Davidson: Truth and Meaning

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Continuing the discussion from Davidson: Actions, Reasons, and Causes, I’d like to move on to Davidson’s ideas concerning meaning.

The paper being considered is Truth and Meaning. The pretence is that of building a theory of meaning from as few presumptions as possible. Davidson begins by noting that while we have a finite vocabulary, we are able to construct novel and innumerable sentences. Hence, the meaning of a sentence must somehow depend on the meaning of constituent words. The question considered in this paper is what a theory needs in order for this to be so.

His first approach is to consider the consequences should we assign some entity to each word, called its “meaning”. The meaning of a sentence would then be somehow derived from the concatenation of those words. We want to analyse a basic sentence like “Theaetetus flies”, so we assign meaning to the words - Theaetetus to “Theaetetus”; and flies to “flies”… and concatenation (writing the two words side by side) is the only syntactic resource we’ve used to build the sentence; so the concatenation somehow gives a meaning to the sentence “Theaetetus flies”; the concatenation has some semantic place in the construction.

The idea here is no so far from a naive notion often proposed, that the meaning of a sentence is given by what it refers to.

So now we need to go to the next step, and explain the place of the concatenation. If meaning is assigning entities to words, then what entity do we assign to “concatenation”? But before you answer that, notice that whatever answer you give, you will then need to explain its role in giving a meaning, and so on.

There’s the regress to which Davidson points. Although unnamed, it’s an instance of Bradley’s regress. The general form is that if we seek to explain how say A stands to B, by claiming they are related by C, then we are faced with explaining how both A and B stand to C; and if our answer is that they are related by D, then… well, you get the idea.

The problem isn’t dissipated by Frege’s treatment. What does “The father of…” mean in “The father of Annette” is not settled by what it refers to, since “The father of…” must do the same trick twice in “The father of the father of Annette”. It can’t explain the progress from Annette to her father to her grandfather. The conclusion is that assigning some entity to every word is insufficient to our task; we also need some account of the way these entities are combined.

So it seems that just assigning an entity to each word won’t get us quite to what we want.

But we now have in outline the sort of theory we are working with. We want to give the meaning of any sentence, and in terms of the structural elements of that sentence. The theory at hand is that we set out each of the structural elements of the sentence, and that to which they refer: t refers to x. So “The father of Annette” has a referent, despite “The father of…” not having a referent; it instead has a structural place within the sentence that serves to fix the referent. The sentence does the referring, not the structural elements. “The father of” doesn’t refer, but “the father of Annette”, the complete term, does.

So we have in outline a theory of meaning in terms of reference. Now comes a more infamous difficulty, the slingshot.

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Morphemes? The smallest unit of language that has meaning can be phrasal, like “the greenery of”. Some referents are more complex and require multiple words to sign.

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Sure, use morphemes if you like. Whatever atoms one choses the structure can remain the same. From finite resources we generate innumerable novel sentences. Any successful theory of meaning must be able to account for this. The task at hand is to show how the meaning of a sentence can depend on those atoms.

So to the next point: if the idea is that such atoms stand for something, what is it that “the greenery of” stands for? What entity does it refer to? And the answer seems to be - nothing.

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I’d only be repeating myself because you don’t seem to accept my interpretation of the issue.

Every word has a meaning i.e. every word in the dictionary has a meaning. The sentence, “a cup on the desk” is meaningful because we know what a cup is and what a desk is and the sentence describes how the 2 are in relation to each other. There are other words but you must’ve picked their meaning up while learning grammar.

Compare the sentence above to, the camera is on the car. Think of it as spoken in Jesus’ time. It would be meaningless because cameras and cars didn’t exist back then; one of several issues with religions.

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Where do the meanings for abstract objects come from such as God, mind or consciousness?

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We are no where near looking at such things yet.

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I see. Will keep monitor the progress.

