Truth and Meaning in Davidson

Introductory Post

This web log will be used in conjunction with the Kompaktseminar on Truth and Meaning in Davidson: A Critical Assessment in Heidelberg from February 8th - 12th, 2010.  Links to basic information about the seminar and to some associated readings will be in the left hand column.  Links to handouts and any other materials for the course will be in the right hand column.  I will use the web log to make posts that follow up on or clarify issues that come up in the seminar discussion.  Comments will be open on all posts except those that provide organizational information.

The Group Photograph

In what way is a truth theory that meets Convention A superior to one that meets only Convention T?

 

Benjamin Börschinger sent me some questions by e-mail which I have been wanting to respond to.  I think the main question might be put in the following way:

If meaning facts are exhausted by the facts about sentence meanings, as Frege’s Context Principle--which holds that one should “never ask for the meaning of a word in isolation, but only in the context of a proposition”--would seem to suggest, then once we have accounted for the correct interpretations of sentences, what work is there left over to do?  To say that there is work left over is to say, is it not, that the facts about word meaning are something over and above the facts about sentence meaning and so to deny the Context Principle.

So the idea is that if a meaning theory meets Convention T, then it makes the correct assignments of meanings to sentences (the inference to the corresponding M-sentence makes this explicit).  But if there is no more to word meaning than contribution to sentence meaning, everything that needs to be said has been said.  End of story.  Convention A is either trivially satisfied or cannot be an intelligible constraint on a meaning theory.  (It is possible, though, to meet Convention T without meeting Convention A.  An example is given in the post on inscrutability, and there are more complicated examples.  You can add stuff to satisfaction axioms and then do things to strip them out before you get to T-sentences.)

I think the resolution of the puzzle lies in a closer look at the Context Principle.  Why say what Frege does?  Why say, that is, that one should never ask for the meaning of a word in isolation but only in the context of a proposition?  What does this come to?  Here is how I understand the point. 

The basic unit of linguistic understanding is the speech act, for the speech act is the minimal move in the game of conversation.  Speech acts divide into five basic kinds (here I follow  Searle’s taxonomy).  There are assertives (the moon is full), directives (take out the trash), commissives (I promise to be there), directives (you’re fired), and expressives (would that you were here).  All specifically linguistic meaning relates to the performance of speech acts and is understood in terms of its contribution to them. 

There is no reason we cannot use single unanalyzable symbols as conventional ways of performing speech acts with a certain content.  Signals flags often function this way. 

The following flag, for example, when used alone, functions as an unstructured sentence that means ‘Man overboard’.

It is plausible that the first symbol systems used for anything like speech acts were unstructured and relatively limited in expressive potential for that reason.  But they nonetheless can get the basic work of communication done because that involves the recruitment of a certain observable act or the product of such an act to perform a certain role with respect an appropriate audience, such as the conveyance of information (something that presupposes both sincerity and competence on the part of the speaker).  This requires a shared understanding on the part of both the utterer and the auditor with respect to the circumstances under which the act (either token if there is a one off use anticipated, or type if it is to be used for recurring circumstances) is  to be performed.  It is this that allows the act token or type to be recruited for the function of, say, indicating something: the speaker and auditor know the speaker is to utter it only if such and such a thing obtains.  The uttering of it, taken as a matter of participation in the agreed upon practice, then (fixing sincerity and competence) is taken as an indicator of the relevant circumstances, and the speaker may be said to have represented it as being so. 

