Adding a Conditional? Curry and Lukasiewicz

This chapter discusses the Lukasiewicz continuum-valued semantics as a way of improving upon the Kleene semantics as the basis for an account of truth. It is shown that it gives a very nice treatment of the paradoxes within a quantifier-free fragment of the language, but that it breaks down when quantifiers are added. This account will nonetheless serve as something of a model for the view to be advocated later, and so a number of issues that will arise later are discussed here. These include the Curry paradox, the meaning of semantic values, and the notion of determinate truth.

This chapter discusses the Lukasiewicz continuum-valued semantics as a way of improving upon the Kleene semantics as the basis for an account of truth. It is shown that it gives a very nice treatment of the paradoxes within a quantifier-free fragment of the language, but that it breaks down when quantifiers are added. This account will nonetheless serve as something of a model for the view to be advocated later, and so a number of issues that will arise later are discussed here. These include the Curry paradox, the meaning of semantic values, and the notion of determinate truth.