Conditionals in Possible Worlds: Times Three

Stanley Peters, Stanford University
(joint work with Makoto Kanazawa and Stefan Kaufmann)

The ordering semantics for conditionals (Lewis, Pollack) wrongly predicts that "If a different animal had escaped instead, it might have been a gazelle" is false if the animal that actually escaped was a zebra caged with another zebra and a gazelle. The naive premise semantics (Kratzer) wrongly predicts that "If Paula weren't buying a pound of apples, the Atlantic Ocean might be drying up" is true if Paula is buying a pound of apples and the Atlantic Ocean is not drying up. Kratzer (1989) proposed a lumping semantics for conditionals to solve both of these problems.

We show that lumping semantics does not touch the first problem at all. It solves the second problem only at the cost of predicting that "If the authors hadn't written this paper, they might have done something else with their time" and countless other true sentences are false. In fact, Kratzer's lumping semantics for conditionals makes would-conditionals equivalent to the material conditional and might-conditionals equivalent to conjunction.

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