Davidson: Truth and Meaning

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21

Exactly the point. The parenthetical syntax gives the impression of recursion, but that’s not the semantics of belief. Joe’s belief does not contain Jill’s belief as a proper part, since it might be that Jill has no such belief, and yet the statement of Joe’s belief still be true, and meaningful. The semantics drifts from the syntax.
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Husserl’s was no formal logic, not a formal semantics with truth-conditions, compositionality, or a treatment of embedding. It can’t be a rival account here because it isn’t answering the same question. Too far off topic.

22

Ahhh. Ok. Yes that adds another layer of complexity. Joe’s belief about Jill does not imply Jill’s belief.

But then that need not be in the rules. We just can’t automatically believe Joe, snap off it off as a new theorem on the list. We might still encode the belief. Jill’s belief about Joe’s belief might be “true” ? And so on ?

23

The proposition within the scope of the belief statement is the content of the belief, not its object. The belief does not have parts.

24

If we are talking about formal systems, then that is up to us. It’s your show, of course.

Presumably a belief here would formalize an assertion.

For instance, x is the father of y. So xFy, where x and y are people.

Then we could also have xBa, where x is a person and a is an assertion.

Then we might use xB(yFz) to formalize that x believes that y is the father of z.

Does xFy have parts ? We can change out fathers and sons. So some might say yes. But it’s a formalization, so it’s whatever we decide.

I thought the point was to dig into the relations of words-as-parts functioning within assertions ?

25

You will be aware of the difficulties of parsing belief statements.

Propositional Attitude Reports shows how words within the scope of a propositional attitude verb don’t function as they ordinarily do outside those contexts.

It seems odd to me that of all the stuff in Davidson’s paper, it’s this that has drawn attention. If there is sufficient interest we might look at his Saying That.

Added: If A is the father of the father of C, we can conclude that there is a B who is the father of C. If A believes that B believes C, We cannot conclude that B believes C. While the surface grammar looks similar, the semantics are different. Hence the need for paratactic/hypotaxis analysis.

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26

That’s much better than Davidson’s “singular term”. You refer to “metalanguage” further on, and that would work, too.

I can see that these are different projects.

I think that last sentence is ambiguous. I’m not sure whether you are saying that W does get outside language with use and showing, or that he manages to avoid it? Or, possibly, evading the issue?
Of course, it’s hard to know exactly what might count as getting outside language. Perhaps it’s just that that’s bothering me.

There’s a feeling of surprise, like the surprise of a magician producing the rabbit. But I wouldn’t dream of accusing him of being duplicitous. That criticism is itself a bit too easy and doesn’t address the text itself.

Thanks for this explication. I think I understand what’s going on better than I did. I’m still puzzled about what the project amounts to, but that’s a different issue.

I have read “On Saying That”. I would rather tackle “Mental Events”, if it’s all the same to you.

27

The mention of Wittgenstein is of course a side issue. Wittgenstein can say that the meaning of a sentence is its use in a language game, a game which includes things outside of the language as such. So the builder game includes blocks and slabs. Davidson focuses instead on how we might set out the meaning of one language in the terms of another, an issue of interpretation rather than of use. These two projects are not directly in competition with each other as theories of meaning, but are answering somewhat different questions.

28

Davidson’s suggestion is that we will have an account of meaning for a language if we have a recursive definition of truth for that language.

Tarski set out two languages that were able to talk about the same things, thereby in effect fixing meaning for those languages using satisfaction. He was then able to set out the nature of truth using Convention T. In doing this he set out for us the relation between meaning and truth that Davidson takes advantage of here. We know the meaning of the sentences of a language if we know when those sentences are true. If we are able to give necessary and sufficient conditions for the truth of each sentence of a language, then we understand the language.

The theory of meaning here does not provide an account of meaning ex nihilo, as such, but in terms of another language. It therefore is dependent on our being able to verify that the sentences of the target language are true, and so in this sense it is an empirical theory. Hence the example, on p. 311. If our target language contains the sentence “Snow is white”, and we construct the hypothesis <“Snow is white” is true if and only if snow is white>, it remains to verify that snow is indeed white, and also to verify that “snow is white” is used by speakers of the object language in circumstances were we might have said that snow is white. The mistake

(S) “Snow is white” is true IFF grass is green

is to be verified by looking to see how “snow is white” is used. Notice that it might turn out that (S) is correct, in the case in which “snow” refers to grass and “white” to green. If we are to understand the object language, we must presume that it says much the same sorts of things as we would say, and does so in a consistent fashion. We must be charitable.

