Online research in philosophy

In his ‘Causation as Influence’,1 David Lewis proposed a counterfactual theory of cause which was designed to improve on his previous account.2 Here I offer counter-examples to this new account, involving early preemption and late preemption, and a revised account, which is no longer an influence theory, that handles those counter-examples.

Cases of overdetermination or preemption continue to play an important role in the debate about the proper interpretation of causal claims of the form "C was a cause of E". I argue that the best treatment of preemption cases is given by Mackie's venerable INUS account of causal claims. The Mackie account suffers, however, from problems of its own. Inspired by its ability to handle preemption, I propose a dramatic revision to the Mackie account – one that Mackie himself would certainly have rejected – to solve these difficulties. The result is, I contend, a very attractive account of singular causal claims.

We investigate the discrete (finite) case of the Popper–Renyi theory of conditional probability, introducing discrete conditional probabilistic models for knowledge and conditional belief, and comparing them with the more standard plausibility models. We also consider a related notion, that of safe belief, which is a weak (non-negatively introspective) type of “knowledge”. We develop a probabilistic version of this concept (“degree of safety”) and we analyze its role in games. We completely axiomatize the logic of conditional belief, knowledge and safe belief over conditional probabilistic models. We develop a theory of probabilistic dynamic belief revision, introducing probabilistic “action models” and proposing a notion of probabilistic update product, that comes together with appropriate reduction laws.

In traditional Frankfurt cases some conditions that make an outcome unavoidable fail to bring about that outcome. These are cases of causal preemption. I defend this interpretation of traditional Frankfurt cases, and its application to free will, against a dilemma raised by various libertarians. But I go on to argue that Frankfurt cases involving gen- uine (symmetric) causal overdetermination are even more effective at achieving the compatibilist’s purposes. Such cases avoid the “flicker of freedom” debate and better display the central disagreement with regard to the Principle of Alternate Possibilities.

We must rethink our assessment of Hume’s theory of probabilistic inference. Hume scholars have traditionally dismissed his naturalistic explanation of how we make inferences under conditions of uncertainty; however, psychological experiments and computer models from cognitive science provide substantial support for Hume’s account. Hume’s theory of probabilistic inference is far from obsolete or outdated; on the contrary, it stands at the leading edge of our contemporary science of the mind.

In this paper I start by briefly presenting an analysis of token cause and of token causal relevance that I developed elsewhere, and then apply it to the famous thirsty traveler riddle. One general outcome of the analysis of causal relevance employed here is that in preemption cases (early or late) the preempted cause is not a cause since it is causally irrelevant to the effect. I consider several variations of the thirsty traveler riddle. In the first variation the first enemy emptied the canteen and the second enemy threw it away. On this variation, the act of neither enemy comes out, on the analysis employed here, as causally relevant to, and thus not as a cause of, the fact that the traveler died, but the conjunction of the two acts is a cause of it. This version is a case of mutual preemption. I argue that it has the same structure as the voting paradox, which thus has an analogous solution. In the standard version, in which the first enemy added poison to the water in the traveler's canteen, the act of the second enemy (who threw the canteen away) comes out, on the analysis used here, as causally relevant to and as a cause of the fact that the traveler died, but the act of the first enemy comes out as neither. I also make a comparison with Lewis' accounts, and discuss alternative treatments of the puzzle such as those of Hart and Honore and of Gavison, Margalit, and Ullmann-Margalit.

I explore the problem of ``probabilistic causal preemption'' in the context of a``propensity trajectory'' theory of singular probabilistic causation. This involvesa particular conception of events and a substantive thesis concerning events soconceived.

Counter factual theories of Causation have had problems with cases of probabilistic causation and preemption. I put forward a counterfactual theory that seems to deal with these problematic cases and also has the virtue of providing an account of the alleged asymmetry between hasteners and delayers: the former usually being counted as causes, the latter not. I go on to consider a new type of problem case that has not received so much attention in the literature, those I dub catalysts and anti-catalysts, and show how my account needs to be adjusted to deliver the right verdicts in these cases. The net result is a particular conception of a cause that I try to spell out in the closing section of the paper. In that section, I also briefly discuss causal asymmetry and the purpose behind providing a counterfactual theory of causation.

In response to counterexamples involving late preemption, David Lewis (1986) revised his original (1973) counterfactual analysis of causation to include the notion of quasi-dependence. Jonardon Ganeri, Paul Noordhof and Murali Ramachandran (1998) argue that their ‘PCA*-analysis’ of causation solves the problem of late preemption and is superior to Lewis’s analysis. I show that neither quasi-dependence nor the PCA*-analysis solves the problem of late preemption.