Embedding If and Only If

Compounds of indicative conditionals present some puzzling phenomena. Perhaps most striking, some nested indicative conditionals are uninterpretable. Proponents of NTV hold that indicative conditionals do not have truth values, and they use this to explain why nested indicative conditionals are sometimes uninterpretable: the embedded conditional does not provide the truth conditions needed by the embedding conditional. Cases where nested conditionals are interpretable are then explained away as ad hoc, pragmatic interpretation. We challenge the NTV explanation for why nested conditionals are sometimes interpretable, sometimes not. The standard reasons for NTV about indicative conditionals— triviality results, Gibbardian standoffs, etc. — extend naturally to NTV about biconditionals. So NTVers about conditionals should also be NTVers about biconditionals. But biconditionals embed much more freely than conditionals. If NTV explains why some nested conditionals are uninterpretable, why do biconditionals embed successfully in the very contexts where conditionals do not embed?