The point remains that the answer to the “Grass is green” problem is found in the implementation the theory. That, roughly, is Davidson’s answer to the suggestion that while his account might lead to a consistent interpretation, there is no guarantee that it is the right interpretation, a line of thought that leads to On The Very Idea of a Conceptual Schema.

The above glosses over a few aspects of the text, but hopefully gives a broad picture.

29

Davidson next considers two problems Tarski saw in attempting to formalise a natural language. A natural language by its very nature includes its own truth-predicates, and so permits problems such as the Liar that are incompatible with a formal interpretation. And also, interpreting a natural language formally would involve changing what is being said in that language. To the first, Davidson suggests that we carry on, as we might well apply his method to at least a suitably interesting fragment of a natural language, even if that fragment does not include set theory. For the second, he suggests we might give as close an interpretation as we can, and crucially we can modify that interpretation as required. The issue here relates to that later addresses in “A nice derangement of epitaphs”, where Davidson argues that there may always be stuff left out of what he there calls a “passing theory”. The rough point is that the formal interpretation is partial, remaining incomplete in that some parts of the language will remain outside of the interpretation.

The approach here is to acknowledge these potential theoretical difficulties, yet to take a pragmatic approach - how much of a natural language might we usefully formalise?

30

Davidson is proposing that we might develop on the work of Frege, who formalised quantification, and Tarski, who formalised truth and meaning. While logicians explore and develop formal languages, then look to see how these might be applied to natural language, linguists look at natural languages and seek a theory that encompasses and explains them. Davidson’s proposal is a project that brings these together, applying formal logical methods to natural languages, by interpreting natural language in a formal language.

The theory would, give some sentence in say English, provide us with a T-sentence for that sentence, setting out in formal terms the conditions under which the sentence is true. Given a sentence “s” it would provide us with a truth conditional sentence “p” such that “s” is true ≡ p.

If there is an ambiguity in a natural language, an interpretation of that ambiguity in a formal language does not need to remove the ambiguity; indeed if it is to be accurate to the task of interpretation, it ought bring that ambiguity into the formalisation.

At p.316 of the text, explicitly, the place of such a theory of meaning is to exhibit the structure of the sentences of a natural language by exhibiting their logical form. Over the next few pages Davidson sets out the requirements for such a theory, for a series of special cases. He first turns to the problematic case of belief sentences, and extensionally opaque sentences more generally. He considers Carnap’s approach to such sentences in order to characterise the answer given as analysing the concept of belief rather than the structure of statements of belief. He applies this to normative sentences. If our theory of meaning takes “Bardot is good” and generates some formally equivalent sentence “p”, such that p is true if and only if “Bardot is good” is true, it will have set out the truth conditions for “Bardot is good”; and this whether or not it has provided an analysis of “…is good”.

…the mystery is transferred from the word ‘good’ in the object-language to its translation in the metalanguage.

It might be worth dwelling on what is proposed here. It would not suffice that “p” in such a sentence stand alone; the structure of “p” must be shared across other sentences of the metalanguage, so that the similarity between “Bardot is good” and “Bogart is good” is also seen in that metalanguage. Hence the requirement that there be some shared structural elements between formal interpretations of “Bardot is a good actress” and “Fido is a good companion dog”. Crucially, the interpretation must be in truth-conditional terms - and here we might read this as the requirement that the interpretation be extensional, and so allowing for substitution preserving truth. To do otherwise is to “…lapse into (or create) language for which we have no coherent semantical account” (top p. 318).

In a similar vein, the theory doesn’t separate analytic sentences. They are to be treated by the theory just as are other sentences.

