 While the philosophical divide between Realists and Anti-realists remains vast, proof-centered and model-centered accounts of consequence have been united (at least with respect to extension) in many cases. The great soundness and completeness theorems for different proof systems (or, from the other angle, for different model-theoretic semantics) show that, in an important sense, the two approaches often coincide, at least in extension. A proof system is sound with respect to a model-theoretic semantics if every argument that has a proof in the system is model-theoretically valid. A proof system is complete with respect to a model-theoretic semantics if every model-theoretically valid argument has a proof in the system. While soundness is a principal condition on any proof system worth its name, completeness cannot always be expected. Admittedly, these definitions are biased towards the model-theoretic perspective: the model-theoretic semantic sets the standard to what is “sound” and “complete”. Leaving terminological issues aside, if a proof system is both sound and complete with respect to a model-theoretic semantics (as, significantly, in the case of first order predicate logic), then the proof system and the model-theoretic semantics agree on which arguments are valid.