  We are left with two significant challenges for LNC: (i) the case of the Liar and related paradoxes of self-reference as touched on in §3 and work cited therein (see the entries on Liar Paradox, Russell’s Paradox, Dialetheism, Paraconsistent Logic) and (ii) the case of vagueness and its implications for borderline truth, discussed in this section. As we have seen, the admission of truth-value gaps (exceptions to LEM) is mirrored by the admission of truth-value gluts (exceptions to LNC). As intellectual heirs of the Hegelian tradition, Marxists have willing to accept paradox, and indeed the pre-Revolutionary theorist Plekanov (1909) suggests that Sorites (in the form of the bald man; see sorites entry) can be resolved by rejecting LNC. Hyde (1997) traces the history of vagueness-based arguments for paraconsistency from Plekhanov through Jaśkowski, McGill, and Parry in the 1940s to the dialetheist logics of today. Pointing out the parallels between treatments of vagueness via truth-value gap theories (including the supervaluation theory of van Fraassen 1969) and their truth-value glut counterparts, Hyde laments the unwarranted neglect of the latter option: “The thought that an adequate response might require the recognition of cases of overdetermination and and truth-value gluts has few supporters” (Hyde 1997: 641). In the two decades since the publication of his important paper, that neglect has been largely rectified, especially with the accretion of empirical support for glut-oriented approaches endorsing the acceptability of a range of true contradictions of the form a is P and a is not P, in particular when P is a vague predicate like tall, vague, or red.