I’m trying to work out some thoughts on the topic of semantic self-sufficiency. My jumping off point for this is the exchange between McGee, Martin and Gupta on the Revision Theory of Truth. My post was too long, even with part of it incomplete, so I’m going to post part of it, mostly expository, today. The rest I hope to finish up tomorrow. I’m also fairly unread in the literature on this topic. I know Tarski was doubtful about self-sufficiency and Fitch thought Tarski was overly doubtful. Are there any particular contemporary discussions of these issues that come highly recommended?

In their criticisms of the revision theory, both McGee and Martin say that a fault of the revision theory is that it is not semantically self-sufficient. The metalanguage for its characterization of truth must be stronger than the object language. Martin puts the point as follows.

[Gupta and Belnap] dismiss the goal of trying to understand truth for a language entirely from within the language. Although they point out some problems with the very notion of a universal language… The problem that the semantic paradoxes pose is not primarily the problem of understanding the notion of truth in expressively rich languages, it is the problem of understanding our notion of truth. And we have no language beyond our own in which to discuss this problem and in which to formulate our answers. 

McGee expresses a similar sentiment.

Gupta, in his reply to Martin and McGee, presents the objection in the following way. (I follow Gupta pretty closely here.) (1) a semantic description of English must be possible. (2) This description must be formulable in English itself, i.e. English must be semantically self-sufficient. (3) The revision semantics for a language can only be constructed in a richer metalanguage. (4) Revision semantics is therefore not suitable for English. (5) Therefore, revision semantics doesn’t capture the notion of truth in English. The problem Gupta diagnoses is that this takes the aim of the project of investigating truth to be one thing, while he sees it as another. McGee and Martin see the goal as the constriction of of a language L that can express its own semantic theory. Gupta sees the goal as giving a semantics of the predicate “true in L” of L, generally. He calls the former the self-sufficiency project and the latter the truth project. Gupta points out that the truth project, the goal of the revision theory, is independent of the self-sufficiency project, which is not independent of the truth project. (Gupta also gave a partial, positive answer to the self-sufficiency project, for languages that lack certain sorts of self-reference.) Gupta expresses some doubt about the prospects of full success in the self-sufficiency project. In what follows I’ll present Gupta’s arguments.

To set the stage for the doubts, we need to idealize English, or any language, as frozen in some stage in its development. Otherwise there are possibly extraneous concerns that arise about the self-sufficiency at different times and with respect to different times. If we take English to be fixed at some stage of its development, there is a problem about spelling out what conceptual resources it contains and that are at the disposal of the semantic theory. Part of the reason for thinking that English is semantically self-sufficient is that has a great deal of expressive power and flexibility. Expressions can be cooked up to denote any expression or thing one might want. Gupta puts it this way: there are expressions whose interpretations can be varied indefinitely.

Gupta poses a dilemma. Either the semantic self-sufficiency of English is due to this flexibility or it is not. If it is, then there is no motivation for semantic self-sufficiency. The self-sufficiency project supposes fixed conceptual resources, so the flexibility of English cannot motivate that project after all. If not, we can suppose that English has fixed conceptual resources. Given that, what reason is there to think that English is self-sufficient? There is no empirical confirmation of this. There doesn’t seem to be much by way of a priori reason for thinking it either. In either case, there doesn’t seem to be any motivation for taking English to be self-sufficient. He gives one motivation, although the discussion and criticism of that could stand independently of the dilemma posed here.

Gupta notes that the thing most often cited in favor of thinking that English is semantically self-sufficient is the “comprehensibility of English by English speakers.” This has an ambiguity. In one sense, ‘comprehensibility’ is the ability to use and understand the language. In another sense, it is the ability to give a systematic semantic theory for the language. The claim is then that English speakers can give a systematic semantic theory for their language. In the former sense, the claim is trivial. In the latter sense, there is not really any reason to believe it.

This point seems to me to be allied to thoughts about following rules and norms. One can follow rules quite easily. It is often quite hard to make explicit the rules and norms one is following and how they systematically fit together. If giving a semantic theory involves something like this, then it wouldn’t be unexpected that some difficulties would arise. I don’t think Gupta has this in mind though.

Gupta raises a second worry. Even if the previous one can be overcome, there is the problem of giving a semantic theory for the stage of English in that stage because there is gap between the ability of English speakers and the resources available at a given stage of English. The speakers can, and do, enrich their vocabulary with mathematical and logical resources, and the ability to do this might be intimately bound up with the ability to give a semantics for English. Appealing to the abilities of speakers of a language to motivate semantic self-sufficiency then seems to create a problem. One could idealize the speakers as similarly frozen at a given stage, along with their language, so that no developmental capacities enter into the picture. To claim semantic self-sufficiency here is to simply disregard the previous objection. It is also unclear why one would think that in such a scenario semantic self-sufficiency would obtain.

The point of Gupta’s criticism is not to refute all hope of semantic self-sufficiency. It is rather to cast doubt on it and its motivations. If he is right, then it shouldn’t be taken as a basic desideratum of a theory of truth, or any semantic theory. Then those parts of McGee’s and Martin’s objections lose their force. I think it also indicates some of the places where claims about semantic self-sufficiency need to be sharpened, which I’ll try to address in a post in the near future.