Where do words get in the picture?   Words have a linguistic purpose only relative to their contribution to the basic business of conversation, i.e., to the production of speech acts with certain contents.  Their point is to make the symbol system we are using more flexible, more powerful, and more expressive.  Take a very simple innovation, the introduction of subject-predicate structure into sentences.  This rests of course on an antecedent conceptual distinction between objects and properties (for purposes of exposition I’ll put aside nominalistic scruples).  Say previously I had used an unstructured symbol to perform the speech act whose content is: man overboard.  Now I conceive that it is useful sometimes to perform a speech act where what I say is some particular or other is overboard, Tom, or Jen, or the ship’s clock, and the like.  There can be displacement of objects overboard in all of these cases, but different objects for the different cases.  I conceive of introducing a two component system of symbols.  I will always, say, hold up a red flag when something is overboard, but then hold up another flag with a shape on it that resembles Tom, Jen or the ship’s clock depending on which it is that I want to indicate is overboard.  It is then the tokening of the complex symbol that does  the work of indication (relative to the assumptions of sincerity and competence)—all of this presupposing the speaker and audience have a shared understanding of how they are to be treated.  Clearly, given this, the introduction of a new flag understood to function like the Tom or Jen flags immediately gives one the ability to say of the newly named item that it is overboard as well.  And the introduction of a new flag that is understood to function like the overboard flag, perhaps a green flag for onboard, immediately gives one the ability to represent a range of things as onboard.  So in this simplified context, what does it come to to say that we should ask after the meaning of a word only in the context of a proposition?  It means that its function relative to the basic task of linguistic communication is to be understood in terms of what its systematic contribution to speech acts performed in accordance with the conventions attaching to it is.  What is the meaning of the red flag in our symbol system?  Well, how does it function to contribute to speech acts?  It is used in all and only speech acts (exploiting the symbol system) whose content is to the effect that some particular thing is overboard.  I.e., it says of things that they are overboard.  What about the flag with the Tom-shape?  It is used in all and only speech acts (exploiting the symbol system) which say something about Tom.   That is the basic meaning of the Context Principle.  The Context Principle does not say that only sentences have meanings; words do as well but their meanings are to be understood in terms of what they are supposed to systematically contribute to the speech acts performed using sentences in which they appear. (Of course, someone might have more in mind by the Context Principle, but I do not.)

When people learn a natural language, they acquire of course a mastery of its semantical primitives.  They learn how they are combined so as to be used to say various things (assert, command, question, promise, etc.).  They don’t acquire explicit knowledge of the rules that govern them but rather a kind of skill in deploying them and interpreting them in accordance with the rules implicit in the practice in their community.  There is no question that understanding of sentences rests upon understanding in this sense of words.  When you hear a completely novel sentence in any of the languages you understand, you understand it on the basis of your prior mastery of its component expressions and the rules governing them in the language.  This is completely compatible with saying that the meanings of the words are to be understood in relation to their contribution to sentence meaning.  It is because the meanings of the words are understood in relation to their contribution to sentence meaning that we can understand novel sentences on the basis of prior understanding of words. 

None of this is to say, of course, that in acquiring a mastery of words in a language, we do so independently of learning sentence meanings.  We learn both at the same time, for what it is to learn the words cannot be divorced from understanding their contributions specifically to sentence meanings, and so what combinations of them with other words mean as sentences.

Now let’s return to Convention A and Convention T (and for convenience I’ll subsume the extension to a context sensitive language under the same heading).  What would a truth theory that met Convention T but not Convention A be missing? 

A truth theory for a context sensitive language meets Convention T (i.e., the extension of Tarksi’s Convention T) provided it is formally correct and it entails for every sentence of the object language a theorem of the form

                s is true(s,t) iff p

which yields a true sentence when ‘is true(s,t) iff’ is replaced by ‘means(s,t) that’.  Such a theory would enable us in a straightforward sense to interpret every object language sentence. 

I said, however, that there was another goal that the theory was to meet.  That was to provide insight into the compositional structure of object language sentences and to capture or represent in some sense the “structure” of a complex practical ability.  It is relative to this latter goal that we require more of a truth theory that is to serve its role in a compositional meaning theory than just that it meet Convention T.

What more do we want?  We want the truth theory to provide us with a kind of model of competence.  As I put it in an earlier post (The content of a meaning theory and knowledge of a language):

“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 taken to express what the competencies are competencies in doing.”

The axioms express rules for the use of words.  The canonical proofs show how they contribute in virtue of the rules that govern them, interacting with those that govern other words they combine with, to determine their contribution to the conditions under which the sentence containing them is true, in virtue of the meanings of the contained expressions. 

But if the axioms are not interpretive, that is, if the theory does not meet Convention A, then they will not model speaker competence, and the theory will not meet one of our goals.

So that is the answer to what more meeting Convention A adds, and what is missing from a theory that meets Convention T without meeting Convention A. 

