Glenn Ross

It is argued that an analysis of causation using counterfactual conditionals can be given. Causes and effects are considered to be propositional entities, and a semantics for counterfactuals employing possible worlds is presupposed. The analysis stems from an attempt to handle cases proving problematic for other counterfactual analyses. Preempted causes, which would have been causes had they not been preempted by causes, are distinguished from causes by requiring that a causal chain connecting cause and effect exist. The condition is strengthened to require that the causal chain still would have existed even had the preempted causes been false. Causal chains are analyzed as sequences of true propositions satisfying two conditions: any member after the first would not have been true had its immediate predecessor alone been false, and the truth of any member of the sequence is sufficient for the truth of any subsequent member. The analysis is weakened slightly to permit many causes to overdetermine an effect. The analysis is then amended to exclude certain noncausal connections. Though it is true that had Socrates not died, Xanthippe would not have become a widow, his dying did not cause her to become a widow. To yield this result, an analysis is offered of the relation that logically simple propositions bear to the more complex propositions that they make true. It is then proposed that the sets of simple propositions making the cause and effect true not entail the effect and the cause, respectively. Finally, an attempt is made to distinguish between cause and effect. It is argued that cases of backward causation are possible, and thus no analysis should require causes to be temporally prior to effects. It is proposed that only when there is symmetry with respect to the subjunctive conditions of the analysis should temporal considerations be employed to discriminate cause and effect

In this paper, I propose that one can have reason to choose a few tickets in a very large lottery and arbitrarily believe of them that they will lose. Such a view fits nicely within portions of Lehrer's theory of rational acceptance. Nonetheless, the reasonability of believing a lottery ticket will lose should not be taken to constitute the kind of justification required in an analysis of knowledge. Moreover, one should not accept what one takes to have a low chance of being true. Accordingly, one should take care not to believe of too many tickets that they are to lose. Finally, while arbitrariness is no absolute barrier to epistemic reasonability, one may not be able to believe that one's lottery ticket will lose if one cannot regard oneself as knowing it will lose