 If, in fact, v-Curry paradoxes aren’t amenable to weakly contraction-free or strongly detachment-free responses, then (assuming the rule Id is retained) the space of Curry-complete responses is restricted to strongly contraction-free and weakly detachment-free responses. The former responses, as explained in  section 4.2.1,  are typically presented by reformulating modus ponens (or detachment for the validity predicate) in a substructural deduction system and rejecting the structural contraction rule sCont. The latter responses, as explained in  section 4.2.2,  reject the structural principle of transitivity. For this reason, v-Curry paradoxes have sometimes been taken to motivate substructural consequence relations (e.g., Barrio et al. forthcoming; Beall &amp; Murzi 2013; Ripley 2015a; Shapiro 2011, 2015).[32]