How does this meet the initial puzzle about the Context Principle?  I think that dissolves once we see what that really comes to.  To say that words are understood in relation to their contributions to sentence meaning, so that that is the canonical way to ask after what it is that they mean, is not to say that we are not interested in exactly how they do that.  And meeting Convention A is supposed to guarantee, relative to a canonical proof procedure, that the truth theory will help do exactly that.

 

Loose Ends Will Be Cleared Up

This is just to say  that I have it in mind to address a number of issues that came up in discussion over the week in posts, but have not had the time to do so yet.  So if you want to you can check back in about a week for more follow  up.  I'll leave the site up also, and I am planning on posting at least a few pictures from the seminar, in particular the group pictures at the end.

Thanks so much to everyone who participated.  I enjoyed everything, even the snow.

The content of a meaning theory and knowledge of a language

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.

Inscrutability

Inscrutability of reference is the thesis that we can scramble the referents of singular terms and extensions of predicates freely so long we preserve the distributions of truth values across sentences without thereby affected the adequacy of the theories as theories usable for interpreting object language sentences.

 We can see right away that the crucial issue has to do with the claim that preserving the distributions of truth values across sentences suffices for preserving adequacy for interpretation.  Since we know being true is not ipso facto adequate, it is a mystery why anyone would accept this.  Even if we required that the scrambling be compatible with maintaining the lawlike status of the theorems there is no reason to think it would preserve interpretability.  And even if it preserved lawlikeness there is no reason to think that such a theory would be equally confirmable -- in the first instance -- from the standpoint of the racial interpreter.

 Having said all of that, let us take a quick look at some of the issues that came up in discussion in regard to the use of the permutation function and what you can do with the theories generated from it.

 First, the standard story: Let P(x) be a permutation function.  For  every object x, it maps it to just one other, and every object has some object mapped onto it, and not every object is mapped onto itself.  if P(x) = y we say that y is the image of x under the permutation.  For a set or extension {x, y, z, ...} we say that the image of the set or extension is the set consisting of the images of each member of the first set, {P(x), P(y), P(z),...}.

 A reference scheme is a set of reference and satisfaction axioms for a truth theory.  Let our starting scheme be R.  Take some sample reference and satisfaction axioms.  (I'll use square brackets as Quinean corner quotes, forming a description of a expression in terms of the concatenation of the enclosed elements.)

 R

 1.      Ref('KL')=Kirk Ludwig

2.       For any function f, f satisfies 'phil(x)' iff f('x') is a philosopher.

3.       For any name N, function f, f satisfies [phil(N)] iff ref(N) is a philosopher.

Sample canonical T-theorem.

 4.       'Phil(KL)' is true iff Kirk Ludwig is a philosopher.

Now we  construct a new reference scheme R' using P.  On R', every proper name in the object language is assigned as a reference the image of its reference on R.  If 'N' is the original name used in the metalanguage to give the referent of a given object language name, let 'N*' be  the metalanguage name used on scheme R' to assign to the object language name its new referent.  Every predicate is said to be satisfied by an object just in the case a predicate is true of it whose extension is the image of the extension of the predicate used to give the satisfaction conditions on R.  If 'F' is the original predicate, we let 'F*' represent the predicate we use on the new scheme whose extension is the image of F.  Then for our corresponding axioms, on R', we have

R’

1’. Ref('KL')=Kirk Ludwig*

2’. For any function f, f satisfies 'phil(x)' iff f('x') is a philosopher*.

3’. For any name N, function f, f satisfies [phil(N)] iff ref(N) is a philosopher*.

Canonical T-theorem:

4’. 'Phil(KL)' is true iff Kirk Ludwig* is a philosopher*.

Given the construction, we know that

5. Kirk Ludwig is a philosopher iff Kirk Ludwig* is a philosopher*,

and so we can be sure that we have preserved the truth value of this, and, as it turns out, every other sentences in the object language.

I complained that this was not interpretive, and in particular that the T-theorems of the new theory would NOT be interpretive if those of the old one were (and vice versa for that matter).

Miguel suggested that if the only goal was to provide a theory that met Convention T (or the appropriate analog for a natural language) then we could mess with the reference scheme and still get a a theory that worked in that sense.

Miguel suggested (I believe) the following.  Let us illustrate with just the axioms we’ve given as examples.  1' is drawn from R', and 2 from R, and 3'' is the new axiom and 4’’ the new T-theorem.  Let PI(x) be the inverse of P(x), i.e., if P(x) = y then PI(y)  = x.

