Truth and Dependence
Ruiting Jiang

Abstract:
Beginning with the study of the Liar paradox, philosophers have proposed several competing theories of truth, each built on different intuitions, and they provide distinct classifications of sentences as true, false, paradoxical, or hypodoxical. In the current literature, the two dominant approaches are Kripke’s minimal fixed point construction and the Revision Theory of Truth. This thesis introduces a novel alternative: resting on a new underlying intuition that yields an alternative classification. I will argue that this theory is very natural and, in many respects, superior to existing accounts.
In our framework, every sentence corresponds to a function, which is determined by the sentences it depends on together with the T -schema. We then classify each sentence by the number of fixed points its associated function has. After presenting the formal theory, we compare our theory with Kripke’s minimal fixed points and with the Revision Theory, showing how our approach admits certain circular tautologies without arbitrariness and captures a broader range of non-paradoxical puzzles. Finally, although the development takes place in an infinite propositional language, the last chapter sketches how these ideas can be adapted to first order logic, outlines the remaining obstacles, and suggests possible strategies for overcoming them.