  Many of the non-classical logics that have been proposed to underwrite responses to Russell’s paradox and the Liar paradox are paracomplete logics, logics that reject the law of excluded middle. These logics make possible “gappy” theories. In particular, where \(\lambda\) and \(\lnot\lambda\) are intersubstitutable according to such a theory \(\mathcal{T}\), it will fail to be the case that \(\vdash _{\mathcal{T}} \lambda \lor \lnot \lambda\). Some of these paracomplete logics likewise meet conditions (a) and (b).