Online research in philosophy

Nicholas Rescher claims that rational decision theory “may leave us in the lurch”, because there are two apparently acceptable ways of applying “the standard machinery of expected-value analysis” to his Dr. Psycho paradox which recommend contradictory actions. He detects a similar contradiction in Newcomb’s problem. We consider his claims from the point of view of both Bayesian decision theory and causal decision theory. In Dr. Psycho and in Newcomb’s Problem, Rescher has used premisses about probabilities which he assumes to be independent. From the former point of view, we show that the probability premisses are not independent but inconsistent, and their inconsistency is provable within probability theory alone. From the latter point of view, we show that their consistency can be saved, but then the contradictory recommendations evaporate. Consequently, whether one subscribes to evidential or causal decision theory, rational decision theory is not in any way vitiated by Rescher’s arguments.

This essay examines a conflict between God's omnipotence and His omniscience. I discuss our intuitions regarding omnipotence and omniscience and describe a method by which we can decide whether a being is omnipotent. I consider the most promising versions of omnipotence and argue that they produce a genuine conflict with omniscience. Finally, I suggest that we can take the example of omniscience and generalize it to several of God's essential properties and thereby reveal incompatibilities that result even from sophisticated conceptions of divine attributes. (Published Online August 11 2004).

A recent slew of arguments, if sound, would demonstrate that realism about value involves a kind of paradox-I call it the BAD paradox.More precisely, they show that if there are genuine propositions about the good, then one could maintain harmony between one’s desires and one’s beliefs about the good only on pain of violating fundamental principles of decision theory. I show. however, the BAD paradox turns out to be a version of Newcomb’s problem, and that the cognitivist about value can avoid the paradox by embracing casual decision theory.

In order to refute the widely held belief that the game known as ‘Newcomb's paradox’ is physically nonsensical and impossible to imagine (e.g. because it involves backward causation), I tell a story in which the game is realized in a classical, deterministic universe in a physically plausible way. The predictor is a collection of beings which are by many orders of magnitude smaller than the player and which can, with their exquisite measurement techniques, observe the particles in the player's body so accurately that they can predict his choice (in much the same way as we can predict the motion of celestial bodies). I argue that the player, by choosing whether to take only one box or both boxes, influences whether or not, in the past, the predictor put a million pounds into the second box. Yet, I establish that no causal paradox can arise in this set-up.

In their development of causal decision theory, Allan Gibbard and William Harper advocate a particular method for calculating the expected utility of an action, a method based upon the probabilities of certain counterfactuals. Gibbard and Harper then employ their method to support a two-box solution to Newcomb’s paradox. This paper argues against some of Gibbard and Harper’s key claims concerning the truth-values and probabilities of counterfactuals involved in expected utility calculations, thereby disputing their analysis of Newcomb’s Paradox. If we are right, then Gibbard and Harper’s method of calculating expected utility does not adequately represent rational choice.

Abstract In an engaging and ingenious paper, Irvine (1993) purports to show how the resolution of Braess? paradox can be applied to Newcomb's problem. To accomplish this end, Irvine forges three links. First, he couples Braess? paradox to the Cohen?Kelly queuing paradox. Second, he couples the Cohen?Kelly queuing paradox to the Prisoner's Dilemma (PD). Third, in accord with received literature, he couples the PD to Newcomb's problem itself. Claiming that the linked models are ?structurally identical?, he argues that Braess solves Newcomb's problem. This paper shows that Irvine's linkage depends on structural similarities?rather than identities?between and among the models. The elucidation of functional disanalogies illuminates structural dissimilarities which sever that linkage. I claim that the Cohen?Kelly queuing paradox cloaks a fine structure that decouples it from both Braess? paradox and the PD (Marinoff, 1996a). I further assert that the putative reduction of the PD to a Newcomb problem (e.g. Brams, 1975; Lewis, 1979) is seriously flawed. It follows that Braess? paradox does not solve Newcomb's problem via the foregoing and herein sundered chain. I conclude by substantiating a stronger claim, namely that Braess'paradox cannot solve Newcomb's problem at all.

Abstract Newcomb's problem is regularly described as a problem arising from equally defensible yet contradictory models of rationality. Braess? paradox is regularly described as nothing more than the existence of non?intuitive (but ultimately non?contradictory) equilibrium points within physical networks of various kinds. Yet it can be shown that Newcomb's problem is structurally identical to Braess? paradox. Both are instances of a well?known result in game theory, namely that equilibria of non?cooperative games are generally Pareto?inefficient. Newcomb's problem is simply a limiting case in which the number of players equals one. Braess? paradox is another limiting case in which the ?players? need not be assumed to be discrete individuals. The result is that Newcomb's problem is no more difficult to solve than (the easy to solve) Braess? paradox.