6.9.3—
Field's Argument

In a justly famous article, Hartry Field (1972) undertakes an extensive examination of Tarski's theory of truth. Field argues that Tarski succeeded in reducing truth to what Field calls "primitive denotation," but failed to define primitive denotation in nonsemantic terms. And thus, in Field's view, the remaining project in semantics for naturalists such as himself is to provide a nonsemantic account of primitive denotation. The crux of Field's argument is that merely extensional characterization of semantic notions such as denotation or satisfaction, while adequate for model-theoretic purposes, does not constitute a genuine reduction of semantic terms, any more than we may produce a genuine reduction of the notion of valence that proceeded by saying

("E ) ("N ) (E has valence nºE is potassium and n is +1, or . . . or E is sulphur and n is -2). (Field 1972: 363)

There seem to be at least two problems with merely extensional characterizations, on Field's view. First, they do not reduce semantic properties to nonsemantic properties in the sense of "reduction" employed in the sciences and relevant to the incorporation of semantics within the project of physicalism. Second, they seem to license unfortunate would-be "reductions": "By similar standards of reduction, one might prove that witchcraft is compatible with physicalism, as long as witches cast only a finite number of spells: for then 'cast a spell' can be defined without use of any of the terms of witchcraft theory, merely by listing all the witch-and-victim pairs" (ibid., 369).

Field seems right in his claim that Tarski's extensionally based account of his primitive semantic properties fails to yield any robust account of their nature. What Field directly argues is that Tarski's characterizations do not yield a reduction of these properties in terms that demonstrate compatibility with physicalism, but we shall see below in Blackburn's criticisms that this point can be generalized beyond Field's physicalistic agenda as well.