Patrick Todd
University of Edinburgh
Brian Rabern
University of Edinburgh
The principle of Conditional Excluded Middle has been a matter of longstanding controversy in both semantics and metaphysics. According to this principle, we are, inter alia, committed to claims like the following: If the coin had been flipped, it would have landed heads, or if the coin had been flipped, it would not have landed heads. In favour of the principle, theorists have appealed, primarily, to linguistic data such as that we tend to hear ¬(A > B) as equivalent to (A > ¬B). Williams (2010), provides one of the most compelling recent arguments along these lines by appealing to intuitive equivalencies between certain quantified conditional statements. We argue that the strategy Williams employs can be parodied to generate an argument for the unwelcome principle of Should Excluded Middle: the principle that, for any A, it either should be that A or it should be that not A. Uncovering what goes wrong with this argument casts doubt on a key premise in Williams’ argument. The way we develop this point is by defending the thesis that, like "should", "would" is a so-called neg-raising predicate. Neg-raising is the linguistic phenomenon whereby “I don’t think that Trump is a good president” strongly tends to implicate “I think that Trump is not a good president,” despite the former not semantically entailing the latter. We show how a defender of a Lewis-style semantics for counterfactuals should implement the idea that the counterfactual is a “neg-raiser”.
Keywords counterfactuals  conditional excluded middle  neg-raising  counterfacts  homogeneity  indeterminacy  quantified conditionals
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