUNBAUM GERALD J. MASSEY NICHOLAS RESCHER RICHARD S. RUDNER TABLE OF CONTENTS PREFACE V PAUL OPPENHEIM: Reminiscences of Peter 1 w. v. QUINE: Natural Kinds 5 JAAKKO HINTIKKA: Inductive Independence and the Paradoxes of Confirmation 24 WESLEY c. (shrink)

"[This book] proposes new foundations for the Bayesian principle of rational action, and goes on to develop a new logic of desirability and probabtility."—Frederic Schick, _Journal of Philosophy_.

Reminiscences of Peter, by P. Oppenheim.--Natural kinds, by W. V. Quine.--Inductive independence and the paradoxes of confirmation, by J. Hintikka.--Partial entailment as a basis for inductive logic, by W. C. Salmon.--Are there non-deductive logics?, by W. Sellars.--Statistical explanation vs. statistical inference, by R. C. Jeffre--Newcomb's problem and two principles of choice, by R. Nozick.--The meaning of time, by A. Grünbaum.--Lawfulness as mind-dependent, by N. Rescher.--Events and their descriptions: some considerations, by J. Kim.--The individuation of events, by D. Davidson.--On properties, by (...) H. Putnam.--A method for avoiding the Curry paradox, by F. B. Fitch.--Publications (1934-1969) by Carl G. Hempel (p. [266]-270). (shrink)

We introduce a St. Petersburg-like game, which we call the ‘Pasadena game’, in which we toss a coin until it lands heads for the first time. Your pay-offs grow without bound, and alternate in sign (rewards alternate with penalties). The expectation of the game is a conditionally convergent series. As such, its terms can be rearranged to yield any sum whatsoever, including positive infinity and negative infinity. Thus, we can apparently make the game seem as desirable or undesirable as we (...) want, simply by reordering the pay-off table, yet the game remains unchanged throughout. Formally speaking, the expectation does not exist; but we contend that this presents a serious problem for decision theory, since it goes silent when we want it to speak. We argue that the Pasadena game is more paradoxical than the St. Petersburg game in several respects. We give a brief review of the relevant mathematics of infinite series. We then consider and rebut a number of replies to our paradox: that there is a privileged ordering to the expectation series; that decision theory should be restricted to finite state spaces; and that it should be restricted to bounded utility functions. We conclude that the paradox remains live. (shrink)

Pascal’s Wager is simply too good to be true—or better, too good to be sound. There must be something wrong with Pascal’s argument that decision-theoretic reasoning shows that one must (resolve to) believe in God, if one is rational. No surprise, then, that critics of the argument are easily found, or that they have attacked it on many fronts. For Pascal has given them no dearth of targets.

The Pasadena paradox presents a serious challenge for decision theory. The paradox arises from a game that has well-defined probabilities and utilities for each outcome, yet, apparently, does not have a well-defined expectation. In this paper, I argue that this paradox highlights a limitation of standard decision theory. This limitation can be (largely) overcome by embracing dominance reasoning and, in particular, by recognising that dominance reasoning can deliver the correct results in situations where standard decision theory fails. This, in turn, (...) pushes us towards pluralism about decision rules. (shrink)

This collection of papers in epistemic logic is oriented towards applications to game theory and individual decision theory. Most of these papers were presented at the inaugural conference of the LOFT (Logic for the Theory and Games and Decisions) conference series, which took place in 1994 in Marseille. Among the notions dealt with are those of common knowledge and common belief, infinite hierarchies of beliefs and belief spaces, logical omniscience, positive and negative introspection, backward induction and rationalizable equilibria in game (...) theory. (shrink)

This unique textbook--the first to offer balanced, comprehensive coverage of all major perspectives on the rational justification of religious belief--includes twenty-four key papers by some of the world's leading philosophers of religion. Arranged in six sections, each representing a major approach to religious epistemology, the book begins with papers by noted atheists, setting the stage for the main theistic responses--Wittgensteinian Fideism, Reformed epistemology, natural theology, prudential accounts of religious beliefs, and rational belief based in religious experience--in each case offering a (...) representative sample of papers by leading exponents, a critical paper, and a substantial bibliography. A comprehensive introductory essay and ample cross-references help students to contrast and evaluate the different approaches, while the overall arrangement encourages them to assess the full range of philosophical positions on the issue. Carefully selected to provide both a comprehensive overview of current work and a series of modern perspectives on many classic sources--Swinburne's detailed discussion of Hume's critique of the design argument, for example, as well as an entire section evaluating and extending Pascal's famous Wager--the essays also provide a uniquely readable survey that will be useful in a wide range of undergraduate and graduate courses in philosophy of religion and epistemology. (shrink)