Structural Reflexivity and the Paradoxes of Self-Reference

Many logicians now think that in order to give a uniform solution to the paradoxes of self-reference one must revise logic by dropping one of the usual structural rules. To date almost all such approaches have focused on dropping structural transitivity or structural contraction, and have largely overlooked or ignored the prospects for resolving the paradoxes by dropping structural reflexivity. Here we argue that we have paradox-independent grounds to be dubious of structural reflexivity, and present a way of resolving the paradoxes of selfreference by dropping structural reflexivity altogether, the resulting approach allowing us to recapture classical reasoning as being enthymematic in a particular way.