R''

1'. Ref('KL')=Kirk Ludwig*

2. For any function f, f satisfies 'phil(x)' iff f('x') is a philosopher.

3''. For any name N, function f, f satisfies [phil(N)] iff PI(ref(N)) is a philosopher.

Canonical T-theorem:

4''. 'Phil(KL)' is true iff PI(Kirk Ludwig*) is a philosopher.

Given that PI(Kirk Ludwig*) = Kirk Ludwig, and assuming a direct reference theory of proper names, 4'' is equivalent to our original 4.

So this is an illustration of a theory that doesn’t meet Convention A but does meet Convention T.  Does it show inscrutability?  No, for in giving the goal as meeting Contention T and admitting it requires reproducing the original (whether or not we know a change of truth value has occurred) means that we are tacitly accepting that meaning (in the relevant dimension) varies with extensions of contained terms.

I suggested we might get something going with our original R' to prove interpretive T-sentences.  But I don’t think it quite works now.  Here is the idea.  We don’t achieve the right result with the canonical theorems, using the same canonical proof procedure.  But if all we want is that the theory satisfy Convention T we might try to add some additional axioms, for example, like 5, which would enable us to get from 4' back to 4, after all.  Well that works if we add 5 to get back to 4 from 4', but that’s just for one of the many cases we want to treat.  If we had to add one for each T-theorem the theory would not be finitely axiomatizable.  With the permutation function in hand we could always use the inverse to produce a predicate  that would have the extension of the orginal, but extension is not guaranteed to preserve meaning.  We’d have to be able to recover  predicates the same in  meaning.  Is there a way?  I suppose if you add enough there is.  For example, we could add the original theory to the new one and then there would be a route from the new T-theorems to the old!  But that would not be very interesting.

Truth-theoretic Semantics and Speaker Competence

What is the relation between truth-theoretic semantics and speaker competence? 

We distinguished between what I called the initial and extended projects in Davidson's work.  The first question in this connection is which of these projects we have in mind here.  The initial project aims to shed light on the compositional structure of natural language, but not to say what it is for the semantical primitives of a language to mean what they do.  The extended project may be thought of as addressing the general question "What is it for words to mean what they do?"  It subsumes the first but also addresses the question of what it is for the primitives of a language to mean what they do.  The first only aims to illuminate the connection between the primitives and the complexes. I will consider only the initial project here, the project of giving a compositional semantics for a language.

This aims to do the following: (a) to "give the meaning" of every object language sentence (b) on the basis of axioms attaching to primitives  which reveals how the primitives contribute to fixing what those sentences mean.

Truth-theoretic semantics is one way of trying to implement this aspiration.  I've described it as employing an ingenious bit of indirection.  The idea is to exploit the recursive machinery of a truth theory to link axioms attaching to semantical primitives, where we use metalanguage terms which interpret the object language terms for which truth/reference/satisfaction conditions are being given, via proofs that draw only on the content of the axioms, to T-sentences in which the sentence in the metalanguage used to give truth conditions for the object language sentence interprets the object language sentence.  This is a way of satisfying the goal specified in (a) and (b) -- relative to appropriate knowledge about the truth theory, as we have been saying.  A benefit is that it does it without appeal to assigning entities to every expression (a silly idea on the face of it).  An additional and important benefit is that it shows something about the connection between meaning and truth in a systematic way.  We see in each step in a proof the contribution of a particular object language expression to fixing the interpretive truth conditions of the sentence containing it.  The axiom for each is employed, and so we see for each object language expression in the sentence how it contributes to fixing the interpretive truth conditions of the sentence.

What is the relation of all of this to semantic competence?  One might disclaim any ambition to say anything about what competence in the language comes to, other than that it of course respect the output in the sense of requiring competent speakers to interpret sentence as the theory says.  At times Davidson talks as if he has nothing more in mind.  But whatever the case with Davidson, I think we learn more.  But what?

