Tuesday, November 15, 2005

Semantic Paradoxes In Natural Language

There hasn't been a lot of philosophy here recently.

In "Truth and Meaning" Davidson attempts to extend the Tarski style definition of truth in a formal language to natural language, and use this as a theory of meaning. In the case of the formal language, you have an object language "L" and a metalanguage, which is capable of expressing everything expressible in L, and which also contains a predicate "true-in-L." You give a recursive algorithm for translating sentences in L into the metalanguage. If s is a sentence in L and p is it's formulation in the metalanguage, you get a sentence of the form
"s is true iff p"
The reason that you have to do this in a metalanguage is to avoid the liar paradox, in which you have a sentence of the form
"This sentence is false."
Since the metalanguage only defines truth in L, rather than truth generally and L has no truth predicate, there is no possibility of having a liar sentence in either language. Davidson's extension of Tarski's proposal gives you sentences of the form
" 'Snow is white' is true iff snow is white."
The account looks completely vacuous in English, but there are at least some more interesting sentences in the vicinity
" 'Der schnee ist weiss' is true iff snow is white"
" 'Snow is white' est vrai si et seulement si la neige est blanche"
Moreover, the theory of meaning itself is given not by these sentences, which are theorems of that theory, but rather the meaning postulates attaching to individual words and composition rules which tell you how to give the truth conditions of any sentence in terms of its constituent parts.

Now, most logicians had thought that Tarski's idea was inapplicable to natural languages, in part because natural languages seem to have a universality that makes the proposal untenabile. That is, English is it's own metalanguage, "true-in-English" seeming to be an English predicate. Davidson's answer is decidedly odd. Without claiming to have a decisive answer, he puts forth the following suggestion.
The semantic paradoxes arise when the range of the quantifiers in the object language is too generous in certain ways. But it is not really clear how unfair to Urdu or to Wendish it would be to view the range of their quantifiers as insufficient to yield an explicit definition of 'true-in-Urdu' or 'true-in-Wendish.' Or to put the matter in another, if not more serious way, there may in the nature of the case always be something we grasp in understanding the language of another (the concept of truth) that we cannot communicate to him."
Your ability to translate Urdu into English implies that the resources to define 'true-in-Urdu' in English are available (and they can define the same thing about English in Urdu). But that seems to create an obvious problem. An Urdu speaker can just say "['snow is white' is whatever those British people mean by]'true-in-Urdu'[iff snow is white]" putting everything in brackets into Urdu, and they have seemingly just reintroduced the possibility of generating semantic paradoxes. It is therefore quite unclear to my how Davidson's project is supposed to avoid the semantic paradoxes (he does say he feels justified in proceeding without having definitively shown that there are no semantic paradoxes in natural language).


ben said...

Being a fan of truth-conditional semantics generally (though I like Davidson's official program less and less as time goes by), I have to say that this problem really bothers me. I've no clue what to do about it that would be satisfactory...in fact I know very little about the proposed solutions to the liar paradox itself. I do know, however, that THE Bill Lycan has a paper entitled "A Truth Predicate in the Object Langugae" (I think) that deals with this issue. He hasn't published it because Keith Simmons found a nasty flaw in the solution.

Dialetheism anyone?

Justin said...

I'm generally attached to inferential role semantics, read from a more or less behaviorist stance, so I'm not equally worried by this.

I'm in the same boat with regards to the liar paradox. I wonder if Keith's book would just kick my ass if I tried to read it or not.

ben said...

I'm sure Keith's book isn't easy. I tried to check it out about two weeks ago only to find that someone has it out right now, and for quite a long time. I understand that his treatment of semantic paradox in general relies on elements from Discourse Representation Theory, Update Semantics and other so-called "dynamic" approaches to semantics (though, at least with respect to DRT, "dynamic" isn't quite the right term officially). There are so many things to read after this semester!

Justin said...

Lord, that's too much for me since I'd just be taking the first semantics course next semester.