  The Stoics recognized the importance of both the Liar and the Sorites paradoxes (Cicero Acad. 2.95–8, Plut. Comm.Not. 1059D–E, Chrys. Log. Zet. col.IX). Chrysippus may have tried to solve the Liar as follows: there is an ineliminable ambiguity in the Liar sentence (‘I am speaking falsely’, uttered in isolation) between the assertibles (i) ‘I falsely say I speak falsely’ and (ii) ‘I am speaking falsely’ (i.e. I am doing what I’m saying, viz. speaking falsely), of which, at any time the Liar sentence is uttered, precisely one is true, but it is arbitrary which one. (i) entails (iii) ‘I am speaking truly’ and is incompatible with (ii) and with (iv) ‘I truly say I speak falsely’. (ii) entails (iv) and is incompatible with (i) and (iii). Thus bivalence is preserved (cf. Cavini 1993). Chrysippus’ stand on the Sorites seems to have been that vague borderline sentences uttered in the context of a Sorites series have no assertibles corresponding to them, and that it is obscure to us where the borderline cases start, so that it is rational for us to stop answering while still on safe ground (i.e. before we might begin to make utterances with no assertible corresponding to them). The latter remark suggests Chrysippus was aware of the problem of higher order vagueness. Again, bivalence of assertibles is preserved (cf. Bobzien 2002). The Stoics also discussed various other well-known paradoxes. In particular, for the paradoxes of presupposition, known in antiquity as the Horned One, they produced a Russellian-type solution based on a hidden scope ambiguity of negation (cf. Bobzien 2012)