First, what we don't learn: we  don't learn anything about how a speaker's competence is realized (ipso facto, anyway), in the sense of what realizes the speaker's dispositions to use words as he or she does.  It is no part of truth-theoretic semantics (as I understand it) to say anything about that. Someone might have that project and fold truth-theoretic semantics into it.  This is what Larson and Segal do in their book Knowledge of Meaning.  They suggest that semantic competence consists in a speaker's propositional knowledge of a truth theory.  This clearly goes beyond what could be gleaned from just keeping track of how speaker's use words.  It is an empirical hypothesis about how the competence speakers have is realized--an implausible one.  (Anyway, how would we confirm or disconfirm it?  We might find particular rules suggested don't match the speaker's dispositions.  But suppose a perfect match.  Then consider the hypothesis that the competence is physically realized and that there is NO level of description of the speaker at which there is any explicit representation of the axioms of the theory.  The speaker is not supposed to have conscious access to any of his knowledge.  So what favors, what could favor, accepting the L&S sort of account over the more minimalist view?) 

But truth-theoretic semantics does have a clear relation to speaker competence, particularly if it is thought of in the way I have urged, for it aims to reveal the structure of what is known by a competent speaker of the language.  So: in what way?

Think of it this way.  For a competent speaker, each word in her language is one that she knows, i.e., is competent in the use of.  This amounts to having an ability to use it in conjunction with other words in the language to say various things (to keep it simple, we ignore nondeclaratives).  That ability is sensitive to what contribution the word makes to fixing the conditions under which any sentence containing it would be true .  Each axiom of the theory gives a rule for the use of an expression in the object language.  They specifies how the word contributes to fixing interpretive truth conditions for the sentence.   In seeing what that rule is, we see also what having the ability to use the word comes to in a very detailed way.  For each axiom for a primitive, there corresponds in the speaker a skill in using the word, and what the skill is a skill in doing is expressed precisely by the rule given by the axiom.

Take conjunction as an example.  Ignore quantifiers for the moment.  We then give the following recursive rule:

For any sentences X,Y, X+'et'+Y is true iff X is true and Y is true.

What does this show about the skill a speaker of the language in the use of the word?  It shows that the speaker will be prepared to assert (if she wishes to be sincere) a sentence of the form 'X et Y' only if she accept both X and Y; that if she accepts 'X et Y' then she will assent to X and assent to Y, and that if she assents to X and assents to Y, then she will be prepared to assent (other things being equal) to 'X et Y'.  (It is more complicated with quantifiers and noun and verb phrase conjunction, and additional complications are added with interrogatives and imperatives, so this just illustrates a small part of what the competence really comes to--but in the full theory all is captured.)  This is not something of course that the axiom says.  It is something we glean from the axiom, knowing what it says, and knowing that the axioms meet Convention A.

One might say the following: okay, but this is trivial.  What is trivial?  It is trivial that if you set up the truth theory as you suggest, and know what you say, then the axioms express rules that are realized in the skills the speaker attaches to them in the way you suggest, and we can articulate it in the fashion you indicate.  Okay: but sometimes trivial things have to be explained before we grasp them. 

In any case, it is an empirical project to develop for a natural language an adequate representation in this form of what it is to have the skills relevant to speaking the language.  And that is very far from being trivial, for it involves articulating what is merely implicit in how we use words, and it is a delicate and difficult task to trace out what all is contained in that, and see through the "haze of usage" (Higginbotham) to the contribution specifically of semantic competence.  We look at actual use, we use thought experiments, we ask ourselves straight out whether one thing entails another, whether this and that can be said truly at the same time, what in our reactions is due to what our words mean as opposed to reactions to pragmatic implicatures or an affective reaction to a case, and so on.  Carrying out the project successfully will tell us a lot about what the skill we have in possessing a language comes to.  It amounts to giving a reflective account of that skill, which is something we certainly don't start out with, and is not easy to attain.  And this is what it comes to, as Dummett put it, to give a theoretical representation of a practical ability, by developing an interpretive truth theory for a natural language.

What about the relation of this project to what realizes the competences we possess in possessing a language?  You would think you'd want to complete this one first, for if you don't have a detailed representation of the competence whose realization you are trying to give an account of, it's going to be hard to say how it is realized. 

Does Knowledge of a Compositional Language "beg the question"?

I  wanted to at least record the worry raised by Miguel at several points and in several ways about whether we could get a perfectly general understanding of compositionality as a feature of natural languages if we had to presuppose (in some sense) that we had such a language in order to know about a particular language how it  worked compositionally.

