Abstract

This chapter examines other ways the Argument from Completeness might be attacked. It identifies two strategies that the realist might deploy in order to avoid the difficulties engendered by the applicability of the Completeness Theorem to the ideal theory. The first is to insist that the theory be cast in some non-first-order language which resists completeness. The second is to allow ideal theory to continue to be rendered in first-order form, but to argue for a semantics in which interpretations take such a new shape that there is no longer any guarantee that any consistent theory has a model in the new sense.