The approach would be the same with demonstrative, and indeed with indexicals generally. Hence the same treatment must be applied to “I am wise” as to “Socrates is wise”. (Top p. 319)

These restrictions are dealt with by another innovation. We have up until now been talking of “s” as a sentence. Davidson now suggests that we need to instead consider “s” as instead an instance of language use, say an utterance, by some individual, with a given time and place. Hence the theory would not treat of the sentence “I am tired” but of ‘I am tired’ spoken by p at t; not “That book was stolen” but “That book was stolen” spoken by p at t. After all,

…sentences are true, and held true, only relative to a speaker and a time. The real task is therefore to translate each sentence by another that is true for the same speakers at the same times.

31

I’m sorry, but I’ve just realized that I don’t really know what “recursive” means and it’s a key concept here. Can you explain exactly? I’m particularly keen to know why “the father of..” is recursive, but “S believes that T believes…” is not.

That helps a lot. It makes D’s project very neat. I like it, though it makes me nervous.

Interesting. I have to say, it isn’t obvious to me how, in this context, one would shoe-horn the two apart. What do correct and incorrect mean in this context?

That makes pragmatic sense, but then won’t someone have to explain what meaning and truth mean in those other parts of the language, (if those terms are applicable to it). But if they are not at least somewhat like meaning and truth as Davidson is working with it, why would we call those other parts parts of the same language?

That’s very odd. I though one of the main points of logical representations of natural language was to clarify ambiguities and make them impossible. Wasn’t that Russell’s project, for example?

I think I need to read these pages again.

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32

An afterthought:-

I’m not at all sure about this. Fair enough “I am tired” uttered by me and by you at different times does have different meanings. If we equate meaning with truth-conditions, what shall we say about “I am tired” and “he is tired” uttered by me and by you (where “he” refers to “me”)? They have the same truth-conditions, but not necessarily the same meaning.
To put it another way, I’m not at all sure that relativizing truth and mean to a speaker and a time deals with all the ways that context can impact on meaning.

33

@Banno
I’ve been following your discussion from the sidelines, very illuminating. Two of your questions are also mine:

Do they have the same truth conditions?

Davidson has always seemed vulnerable to me here, and after reading McDowell’s Mind and World, he seems even more so. But a lot depends on how Davidson wants to understand the idea of a “right interpretation.” My reading of him is that “right interpretation” would be meaningless outside a particular language – is that how (either of) you read him?

34

I would have thought so. S says of himself “I am tired”. I say of S “He is tired”. Surely, both utterances must have the same truth-conditions.

Yes, that’s exactly what I’m saying. I’m not sure whether Davidson is also saying it, but I rather think he may not be.
To put it another way, English, qua language, enable us to make statements. Davidson is saying that statements (made by someone at a particular time) are true or false and therefore have meaning. That I (mostly) agree with.
But the only criterion for saying that I understand the language in which I make the statements is that other people understand me, i.e. that we agree on what the statements mean. To put it another way, the only thing that makes an interpretation right is that the community of speakers think it is right.

35

I know, it looks that way to me too. But that would be such an obvious defeater of the thesis that I’m wondering if a logician sees it differently. No doubt @Banno will tell us.

There’s the rub. Because Davidson equates “what the statements mean” with “what their truth-conditions are.” And the determination of those conditions comes first; we arrive at meaning by ascertaining that we know what would make statement X true in language L. As Banno says, Davison’s scheme “is dependent on our being able to verify that the sentences of the target language are true, and so in this sense it is an empirical theory.”

Here is McDowell:

Davidson says [in “A Coherence Theory of Truth and Knowledge”] that “nothing can count as a reason for holding a belief except another belief,” and he means in particular that experience cannot count as a reason for holding a belief.
. . .
I think we should be suspicious of his bland confidence that empirical content can be intelligibly in our picture even though we carefully stipulate that the world’s impacts on our senses have nothing to do with justification. . . Davidson’s picture is that we cannot get outside our beliefs. (Mind and World, 15-16)

McDowell is critiquing a different essay, but I think his concerns apply to our target essay as well.

36

Sorry, meant to continue but hit Reply. :slightly_smiling_face: To continue:

If we need a concept of truth, and truth-conditions, to arrive at meaning, then we need to be satisfied with what Davidson offers in that regard. We need to understand why the question is not “Is my interpretation of statement X correct or incorrect?” but rather “What would it mean to ‘interpret statement X’ in a way that did not produce meaning at all – which is what Davidson claims would happen if meaning was not dependent on truth-conditions?” I’m not satisfied that Davidson has successfully eliminated the “correct/incorrect as regards experience” problem, but I remain open to hearing more.

