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If one flips an unbiased coin a million times, there are 21,000,000 series of possible heads/tails sequences, any one of which might be the sequence that obtains, and each of which is equally likely to obtain. So it seems (1) ‘If I had tossed a fair coin one million times, it might have landed heads every time’ is true. But as several authors have pointed out, (2) ‘If I had tossed a fair coin a million times, it wouldn’t have come up heads every time’ will be counted as true in everyday contexts. And according to David Lewis’ influential semantics for counterfactuals, (1) and (2) are contradictories. We have a puzzle. We must either (A) deny that (2) is true, (B) deny that (1) is true, or (C) deny that (1) and (2) are contradictories, thus rejecting Lewis’ semantics. In this paper I discuss and criticize the proposals of David Lewis and more recently J. Robert G. Williams which solve the puzzle by taking option (B). I argue that we should opt for either (A) or (C).

DOI: 10.1007/s11229-009-9656-z

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