Abstract: Existing theories of conditionals are "conservative" in this sense: A->C can't differ in truth-value from A->D unless C differs in truth-value from D in some A-world. We look at some possible examples to the contrary.
"If Pete won, Mr Stone lost" ---- true if Pete was playing Mr Stone. "If Pete won, he was playing Mr Stone"---false, Mr Mud is the only one he can beat.
Yet in worlds where Pete wins, we can imagine, Mr Stone loses just in case Pete was playing him.
"If Bizet and Verdi are the same height, Bizet is short"---true because Verdi is short. "If Bizet and Verdi are the same height, Verdi is short"---false because Bizet is (let's say) tall.
Yet in worlds where they're the same height, Bizet is short iff Verdi is.
The truth of A->C turns, sometimes, not on whether A-worlds (like ours) are C---that way lies conservatism--- but on whether our world has what it takes to make true the material conditional A ⊃ C. A ⊃ C and A ⊃ D are not true for the same reasons in A-worlds, granted that they are true in the same A-worlds.
Stephen Yablo is a Professor of Philosophy at MIT.
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