Miguel Hoeltje raised some very good questions about the relation between my statement of the content of an explicit meaning theory and the sort of understanding we seek of the competence of finite beings to understand a potential infinity of sentences.

There is an initial question that arises about whether what I have stated as the content of an explicit meaning theory is in fact sufficient for one to come to understand the object language without granting independently that the person in possession of the theory understands the language of the truth theory.

Then there are some questions about how we should understand the explanatory task to which such a theory is directed, and the suggestion in particular that requiring knowledge of a language in the way that the sort of theory I have sketched would require it would undercut the goal of giving an explanation of how a finite competence can accommodate an infinite accomplishment.

I begin with the first, which will lead us to the second set of issues.

I said an explicit meaning theory should consist in a statement of a body of knowledge sufficient for the person possessing it (the theorist, we are thinking of here, not the person who speaks the language) to be in a position to understand any potential utterance in the language (so far as it is possible).

From this point of view, in truth-theoretic semantics the truth theory is not the meaning theory, because it is rather knowledge about the truth theory that is supposed to put us in a position to understanding object language sentences, because what it does in effect is give us a pairing of object language sentence mentioned by the truth theory with metalanguage sentences (or formulas) used which interpret the object language sentences. I said that what we need to know is what the theory is described as a syntactic object, so that we specify its axioms, and its recursive syntax, a canonical proof procedure for it and that it is a canonical proof procedure (on the version I presented this week that would include in the end a inference rule that takes us from canonical T-theorems to canonical M-theorems), that it meets Convention A, and what each of its axioms mean. The last, in conjunction with the rest of the story, was supposed to put us in a position to understand the truth theory, which is essential for the job it is to do for us.

Miguel has questioned whether that is enough, even in conjunction with the rest of what we know about the theory. I was imagining that we did have knowledge of the syntax of the truth theory in a format which sorted expressions into semantical categories. If we didn't have that, then I don't think knowledge of what the axioms mean would do the job because it wouldn't enable us to come to know how to match expressions we know term by term with expressions in the language of the truth theory. But if we did know that, then the idea would be, to take an example, that in the statement of the meaning of a simple predicate axiom

'(n)(T('F'+n) iff r(n)is G)' means that for any N, the concatenation of 'F' with N is true if and only if the referent of N is a rabbit

we can identify the main connective of the axiom as 'iff' and then match it with the main connective of the complement sentence in the meaning giving sentence 'iff'; then we can match appropriately each sentence on either side of the biconditional with the appropriate sentence in the metalanguage (we will know that 'r(n)' is the reference function because what we know about the reference axioms will indicate that). Then we can parse the structure of each of those sentences in turn and make appropriate matches and so on.

It is a defect of the way that I have stated it that it does not make clear that the person who possesses the stated knowledge is supposed to have enough knowledge of the syntax of the language of the truth theory to be able to parse the structure of the theory's sentences.

But suppose we fixed that. I don't think that would address the underlying worry, because the procedure I've described, even granting that it works, amounts to the theorist exploiting his knowledge of the language of the meaning theory in understanding the truth theory, for it is by his ability to match words in the language in which the theory is stated to words in the language of the truth theory that he comes to knowledge of it. And I take it that Miguel's intention is that anything like this would violate the constraint he has in mind on an adequate explanatory theory of meaning.

We should therefore turn our attention to that issue. I want to begin with the questions that Miguel distinguishes in his comment.

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

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

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

Q2 and Q3 are to be the weak and strong readings of Q1.

The trouble with Q2 as the right interpretation is supposed to be that an answer to it may make reference to a finite being's already having a language L' and an interpretation manual for L into L'. Then it may seem as if we haven't really answered the challenge because we're saying how someone could know one infinite language if he already knows another, but not how it is possible for him to know the first. And didn't we want a general answer?

With this in mind, we turn to Q3, which does not focus on how knowledge of a particular infinite language is possible but on how knowledge of an infinite language as such is possible, not relative to prior knowledge of another. And in light of our disappointment with the answer envisaged to Q2, we may here want to say: no answer will be acceptable if it does not statement a body of knowledge grasp of which does not presuppose that the one grasping it has a language.

What I want to say at this point is that we have got a little bit off track with respect to how truth-theoretic semantics aims to help show how finite competence put us in a position to understand a potential infinity of sentences. They idea is not that we explain this by showing how a theorist could have knowledge of the object language on the basis of a finite body of knowledge *as a model *for how speakers achieve this. It is more indirect. We know, in a way, what the answer is in outline. Speakers acquire a competence in using words in accordance with rules for their combination into complexes which represent things about the world. The trick is turned at the basic level by matching some words to some objects and some words to repeatable features of the world using concatenation of tokens (or some other relation between tokens) to indicate an intention that to convey that the one should be taken to have the other as a feature. Then things get a bit complicated with the recursive machinery of the language but it is all a further exploitation of this opening move. But that's roughly how it is possible. The challenge is to see in detail how it goes so we get past the bit where we say "and so on."

