 The best-developed substructural approach to paradoxes works by attacking the structural rule of contraction. Contraction is the principle that tells us that whenever \(\Gamma , A, A \vdash B\), then \(\Gamma , A \vdash B\); that is, it is the principle that tells us that we can use premises repeatedly while only counting them once. Returning to the argument given in  section 2,  we can see that in two cases, an assumption is used twice in reaching a conclusion: assumption 2a is used twice on the way to 2d, and assumption 3a is used twice on the way to 3d. As we presented the argument, we did not call attention to this feature, but it is one place a noncontractive approach will focus.