Yablo's paradox, The Liar, and referential contradictions from a graph theory point of view

BODANZA, GUSTAVO

Moscú

Congreso; International Conference 'Formal Philosophy 2021'; 2021

International Laboratory for Logic, Linguistics and Formal Philosophy, HSE University, Moscow

I introduce the notion of conglomerate to model maximal (w.r.t. ⊆) subsetsof sentences that can jointly be valued as true. The existence of conglomeratesin a system guarantees the absence of paradox ?at least, those generated by thefalsity predicate. Besides paradoxes, conglomerates also enable to characterize referential con-tradictions and referential tautologies. Referential contradictions (resp. tau-tologies) are sentences that can only take the false (resp. true) value underclassical valuations, due to the interactions with other sentences in the model.For their part, referential tautologies only exist byreference to referential contradictions. As a result, referential tautologies belong to every con-glomerate while referential contradictions are excluded from every conglomerate.