Title: The existence of truthmakers and the definition of logical consequence
Speaker: Ethan Brauer (Ohio State University)
Abstract: In recent philosophical logic, theories of so-called truthmakers have played a significant role, but not much attention has been given to (meta)mathematical questions about these theories. In this talk I introduce a particular theory according to which truthmakers are inductively defined trees roughly analogous to infinitary proofs. I first address the question of what background theory is needed to prove the existence of truthmakers for every true sentence; the answer is RCA_0, and I relate this to now-standard results on the classical completeness theorem. Second, I show how this theory of truthmakers allows for a definition of logical consequence in terms of proof-theoretic normalization. This definition of logical consequence turns out to be equivalent to the Tarskian definition when the set of premises is consistent.