The problem, if I have it right, is supposed to be akin to, say, trying to respond to the skeptic about the external world in the way that Moore  does in his "Proof of an External World," by holding up each of his hands in turn and saying 'Here is a hand' and concluding that there are external things.  The skeptic points out that his knowledge of the premises of his argument presupposes that he knows something about the external world, and so succeeds only by begging the question.  So knowledge of the external world has NOT been explained in general, but only some of it in terms of some other.  There is no explanation of how any knowledge at all of the external world is possible. 

On the other hand, one might say that it is not like that at all.  The objection, one might say, is rather like objecting to someone who speaks a language trying to explain what finite knowledge of rules and syntactical primitives would put one in a position to identify all the grammatical expressions of a language on the grounds that he must know a recursive syntax if he speaks a language! 

Aren't you presupposing understanding of what  you want to explain?  No.  That so and so speaks a language and is explaining what finite knowledge would  suffice  to identify all the grammatical sentences of a language presupposes that he knows (in the sense of being competent in) a recursive syntax for a language.  But that does not mean he has any reflective understanding of his knowledge in that sense. And so undertaking the task  doesn't presuppose that it has already been completed, or presuppose knowledge or understanding (in the relevant sense) of how a recursive syntax turns the trick.  

So which is it?

Convention A and Davidson's Position

I wanted to follow up on the question what Davidson's attitude would have been to Convention A, both with respect to whether it might be thought to be in conflict with the context principle and about whether it might be in conflict what he says later about indeterminacy.

Convention A places a constraint on the axioms of a truth theory that parallels the constraint that Convention T places on its theorems.  The idea is to require the axioms to give reference, satisfaction, and truth conditions for object language expressing using, in an appropriate way, a metalanguage expressions which translates the object language expression.  The point of this is to ensure that we actually start with axioms that express or show what the object language expressions mean, so that in giving proofs of interpretive theorems we exhibit how the primitives contribute systematically to fixing the interpretive truth conditions at each step in virtue of their meanings.

Is this in conflict with the context principle, i.e., the principle  that only in the context of a sentence does  a word have a meaning?  I take the point of this to be that the function of a word in a language is to contribute to what we say or mean in using sentences.  The point of language is to be found in the context of communication and it is the utterance of sentences that serves that point, not of words or other subsentential expressions (except insofar as these are hints as to what sentence or range of sentences might properly to the job in the circumstances--we would not want to deny that people get away with using fragments of sentences for the purposes for which sentences are designed, but this works because we know the functions of the expressions that be constructed from them).  Thus, words have their point in a language in virtue of what they contribute to the sentences in which they can appear.

This is (all of these observations about the import of the context principle), I think, entirely compatible with also recognizing that we do learn words in learning a language -- together with of course a range of sentences, for learning words is to learn their  systematic contributions to sentences -- and then use what we have learned to understand novel sentences, sentences we have never heard before.  The point is about what it is that we learn when we learn words--their systematic contributions to sentences--and it is the fact that  that is what we learn that puts us in a position in fact to understand novel sentences.

Now the idea of Convention A is to constrain the axioms of a theory so that proofs of T-sentences show how the meanings of  complexes depend on the meanings of the parts.  But this also exhibits how the meanings are to be  understood in terms of their contributions to the meanings of the sentences they appear in.  So Convention A does not conflict with the context principle.  This also shows that it does not presuppose that the building block theory of language is correct, the theory according to which we first learn words independently of sentences in which they appear and then come to learn the complex expressions as we go along.

Could Davidson have accepted the constraint imposed by Convention A?  I think so.  In one of the quotations I displayed, he says that requiring metalanguage predicates translate  object language predicates would suffice to have a theory that met Convention T (well, in the general case we need to treat every category of word).  So  I think that so far as the initial project goes, he would have no objection.

