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A Lottery Paradox for Counterfactuals Without Agglomeration



We will present a new lottery-style paradox on counterfactuals and chance. The upshot will be: combining natural assumptions on (i) the truth values of ordinary counterfactuals, (ii) the conditional chances of possible but non-actual events, (iii) the manner in which (i) and (ii) relate to each other, and (iv) a fragment of the logic of counterfactuals leads to disaster. In contrast with the usual lottery-style paradoxes, logical closure under conjunction—that is, in this case, the rule of Agglomeration of (consequents of) counterfactuals—will not play a role in the derivation and will not be entailed by our premises either. We will sketch four obvious but problematic ways out of the dilemma, and we will end up with a new resolution strategy that is non-obvious but (as we hope) less problematic: contextualism about what counts as a proposition. This proposal will not just save us from the paradox, it will also save each premise in at least some context, and it will be motivated by independent considerations from measure theory and probability theory.