L1.3 Lottie’s third lesson on concepts
The next morning, much to everyone’s surprise, pTravis and Masongill decide to crash Lottie’s lesson even though they both left school long ago. Hipparchus fails to hide his evident delight to have keen and voluntary students for a change.
“Today, I am going to say a little bit more about Donald Davidson’s approach to thought and language and then connect that to another important idea from Frege: the distinction between sense and reference. I would not have proceeded in quite this order but Lottie asked about how meaning could fit unmysteriously into nature and that required a detour to think about Fodor’s and Millikan’s reductionist naturalism and Davidson’s aim to ‘naturalise’ meaning – to show how it can be a part of our nature, at least – without reducing it to something more basic. Daniel Dennett has a similar strategy though less well worked out. [Hipparchus returns to this in lesson 9, Ed.]
“I called Davidson’s approach ‘the philosophy of language of the field linguist’ which is what Richard Rorty admiringly called it. But Davidson calls the key idea ‘radical interpretation’. This is interpretation from scratch, without phrase books and dictionaries. By thinking about its conditions of possibility, he can derive some philosophical conclusions about the nature of meaning and mental content.
Theories of meaning
But alongside that, Davidson has another suggestion about meaning. He thinks that the output of radical interpretation should be a ‘theory of meaning’ based on the Polish logician Alfred Tarski’s ‘semantic conception of truth’. Davidson sketches the requirements on such a theory in this way:
The theory will have done its work if it provides, for every sentence s in the language under study, a matching sentence (to replace “p”) that, in some way yet to be made clear, “gives the meaning” of s. One obvious candidate for matching sentence is just s itself, if the object language is contained in the meta-language; otherwise a translation of s in the meta-language. As a final bold step, let us try treating the position occupied by “p” extensionally: to implement this, sweep away the obscure “means that”, provide the sentence that replaces “p” with a proper sentential connective, and supply the description that replaces “s” with its own predicate.
The plausible result is (T) s is T if and only if p. (Davidson 1984: 23)”
There’s a little shuffling and unease among his students for whom this seems to go too quickly. And so Hipparchus pauses and tries again.
“Davidson is being a typical philosopher and trying to think what sort of account or theory would help before actually coming up with one. (In fact, as a philosopher, he never attempts an actual theory. He leaves that for empirically minded minions.) He suggests that what we want from a theory of meaning for an alien language is a way to state the meaning of each alien sentence in our own language. We need to pair their sentences with the right sentences in our language. The way he suggests this is to frame a theory that says alien sentences have some particular property if and only if some state of affairs obtains where that state of affairs is stated in a sentence in our language. So we mention the alien sentence – which is like saying ‘that sentence’ is X if and only if …And here we say something in English. For example: snow is white. And then with a flourish, