  This paper discusses the scope and significance of the so-called triviality
result stated by Allan Gibbard for indicative conditionals, showing that if a
conditional operator satisfies the Law of Import-Export, is supraclassical, and
is stronger than the material conditional, then it must collapse to the
material conditional. Gibbard's result is taken to pose a dilemma for a
truth-functional account of indicative conditionals: give up Import-Export, or
embrace the two-valued analysis. We show that this dilemma can be averted in
trivalent logics of the conditional based on Reichenbach and de Finetti's idea
that a conditional with a false antecedent is undefined. Import-Export and
truth-functionality hold without triviality in such logics. We unravel some
implicit assumptions in Gibbard's proof, and discuss a recent generalization of
Gibbard's result due to Branden Fitelson.