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So we know “cup” stands for cup and “desk” for desk. What does “Is on the” stand for? Also, why “a cup on the desk” and not “the desk a cup on” or “on the desk a cup ” , and how come “the desk on a cup” might mean something quite different, simply because of the word order? The order of concatenation has significance. Hence “the concatenation has some semantic place in the construction”. If the meaning of a sentence were built up from the meaning of the words alone, this would not be so. And if so, and we are going to say that the word order stands for something, Bradley’s regress threatens.

So meaning can’t be explained by “standing for” all the way down.

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Davidson uses the slingshot here to block one way of treating the meanign of a sentence as what they stand for.

In another paper, True to the Facts, he uses the slingshot to shoot down correspondence theories of truth. That’s a seperate issue.

The use here is pretty straight forward. The argument has two premises: Two terms that are logically equivalent have the same referent; and if in some sentence we swap one term for another with the same referent, then the reference of that sentence does not change.

While Frege treated sentences as referring to truth values, the argument here is generalisable to whatever a sentence might refer to.

The argument begins with one sentence, “R”, and using two premises shows that the referent of “R” is the same as that of another sentence, “S”. That is, it shows that all true sentences refer to the same thing.

Here’s the argument:

  1. R
  2. x̂(x=x·R) = x̂(x=x)
  3. x̂(x=x·S) = x̂(x=x)
  4. S

Read x̂(x=x·R) as “the class of things x such that x=x and R”. x̂(x=x·R) picks out the universal class if R is true, the empty class if R is false. Notice that here, we are considering the case that the sentence R is true. Hence x̂(x=x·R) = x̂(x=x). (3) and (4) just show the reverse, for any other sentence. Hence any true sentence stands for the same thing as any other true sentence. A parallel argument can be constructed for false sentences. Hence

…any two sentences have the same reference if they have the same truth value. And if the meaning of a sentence is what it refers to, all sentences alike in truth value must be synonymous - an intolerable result.

We do treat sentences as refering to their truth value, in for example propositional calculus. The slingshot as used here does not refute “sentences refer to truth values.” It refutes the identification of meaning with reference.

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So by the middle of p. 306, we have three objections to analysing meaning in terms of reference.

  1. The structure of sentences plays a part in their meaning, but if it is treated as referential, Bradley’s regress ensues.
  2. Parts of sentences such as “The father of” have no referent until it is included in a sentence.
  3. If meaning is reference, all sentences alike in truth value are synonymous.

The simple view that we build up the meaning of sentences from the referent of the words they include cannot be maintained. Nor will it do to suppose that the meaning of a sentence is reducible to the meaning of its words, since it is no help to be told that the meaning of “Theaetetus flies” is “Theaetetus flies” (bottom p. 306).

But we have the outline of the sort of structure we are after… For a given sentence “s” we are looking for a theory that generates a sentence of the form “s means m”, where s is a structural description of “s” and m is a singular term referring to the meaning of s.

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An observation: Word order matters in cases like, “man in room” and not in cases like “John and Sandra”. These are linguistic matters that have semantic import.

Some words like “of”, “in” are relational words and if they refer to something, like “violin” does, it’s relations.

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Has anyone in the analytic tradition actually proposed such a theory?
Just a question of fact. My reason for asking is that it feels very like a straw argument.

Thanks for the explanation. I wasn’t at all sure how to read his notations here.

I’m bothered by the meaning (!) of “refer” in this context. It is intuitive to me to think of “the father of S” as referring, not only to the father of S but to S. It is not intuitive to me to say that sentences refer to anything, except in virtue of any referring expressions they contain. This seems linked to fact that referring expressions (like other words) are only meaningful in the context of the sentences that contain them.

Quite so, but then don’t the limitations of propositional calculus suggest that even if this is convenient and useful for some purposes, it is not the whole story.

