According to Field’s influential incompleteness objection, Tarski’s semantic theory of truth is unsatisfactory since the definition that forms its basis is incomplete in two distinct senses: 1) it is physicalistically inadequate, and for this reason, 2) it is conceptually deficient. In this paper, I defend the semantic theory of truth against the incompleteness objection by conceding 1) but rejecting 2). After arguing that Davidson and McDowell’s reply to the incompleteness objection fails to pass muster, I argue that, within the constraints of a non-reductive physicalism and a holism concerning the concepts of truth, reference and meaning, conceding Field’s physicalistic inadequacy conclusion while rejecting his conceptual deficiency conclusion is a promising reply to the incompleteness objection.
Hoffmann, Glen A., "The Semantic Theory of Truth: Field's Incompleteness Objection" (2007). Philosophy Publications and Research. Paper 14.