 (3) Borderline cases of vague predicates. Popular approaches to  vagueness  and the  sorites paradox,  such as the ones based on many-valued logics, or supervaluations, require some under-determinacy of reference, and/or the rejection of Bivalence: if an adolescent, \(m\), is a borderline case of adultness, \(A\), then \(A(m)\) may turn out to have an intermediate truth value between truth and falsity, or no truth value at all. But it may be conjectured that a borderline object like \(m\), instead of satisfying neither a vague predicate nor its negation, satisfies them both: an adolescent both is and is not an adult. Given the obvious dualities between the LEM and the Law of Bivalence on the one side, and (respectively, syntactic and semantic formulations of) the LNC on the other, it is not too difficult to envisage a ‘sub-valuational’ semantic approach, dual to the supervaluation strategy. Sub-valuational paraconsistent semantics have been proposed by Hyde (1997), and Varzi (1997). Other ‘glutty’ approaches to vagueness have been proposed by Colyvan (2009), Weber (2010), Priest (2010), Ripley (2013), and Cobreros et al (2010, 2015), motivated on both theoretical and empirical grounds. If inconsistencies due to vague predicates and borderline objects are taken to be due to merely semantic under- and over- determination of ordinary language (de dicto), then this is further evidence for dialetheism about semantics. If the aforementioned phenomena are taken to be not just about words but things (de re), then actually inconsistent objects are admitted, together with vague objects. And this spreads inconsistency all over the empirical world: if borderline cases can be inconsistent, inconsistent objects are more or less everywhere, given how pervasive the phenomenon of vagueness notoriously is: adolescents, borderline bald men, etc. Inconsistency is observable (Beall and Colyvan 2001). Beall argues against the approach in Ch. 5 of Beall 2009, and Beall 2014a.