But while it is true that we treat sentences

I can’t help wondering whether we should not have a rider here, to the effect that, in the case of referring expressions, the meaning of the expression is the object referred to. (But the meaning of the expression includes the criterion that picks the object out.)
I have in mind here Wittgenstein’s discussion of shadow objects in the “Blue Book”. When I expect someone to arrive at 4:00, it is them I expect, nothing else.

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The next example is close to one alluded to earlier in this thread. Suppose we have the syntax of our language, and a dictionary in which we can look up the meaning of a word. We can get recursive stuff going, like we did with “the father of”, so do we get a set of rules that allow us to parse any expression? We can identify the meaning of “The father of the father of the father of Angela” by such an iterative process.

Do the rules of syntax and a dictionary amount to a theory of semantics?

Davidson’s reply is that while this works for “the father of” it doesn’t work for “believe”. The syntax is iterable: Adam believes that Beth believes that Cath believes that the tree is big; the semantics - well, the belief in this is Adam’s, not Cath’s. Each syntactic iteration does not build on the previous, but replaces it with an entirely new sentence.

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Frege, Early Wittgenstein, Russell, all had something along the lines . Yes, it is a set piece, but with substantial background. Treating sentences as referring to their truth value is Frege.

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  1. I don’t see the interesting bit - the explanation how each element of the sentence contributes to its meaning. or is that the province of the theory and the structural description?
  2. How does this not just revive meanings as objects?
    (I am feeling my way to an objection that Davidson is looking to produce more to more language to explain semantics. But I don’t see that language is capable of explaining anything here. But that’s because I’m used to the idea that meaning is use. If it is, then surely semantics should consist of an explanation of the use of the symbols. But there is no reason to suppose that more and more language will do this. The classic solution or example is ostensive definition which, by definition, mediates between language and the world.)

I’m sorry if these are dumb questions.

  1. It would be a systematic description of the semantics of the relevant language. It would likely lead to some interesting questions why this is so and that is like this. But what are the questions that it is designed to answer?
  2. If it is right that logical notation is a meta-language enables us to describe the structure of sentences, what would be needed to describe semantics? I don’t suppose that a natural language would do. That would be a circularity, wouldn’t it?

I don’t see anything wrong with this. Belief has a structure that is different from “father of..”. Why is that a problem?

Another chunk of philosophy that I have forgotten, or possible never knew. OK. I’ll look up about it.

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I’m pleased at least some folk are following along. We have a fair way to go. Have you read on, to see where we are headed?

These are so far general considerations about what a theory that gives the meaning of a given sentence might look like. He began with the observation that it must account for how innumerable sentences are built from a limited vocab, looked at and rejected the suggestion we could do this by having words stand for things—basically treating all words as names, because the concatenation is itself playing a role in providing meaning; that is, we have to consider the sentence structure as well as word meaning.

At p. 307, is a skeletal notion of what a suitable theory of meaning might provide; for any sentence “s”, we want our theory to provide a sentence in the form “s means m” where “m” is a singular term setting out the meaning of “s”. What’s “interesting” here is that this provides a general form for any successful theory of meaning.

Where we are now, at p. 308, is with the further point that we need more than a simple list of word meanings and a syntactic structure.

Speaking roughly, the problem now at hand is that while we must account for how a finite number of words allow us to generate innumerable sentences, we must also admit that often we need the whole sentence, not its parts, to fix meaning—that it is often the case that knowing the meaning of the words alone is insufficient to give us the meaning of the sentence. Our theory seems to involve us in approaching meaning from both directions at once.

Let’s proceed, and see where this leads.

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We not only often only understand the meaning of a word because of its place in a sentence, but also understand the meaning of a sentence form its place in a language; hence:

If sentences depend for their meaning on their structure, and we understand the meaning of each item in the structure only as an abstraction from the totality of sentences in which it features, then we can give the meaning of any sentence (or word) only by giving the meaning of every sentence (and word) in the language.

This is an appeal to our theory having maximum generality; to its applying to the whole of a language, else it is inadequate.

