Singularities
Keith Simmons · Oxford University Press eBooks · 2018
Chapter 3 turns to the second main claim of the proposed solution: our semantic predicates are significant everywhere except for certain singularities, where their application breaks down. A particular use of ‘denotes’, for example, is minimally restricted, applying to all denoting expressions except its singularities. Similarly with ‘extension’ and ‘true’. The singularity solution is contrasted with hierarchical solutions: the singularity solution does not stratify the semantic predicates into levels. The chapter identifies two kinds of semantic networks associated with the paradoxes-loops and chains-and prepares the ground for a representation of these semantic networks via certain kinds of trees. The upshot of the chapter is that the extensions of our semantic predicates shift with certain changes of context, but these shifts are kept to a minimum.