37

To be sure, A believes that B believes C is a recursive application of a syntactic rule, and is syntactically recursive. But it is not semantically recursive.

If we have A is the father of B, who is the father of C, and so on, we know that A is the father of the father of C.

If we have A believes that B believes C, we cannot conclude that B believes C, in the way we might have concluded that B is the father of C. It might be that B has no such belief, and that A’s belief is mistaken, and yet it would despite that remain true that A has such a belief. “A believes that B believes C” tells us nothing about what B believes. That’s very different to the fatherhood example.

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38

It’ll probably help if we set out the main line of grievance to Davidson’s ideas, since his reply might clarify what it is he is doing.

The idea is that a true T-sentence gives the truth condition for the object sentence. We considered before

“Snow is white” is true IFF grass is green

Now notice that snow is indeed white, and grass, at least outside of the present droughts, is green. Since both sides of the T-sentence are true, the T-sentence itself is true. And yet it has told us nothing about the colour of snow.

A further grievance. “p” is truth conditionally equivalent to “p & ~(q & ~q), so <“s” is true iff p”> is equivalent to <“s” is true iff p & ~(q & ~q)">; and to innumerable other equivalent T-sentences. So we do not have one T-sentence that gives the truth conditions of “S”. Which of these gives the interpretation of “S”?

Davidson’s reply is that the T-sentence that gives the meaning of “s” is derived as one in a theory that gives the meaning for any sentence in the object language; that it must not only give a set of truth conditions for “s” but be consistent with every other T-sentence of the theory; hence “grass is green” will not serve as an interpretation of “Snow is white” as other sentences will fail to be consistent - “grass is brown in a drought” will not give us “Snow is brown in a drought”, for example. Similarly, some parts of a T-sentence might be redundant, and removed.

Going over that again, suppose we have at hand a theory that given a sentence of English, generates some truth-functionally equivalent sentence in a first-order extensional language. It remains, as an empirical task, for us to verify that the sentence so generated is indeed a suitable interpretation of the English sentence. If it contains redundant material, or if it is inconsistent with other English sentences, then we have good reason to go back to the theory and modify it so as to produce a better interpretation. The theory, if it were complete, must be compositionally consistent across the whole of English, and track against the use of English by actual speakers.

The strongest objections to Davidson’s approach doubt that this is doable for the whole of English. But we might, along with Davidson, look to see how much of English could be subject to this approach; an ongoing project to interpret parts of English in first-order extensional terms may still show us much about meaning.

So the program might be inherently incomplete, yet still produce interesting results. There are two ways in which the theory might be incomplete; there might be parts of English usage that remain uninterpretable; but also it may be that given a truth functional interpretation there may be meanings that remain unstated.

The interpretation is underdetermined - there is always more to say. That should not be surprising. Charity here leads to On the Very Idea of a Conceptual Scheme, reinforcing the holism of language and belief; while problems with law-like behaviour lead to A Nice Derangement of Epitaphs, relegating the place of convention in language use.

39

The truth sentences might be along the line of

“I am tired” uttered by Ludwig at 17:30 4/8/26 is true IFF Ludwig is tired at 17:30 4/8/26

but

“I am tired” uttered by Banno at 17:30 4/8/26 is true IFF Banno is tired at 17:30 4/8/26

So much for the more direct case. Suppose your utterance had the implicature that it was time to go home, as part of the “context impacting on meaning”. Then we might add

“I am tired” uttered by Ludwig at 17:30 4/8/26 and implying that it was time to go home is true IFF Ludwig is tired at 17:30 4/8/26 and Ludwig implied that it was time to go home.

Presumably any impact from the context can be added, so long ads it is added to both sides of the T-sentence.

40

“Right interpretation”, if I’ve understood you, is for Davidson to be verified empirically, and so subjective to all the various intricacies of observation and verification. That they have the same truth conditions is decided by looking at how the utterance is being used. Perhaps that is not enough, but it is what we have.