We also see the appearance of the term “interpretation”:

While there is agreement that it is the central task of semantics to give the semantic interpretation (the meaning) of every sentence in the language, nowhere in the linguistic literature will one find, so far as I know, a straightforward account of how a theory performs this task, or how to tell when it has been accomplished.

It’s worth noting a difference here between the task of explaining meaning, as addressed by the likes of Wittgenstein, and the task Davidson sets, of giving a theory that interprets our sentences by giving more sentences. There’s a difference in the task at hand here; for want of a better phrasing, Davidson is avoiding trying to get outside of language - as Wittgenstein does with use and showing. The theory stays inside language in the sense that the output of the theory, for any s, is itself a sentence.

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So we have “s means m” where m gives the meaning of s, for whatever we are to make of “the meaning of”. The next step is to recognise that m will be a sentence, giving the meaning of “s”. So we replace “m” with “that p”, where p is a sentence that gives us the meaning of “s”. There’s a note that it’s “s means that p” and not “s means p”; the former would be just a name for “s”, the latter has structure.

The next consideration is, what to do with the ambiguity of “means that”, and here Davidson’s answer is audacious. We have “s” as a sentence in the language we are discussing, the object language; and “p” as a sentence in the language of our theory, the metalanguage. What might work is “p” just being “s”, or an interpretation of “s” in the metalanguage.

Given such a structure, we might take the further step of using the extensional tools we have at hand, those connectives found in logic and which are clearly understood. Since we want symmetry between our object and metalanguage, the obvious candidate is material equivalence, “if and only if”, the truth-functional connective that is true only between two true sentences.

So in our metalanguage we want to name an object sentence, “s”, and assign to it an interpretation, p. Of course, “s” is not truth-functional in the way that is required by “if and only if”, so we need a suitable predicate, let’s say “T”; putting “T” in place we have

(T) s is T if and only if p

I hope this is recognised.

So what are the minimal restrictions on our predicate “is T”? We don’t want it to alter “s” in any way; just to set it out… we want T, in other words, to be true exactly when “s” is true…

What we have here has much the same structure as Tarski’s T-sentences. “T” is truth. But Davidson has come to this via a quite different path. In particular, were Tarski held meaning as fixed and used it to analyse truth, Davidson is here holding truth constant and using it to analyse meaning.

It might appear that this is all a bit too easy, that Davidson was headed to Tarski and is somehow being duplicitous. If you feel that way I’d invite you to read the text again, and notice that he is quite explicit as to his ends throughout, that he’s not anywhere thinking “Tarski has this schema, let’s pinch it!” but rather coming to the same structure via a separate line of thought that stands on its own, independent of Tarski until the last.

There’s much more to come, of course, by way of explanation. But here we have a rather neat rendition of the appeal of truth-functional semantics.

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I can imagine managing a formal “semantics” this way. I thought about writing something in symbols, but it’s easier to understand it this way:

Joe believes ( Jill believes ( Joe is-the-father-of Jill))

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Fun issue !

I seem to recall Husserl acknowledging that we “see” relations. I tempted to say that “is on the” has the same kind of significance as “cup” and “desk.” I see us trained to “quasi-identify” sounds and household objects. The sound “chair” is “not really” the chair, but it is pragmatically “tied” to the chair. I make the sound and people look at the chair. I don’t recall you liking my fuzzy thesis in “cry me an eagle.” But I still smell a quasi-copula here.

The word order issue is fun too. In practical situations, we often “fix” what we here. The context resolves nonsense into sense.

To me it looks difficult indeed to preserve meaning while trying to stay within language, but I can see an approach in terms of equivalence. Of course this is what formal logic does. You start with a list of “truths” and add to the list according to rules.

Perhaps you’ll agree that we don’t need “truth” at all in the formal context. We can just make rules for extending a list of theorems. I wouldn’t be surprised if you already mean “truth” in this very formal way.