What about the later claim that there is indeterminacy of interpretation?  Is this in conflict thinking of the aim of interpretation as being to confirm a theory that meets Convention A as opposed to Convention T?  I think so.  If it is compatible with thinking the theory meets Convention T, why not Convention A, which suffices for a theory to meet Convention T.  How is requiring a theory meet Convention T compatible with indeterminacy?  I think, in the end, it isn't, but let me describe how the story is supposed to go.  Many interpretation in the end are going to be compatible with all the data (and I mean all of the relevant facts).  They all capture the facts of the matter equally well.  They all suffice for interpretation.  They all meet Convention T.  How to understand  this?  The various theories are like different measurement scales for, for example, temperature.  0 Centigrade and 32 Farenheit capture the same facts about the temperature, though they look different.  Well, we'll see whether this really makes sense tomorrow or the next day.  But that's the idea.  If it works for making sense of the requirement compatibly with indeterminacy, then it should work for meeting Convention A compatibly with indeterminacy.

What about a case in which the same T-theorems are proved from different axioms?  I think Davidson would be forced to say that if the theories really did meet all the constraints equally well, they would be equally interpretive, and so both sets of axioms would meet Convention A. 

In "Inscrutability of Reference," Davidson seems to require only that a truth theory have true theorems to be just as good any other.  I think this does not comport well with the rest of his work, and I'll say why when we get to that.  But if that were the standard, I do not think we could plausibly maintain that all the theories that met it satisfied Convention A--but then the same thing, I  would say, goes for Convention T in that case.

I am about to be eaten by a great white shark

Professor Kemmerling raised a question about the claim that

(s)(t)('I am hungry' is true(s,t) iff s is hungry at t)

is interpretive on the grounds that an instance may be something such as

'I am hungry' is true(ludwig,t) iff Ludwig is hungry at t

and 'I am hungry' as used by Ludwig at t does not mean the same as 'Ludwig is hungry at t'.

Why say they differ in meaning?  If two sentences are alike in meaning, they should be intersubstitutable in all (appropriate) contexts salva veritate.  But that isn't true (it may seem) for this pair.  To see this consider a different case.  Contrast (1) and (2).

(1) I believe that I am about to be eaten by a great white shark (as uttered by me at t)

(2) I believe that Ludwig is about to be eaten by a great white shark (as uttered by me at t)

Are the complement sentences synonymous?  If so, then surely if (2) is true than (1) is true.  But suppose I come to believe (2) true because someone yells 'Ludwig is  about to be  eaten by a great white shark' but uses the German pronunciation of my family name.  I  don't recognize it as my name, but I do believe, whoever this Ludwig is, that he is about to be eaten by a great white shark.  Good thing, I think, that I am not  he!

There are lots of proposals about how to handle this.  I like my own, which is in a paper (now or shortly to be in the left hand column) titled "Singular Thought and the Cartesian Theory of Mind."  I maintain that the resistance to the substitution is due to pragmatic factors, but this requires some set up to explain exactly how it works.  So I maintain that the truth conditions are indeed interpretive. 

Suppose you convinced me otherwise.   Then we'd  need  to change the way we give the truth conditions, and how would depend on exactly what more one thought was added to the proposition expressed by the first person pronoun besides the referent of the indexical.

Semantical Primitives

This a brief note on semantical primtives as a follow up to the discussion of that today.  Davidson says: "Let us call an expression a semantical primitive provided the rules which give the meaning for the sentences in which it does not appear do not suffice to determine the meaning of the sentences in which it does appear" (TMLL, p. 9).

I put it this way: an expression is a semantic primitive iff one can understand sentences in which it appears on the basis of understanding sentences in which it does not appear.

These are equivalent for the rules Davidson has in mind are those mastery of which suffices for understanding the sentences in question. If you can understand an expression on the basis of understanding sentences in which it does not appear, then that is because there are rules that apply to significant parts of it which appear in the other sentences and the mastery of which put one in a position to understand the expression in question, and so the expression in question is understood on the basis of understanding its parts and the mode of combination in it.

The primitive expressions are contrasted with complex expressions.  A complex expression is one which is understood on the basis of understanding rules attaching to its parts (understood broadly, for example, tense inflection is  relevant to meaning, so a tensed verb is not a semantical primitive).  We can therefore also characterize a semantical primitive as a term that is not in this sense complex.  

Why does Davidson put it the way he does?  The answer is that (a) it is a very general way of putting it that does make any presuppositions about what sorts of devices can count as primitive in the relevant sense and (b) it is put in terms of rules attaching to (or understanding of) sentences and the meanings of words may be considered abstractions from sentence meaning.