On Truth
This is the articulation of what it is for a statement (propositionally structured content) to be true within the framework of the D-Lewisian possible world semantics. A viable theory of truth must entail the T-Schema: “ P ” is true ↔ P . Here is the formalism of language. Formalism : Language is a function from sentences to meanings, i.e., a set of ordered pairs of sentences and meanings. L : language s : sentence L ( s ): the meaning of s L : {( s 1 , L ( s 1 )), ( s 2 , L ( s 2 )), …} W : possible world w : fact, state of affairs The meaning of a set of sentences is a possible world that serves as a specific model for the interpretation of the set. As Wittgenstein remarks, a world is a totality of all facts, or states of affairs. A theory is a function L that pairs one set of sentences with some model in a particular way. As such, a theory is a relation between two structures (sentences and world); although the relation can be surjective, I will focus on bijective relations for s...