Now, it is clear that the form of explanation does not propose that what makes it possible for speakers to understand a potential infinity of sentences is propositional knowledge at all. It is competence in the use of words in accordance with rules. So if we have this in mind, we are not going to be thinking that when we ask what a theorist could know that would enable him to understand any utterance of a sentence in the object language, we are offering a model of how the speaker does it.

But then what are we doing? What is the point of asking what a theorist could know that would put him in a position to understand any potential utterance of a sentence in a language? As I understand it, the answer is the following. This constraint (and others) that we impose on a compositional meaning theory is designed to help us state something knowledge of which would enable us to see in detail what the rules are attaching to words that determine what the sentences containing them mean, and which are realized in the competences of speakers of the language in the sense that the rules can be take to express what the competencies are competencies in doing. We do this for particular languages, of course, not for language in general--but the form of what we do in the particular case we can recognize to be shared by any of an indefinitely large class of languages with the same basic features. I put it here in terms of enabling us to see in detail what is going on in part because I think there are limits to what can be explicitly stated. There is much that what we know shows us that is not explicitly stated. This is implicit in what I have said about what canonical proofs show us about the compositional structure of object language sentences.

Now, relative to this conception of how the compositional meaning theory is supposed to help us gain insight into how a finite being can know an infinite language, I do not think that the charge that it presupposes that the person with the body of knowledge himself has an infinite language is damaging. For the force of that charge came from thinking of it as on the model of the imagined answer to Q2, where we were thinking you explain how x could have knowledge of L by citing his possession of a language L' and a translation manual from L into L'. But we are not in the project I have in mind explaining how x has knowledge of L by citing his possession of the meaning theory we have described. The constraints on the meaning theory are supposed to ensure that the resulting theory helps in showing what rules govern words in the language such that combinations of them can be true or false (etc.). it is supposed to help us see what the competencies attaching to individual words comes to. It is put forward already against a certain background understanding of what is going on. It is intended to help us understand how it works in detail by filling in in a certain way what the details are.

This is connected with another issue that came up in discussion on Friday and I think there is something very interesting and important here. Once we start thinking about the project in the way encouraged by starting with Q2 and rejecting it in favor of Q3 conceived of as requiring in answer a body of propositional knowledge that suffices to understand a language, we can ask whether what I have done meets that challenge and whether that challenge in fact could be met. What I have suggested does not meet that challenge, but I suspect that that challenge cannot be met. And if that is right, it is an important and perhaps surprising result.

The question is this: could what we think of as propositional knowledge that would put anyone possessing it in a position to understand a language without tacit reliance on a matching of the sentences or expressions of the language with his own antecedently understood expressions?

That my answer and that Davidson's answer is 'no' is already implicit in the arguments against the utility of meanings in the theory of meaning.

Let us suppose that any such account would issue in propositional knowledge stated in the form

(M) s means that p

The question is whether we could come up with a story about the proposition expressed by (M) such that knowing that proposition would suffice to understand s. It may seem so, because anyone who understands (M) of course thereby knows what s means--and isn't understanding the sentence just a matter of grasping the proposition expressed by it? Well, that is the standard story but language is more artful than we give it credit for. We have noted that 'p' is used in (M) and a requirement on the truth of (M) is that what goes in for 'p' translate s, and anyone who understands the sentence knows this. So clearly knowledge of the meaning of (M) puts on in a position to know s in virtue of being able to match it to a sentence in his language that he understands already. And in fact I think that is the way these sentences function to give us understanding of s. Suppose you want to deny this. Then you want to say that the proposition expressed does the work. What is the proposition expressed? If we think that 'that p' is say a term that just introduces a proposition into the proposition expressed by (M) in an "argument position" (is there any way of getting away from the idea that propositions are the shadows of sentences?) then it is clear that if understanding a sentence is grasping the proposition expressed by it, we can understand that proposition without understanding s, for let ' Bob' name the proposition expressed by s, and (M') expresses the relevant proposition:

(M') s means Bob.

We might appeal to a Fregean sense as a mode of presentation of the proposition in question and say the proposition expressed by (M) is individuated by the relevant sense of 'that p' in the relevant position in the proposition. But what is this mode of presentation of a proposition the grasp of which guarantees grasp of the proposition of which it is a mode of presentation? For it to do the intended work, it has to present the proposition under a mode of presentation that does not involve picking it out relative to a sentence one already understands. But so far this is only a placeholder in a theory for which no content has been provided. There is nothing that will do the job. You might get someone to understand a sentence by showing him its use. But if you want to state something understanding of which ipso facto suffices (not by way of allowing him, for example, infer, given what you've said, other things that give him the requisite insight) you will have to make use of a device that amounts to using a sentence he understands with, in that use, the same meaning as the sentence whose meaning you are trying to convey.

If this is right, then the conclusion to draw is that a compositional meaning theory, with the aim of producing meaning theorems, can't get around at some point the need of the theorist to rely on antecedent knowledge of a language to come to understand the language being treated. But this does not, in line with what I said above, undercut the explanatory aims of the theory.

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