Causalists and Evidentialists can agree about the right course of action in an (apparent) Newcomb problem, if the causal facts are not as initially they seem. If declining $1,000 causes the Predictor to have placed $1m in the opaque box, CDT agrees with EDT that one-boxing is rational. This creates a difficulty for Causalists. We explain the problem with reference to Dummett's work on backward causation and Lewis's on chance and crystal balls. We show that the possibility that the causal (...) facts might be properly judged to be non-standard in Newcomb problems leads to a dilemma for Causalism. One horn embraces a subjectivist understanding of causation, in a sense analogous to Lewis's own subjectivist conception of objective chance. In this case the analogy with chance reveals a terminological choice point, such that either (i) CDT is completely reconciled with EDT, or (ii) EDT takes precedence in the cases in which the two theories give different recommendations. The other horn of the dilemma rejects subjectivism, but now the analogy with chance suggests that it is simply mysterious why causation so construed should constrain rational action. (shrink)

Newcomb's problem supposedly involves your choosing one or else two boxes in circumstances in which a predictor has made a prediction of how many boxes you will choose. We argue that the circumstances which allegedly define Newcomb's problem generate a previously unnoticed regress which shows that Newcomb's problem is insoluble because it is ill-formed. Those who favor, as we do, a ``no-box'' reply to Newcomb's problem typically claim either that the problem's solution is underdetermined or else that it is overdetermined. (...) We are no-boxers of the first kind, but the underdetermination we identify is more radical than any previously identified: it blocks the very set-up of the problem and not just potential solutions to the problem once it has been set up. The defect is subtle, but it cripples every genuine version of the problem, regardless of variations in such things as the predictor's degree of reliability, the basis on which the prediction is made, or the amount of money in each box. The regress shows that, surprisingly enough, no one can understand Newcomb's problem, and so no one can possibly solve it. (shrink)

I present a game-theoretic way to understand the situation describing Newcomb’s Problem (NP) which helps to explain the intuition of both one-boxers and two-boxers. David Lewis has shown that the NP may be modelled as a Prisoners Dilemma game (PD) in which ‘cooperating’ corresponds to ‘taking one box’. Adopting relevant results from game theory, this means that one should take just one box if the NP is repeated an indefinite number of times, but both boxes if it is a one-shot (...) game. Causal decision theorists thus give the right answer for the one-shot situation, whereas the one-boxers’ solution applies to the indefinitely iterated case. Because Nozick’s set-up of the NP is ambiguous between a one-shot and a repeated game, both of these solutions may appear plausible – depending on whether one conceives of the situation as one-off or repeated. If the players’ aim is to maximize their payoffs, the symmetric structure of the PD implies that the two players will behave alike both when the game is one-shot and when it is played repeatedly. Therefore neither the observed outcome of both players selecting the same strategy (in the PD) nor, correspondingly, the predictor’s accurate prediction of this outcome (in the NP) is at all surprising. There is no need for a supernatural predictor to explain the NP phenomena. (shrink)

Proponents of causal decision theories argue that classical Bayesian decision theory (BDT) gives the wrong advice in certain types of cases, of which the clearest and commonest are the medical Newcomb problems. I defend BDT, invoking a familiar principle of statistical inference to show that in such cases a free agent cannot take the contemplated action to be probabilistically relevant to its causes (so that BDT gives the right answer). I argue that my defence does better than those of Ellery (...) Eells and Richard Jeffrey; and that it applies, where necessary, to other types of Newcomb problem. (shrink)

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. (shrink)

Newcomb's Paradox thus serves as an illustrative vindication of the compatibility of divine foreknowledge and human freedom. A proper understanding of the counterfactual conditionals involved enables us to see that the pastness of God's knowledge serves neither to make God's beliefs counterfactually closed nor to rob us of genuine freedom. It is evident that our decisions determine God's past beliefs about those decisions and do so without invoking an objectionable backward causation. It is also clear that in the context of (...) foreknowledge, backtracking counterfactuals are entirely appropriate and that no alteration of the past occurs. With the justification of the one box strategy, the death of theological fatalism seems ensured. *** DIRECT SUPPORT *** A0985044 00003. (shrink)

‘Ifs’ come washed or unwashed. The washed ifs are embedded in precise theories: the constantly strict implication of deductive inference, the variably strict implication of ‘nearness’ conditionals, and statements of conditional probability. By a nearness conditional I mean the common part of Stalnaker's and D. Lewis's theory of counterfactual conditionals, which depends on a notion that possible worlds are more or less near to each other, as a measure of their over-all similarity to each other.

Examples involving common causes — most prominently, examples involving genetically influenced choices — are analytically equivalent not to standard Newcomb Problems — in which the Predictor genuinely predicts the agent's decision — but to non-standard Newcomb Problems — in which the Predictor guarantees the truth of her predictions by interfering with the agent's decision to make the agent choose as it was predicted she would. When properly qualified, causal and epistemic decision theories diverge only on standard — not on non-standard (...) — Newcomb Problems, and thus not on examples involving common causes. (shrink)

‘Ifs’ come washed or unwashed. The washed ifs are embedded in precise theories: the constantly strict implication of deductive inference, the variably strict implication of ‘nearness’ conditionals, and statements of conditional probability. By a nearness conditional I mean the common part of Stalnaker's and D. Lewis's theory of counterfactual conditionals, which depends on a notion that possible worlds are more or less near to each other, as a measure of their over-all similarity to each other.