Page 186 - Encyclopedia of Philosophy of Language

Truth and Meaning
understood, the semantic rules implicit in ordinary linguistic practice, or very close approximations to these, are coherent and defensible.
5. Contemporary Diagnoses of the Paradoxes as Insoluble
Gupta (1982) has urged that any attempt to assign stable semantic values to paradoxical sentences in natural language be abandoned. He suggests that there is no semantic rule of application associated with the predicate 'is true' in English (no assignment of a set of things of which the predicate is true). Instead, there is only a rule of revision which tells us, given a putative interpretation of 'is true,' how to make marginal improvements. According to Gupta, the interpretation of 'is true' oscillates as more and more improvements are made, until a stabilization point is reached, at which every sentence which will ever stabilize has already stabilized. Paradoxical sentences like the Liar never stabilize: instead, they oscillate endlessly between truth and falsity. Yablo (1985) has developed a similar construction in which better and better approximations to the ideal represented by Tar- ski's convention T are achieved at each stage. Gupta's construction has the advantage that it makes all the- orems of logic stably true, for example, 'the Liar sen- tence is true or it's not true' becomes stably true on his account. On Y ablo's account, not all such theorems of logic come out as definitely and uniquely true, but his account instead respects an intuition about the 'groundedness' of truth: a disjunction should not
count as true unless one of its disjuncts does; a con- junction should not count as false unless one of its conjuncts does, etc.
The principal drawback to approaches such as Gup- ta's and Yablo's is that any attempt to sayanything definite about the paradoxical sentences of natural language runs afoul of another paradoxical diagonal argument. For instance, Gupta's theory leads one to divide the sentences of a natural language likeEnglish into three categories: stably true, stably false, and paradoxical. Since Gupta's theory is presented in English, it would seem that English has the capacity of expressing these concepts. Therefore, it should be possible to express the concept of 'super- heterologicality': a predicate of English is super- heterological if and only if it is either false of itself, or results in a paradoxical sentence when applied to itself. On Gupta's account, the predicate 'is super- heterological' results in a paradoxical sentence when applied to itself. But this means that, by definition, 'is superheterologicaF is superheterological, and so it should result in a true sentence when applied to itself. Gupta's diagnostic theory about semantic paradox is subject to the very same sort of paradox.
Anyone who is really convinced that the semantic paradoxes are insoluble must follow Wittgenstein's dictum from the Tractatus Logico-Philosophicus:
'whereof we cannot speak, thereof must we remain silent.' Semantic theory on this conception must remain radically incomplete: it may assert that certain sentences are true and others false, but it must not try to introduce any tertiwn quid. Any attempt to distinguish the paradoxical as a separate semantic cat- egory will simply reintroduce paradoxically into one's semantic theory itself.
6. Proposed Solutions to the Liar Paradox in Natural Language
6.1 Blocking Self-Reference: The Redundancy Theory of Truth
Frank Ramsey in 1927proposed the redundancy the- ory of truth as a way of averting the semantic para- doxes in natural language. Ramsey denied that 'is true' is a predicate at all. Instead, 'is true' is simply a redundant operator: to say ' "snow is white" is true' is simply a long-winded way of saying 'snow is white.' A Liar sentence, like 'this sentence is not true,' is simple nonsense. Unfortunately, this theory cannot account for sentences in which the place of the truth- bearer is replaced by a variable of quantification, as in: 'whatever the Pope says is true,' or 'I hope that what Jones says is true'.
6.2 Denying the Universality of Pretheoretical Natural Language
Saul Kripke (1975) developed an inductive con- struction in which the extension (the set of sentences of which the predicate is true), and the anti-extension (the set of sentences of which it is false) of the predicate 'is true' are gradually increased, beginning with an empty interpretation, in which both extension and anti-extension are empty, and ending with some sort of fixed point, at which Tarski's Convention T is at least approximated. Kripke's work inspired similar constructions by Gupta (1982), Burge (1979), Herz- berger (1982), and Yablo (1985). At one of Kripke's fixed points, some sentences are true, some are false, and some (like the Liar sentence) have a truth-value 'gap.'
In order to avoid being liable to semantic paradox himself, Kripke distinguishes between pretheoretical natural language, which, he claims, lacks the con- ceptual resources needed to express the trichotomy true/false/neither, and the theoretical metalanguage in which he expresses his theory. Kripke, as well as Herzberger (1982), denies that the claim to uni- versality is essential to natural language. In some sense, Kripke would admit, his theory is expressed in natural language, but it is in natural language at a different stage of conceptual development from the natural language which is its object of investigation. In effect, Kripke introduces a Tarskian hierarchy of languages by suggesting a theory of the dynamics of language change. In fact, however, ordinary English does seem to have the capacity of expressing the con-
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