Ordering semantics and premise semantics for counterfactuals
David Lewis · Cambridge University Press eBooks · 1997
COUNTERFACTUALS AND FACTUAL BACKGROUND Consider the counterfactual conditional ‘If I were to look in my pocket for a penny, I would find one’. Is it true? That depends on the factual background against which it is evaluated. Perhaps I have a penny in my pocket. Its presence is then part of the factual background. So among the possible worlds where I look for a penny, those where there is no penny may be ignored as gratuitously unlike the actual world. (So may those where there is only a hidden penny; in fact my pocket is uncluttered and affords no hiding place. So may those where I'm unable to find a penny that's there and unhidden.) Factual background carries over into the hypothetical situation, so long as there is nothing to keep it out. So in this case the counterfactual is true. But perhaps I have no penny. In that case, the absence of a penny is part of the factual background that carries over into the hypothetical situation, so the counterfactual is false. Any formal analysis giving truth conditions for counterfactuals must somehow take account of the impact of factual background. Two very natural devices to serve that purpose are orderings of worlds and sets of premises. Ordering semantics for counterfactuals is presented, in various versions, in Stalnaker [8], Lewis [5], and Pollock [7]. (In this paper, I shall not discuss Pollock's other writings on counterfactuals.) Premise semantics is presented in Kratzer [3] and [4].