The Liar and other semantic paradoxes from a graph-theoretic view

BODANZA, GUSTAVO ADRIÁN

Aveiro

Conferencia; Conferencia por invitación; 2019

Universidad de Aveiro, Departamento de Matemática

Some semantic paradoxes, like ?This sentence is false? and others, involve sentences that predicate the falsity of other sentences. Those situations can be modeled as F-systems, which are digraphs where the nodes S represent sentences and the set of edges F represents the relation ??says that? is false?. This enables to understand the source of paradox in terms of graph-theoretic properties. In this talk, we will present the concept of counter kernel ?roughly, an independent set of nodes that absorbs every non-sink node- and show that F-systems for which there exist counter kernels are free of paradoxes. Moreover, if the digraph can be partitioned into counter kernels then the system is also free of referential contradictions and tautologies. Other results will show furhter sufficient conditions to avoid or generate paradox.