**Topic:** **HUMAN SEMANTICS**

### Semantics for Deflationists

By Christopher Gauker

According to deflationists, [*p*]is true is in some sense equivalent to *p*. The problem that the semantic paradoxes pose for the deflationist is to explicate this equivalence without relying on a semantics grounded in the sort of real reference relations that a deflationist thinks do not exist. More generally, the deflationist is challenged to give an account of logical validity that does not force us to countenance such relations. (The usual model-theoretic definition seems to presuppose that there is some special interpretation, the intended interpretation, such that truth simpliciter is truth on that intended interpretation. So if the deflationist adopts this sort of definition, the deflationist will be challenged to identify the intended interpretation without positing real reference relations.)

Fortunately, a precise semantics compatible with the deflationist philosophy can be had as follows: First, we define a context as a certain sort of set constructed from a basis of literals (atomic sentences and negations of atomic sentences). This formal account of contexts has to be supplemented with an account of the conditions under which a structure satisfying the formal definition is the structure of that kind pertinent ot a given conversation. For each syntactic type of sentence, we define the conditions under which a sentence of that type is assertible relative to a context. In particular, we define the conditions under which sentences of the form "[*p*]is true" are assertible in a context, and we define the conditions under which sentences of the form "[*p*]is assertible in context G" are assertible in a context. Finally, logical validity is defined as preservation of assertibility in a context. It is demonstrated that this approach to semantics resists the semantics paradoxes.

(To appear in *Deflationism and Paradox*, ed. by JC Beall and Bradley Armour-Garb,Oxford University Press)

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Posted by Tony Marmo
at 00:01 BST

Updated: Friday, 29 October 2004 12:28 BST