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02/08/2010

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Irmela Wagner

I tortured my mind with such questions some time, but Ch. S. Peirce (who was influenced by Kant and who influenced Tarski) and Chomsky solved the mystery for me, together with the phenomenologists and psychologists which say that language is prima facie a social phenomenon. I think (strict) Solipsism is a paradox in itself (you may think of Wittgensteins 'Privatsprachenargument').
And last but not least there is this study by Rumbaugh who could teach apes the use of symbols, showing how a language could have started with 'primitives' and gotten more and more complex with more sophisticated use (Tomasellos 'Wagenhebereffekt').

Maybe a skeptic could refute all that by saying that observation cannot be evidence and that you can never know what an absolute I (maybe you are god, trying to fool yourself because you're so bored of infinity) could do. But even if.. as long as there is some sort of regularity and continuity, you can formulate theories and laws, even if they aren't strict, that can help you interact with things you hopefully identify as not-Me's ;)

Irmela Wagner

but maybe this was not exactly to the point.. yes, I think that the Truth-Theory we're discussing can never explain, nor be interpretive, but only a descriptive tool that reveals more things about the workings of language.

Irmela Wagner

sure that's only an opinion and I'm no authority on the matter whatsoever.. I just wanted to open up the Commentary-Function.

Miguel

My worry does not attach to truth theoretic semantics *in general* (much less to *semantics* in general), but to your specific proposal of how to formulate 'explicit meaning theories'. Especially, the worry is *not* that we can only formulate theories or explain things by *using* language, and that hence linguistic competence on the part of the theorist is required. This I accept and take to be trivial and unproblematic.

I take it that at least one interest in giving meaning theories stems from the fact that we would like to answer the following question:

(Q1) How is it possible that a finite being has knowledge of an infinite language?

(By an infinite language I mean a language that contains infinitely many non-synonymous sentences, and by ‘having knowledge of a language’ I mean knowing of (or being in a position to know of) all the sentences in the language what they mean in that language.) There are at least two readings we can give to Q1. Suppose that L is an infinite language actually known by some finite beings. With respect to *this very language*, we may ask:

(Q2) How is it possible that a finite being has knowledge of this infinite language L?

Q2 could be answered by pointing out that a finite being A could come to know L if he had the knowledge expressed by a complete recursive translation manual from a language A knows, say L*, to the target language L. This answer presupposes knowledge with an infinite language in the sense that this very translation manual is of use to someone only if he understands the infinite language L*, while knowing the translation manual does not suffice to know L*. Q2 corresponds to a weak reading of Q1, and I take it that we are not very interested in it (and that this is--at least in part--the reason why we are not very interested in translation manuals).
Here is a stronger reading of Q1. We may observe that some finite beings in fact know an infinite language and ask ourselves how this is possible in the following sense:

(Q3) How is it possible that there is an infinite language L and a finite being A such that A knows L?

In order to answer Q3 we could specify a finite body of information about a particular infinite language L such that possession of that information would suffice to know L. A theory which expresses such information would be a meaning theory (for L). But now suppose someone were to suggested a body of information INFO about an infinite language L which is such that possession of INFO puts a subject A into the position to know L only if A already knows a second infinite language L*. We should not--I think--say that INFO provides the basis for answering Q3 (and we should not--therefore--call a theory which expresses INFO a meaning theory). All that we can use INFO for is to explain how it is possible for A to know an infinite language *given that he already knows an infinite language*. Consider an analogy. Suppose I wanted to know how it is possible that there is a human being. Now you propose the following answer: Well, suppose there were two human beings and that these two were to have a child. Then there would be a human being, namely this child. Obviously that’s not a satisfying answer to the question under the intended strong reading. And this is precisely the situation that translation-manuals face with respect to Q3. My claim is that your proposal is--in this respect--no better off. You are, in effect, suggesting something along the lines of INFO.

What’s the evidence for my claim? For lack of time, I will be very brief, but I will try to come back to this tomorrow after the seminar. Let MT be a theory for an object language L1 constructed along the lines of your proposal; i.e. MT is what you would call an ‘explicit meaning theory’ for L1, which incorporates a truth theory T for L1 and states various things about this truth theory. Lets say this truth theory is given in a language L2. Suppose someone A knew the content of MT; i.e. for every proposition that p which is expressed by some axiom of MT, A knows that p. (In the following, when I talk about *A’s knowledge of MT*, this is what I have in mind--nothing in this presupposes that A understands the language in which MT is given). Now, here is my argument:

(1) MT is a meaning theory for L1 *only if* A’s knowledge of MT puts A into a position to know L1.
(2) A’s knowledge of MT puts A into a position to know L1 *only if* A’s knowledge of MT puts A into a position to understand all the canonical T-theorems (which are formulated in L2, the language of the truth theory).
(3) But A’s knowledge of MT *does not* put A into a position to understand all the canonical T-theorems.
Therefore:
(4) MT is not a meaning theory for L1.

I would agree that MT can put someone into the position to know L1 *given that she already understands L2* (and hence understands all the canonical theorems). But that’s not enough if we are interested in answering Q3.

But isn’t premise (3) just false? After all, MT explicitly states what the axioms of T mean in L2. But it is hard to see how stating what a few sentences mean--en bloc, as it were--could ensure the understanding of all sentences that can be derived from the initial sentences by syntactic operations such as a canonical proof procedure. But then knowing what the axioms of T mean in L2 does not suffice to know what all the theorems of T mean in L2.

Final, very sketchy remark: There is a similar worry (and an additional one) about your employment of a schema in the first axiom of an ‘explicit meaning theory’. Presumably, this schema belongs to the language of MT, i.e. not to the language of the truth theory. First worry: how do we ensure that A understands all of the relevant infinitely many instances of this schema purely on the basis of his knowledge of MT? Second worry: How is the information provided by these instances (even granted that it is available to A) supposed to connect to the canonical T-theorems (which belong to a different language)?

Kirk Ludwig

I will respond to this in a new post to combine the response with discussion from Friday's session in which we made I think considerable progress in sorting out what the underlying issues are.

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TMD Handouts

  • Handout #1
    The Role of a Truth Theory in a Meaning Theory
  • Handout #2
    Objections and Challenges to Truth-theoretic Semantics Met
  • Handout #3
    What is Radical Interpretation?
  • Handout #4
    The Impossibility of Radical Interpretation
  • Handout #5
    Metaphysics and Epistemology: radically different conceptual schemes, impossibility of massive error, first person authority, inscrutability of reference.
  • Handout #6
    Are There Any A Priori Arguments for Radical Interpretation?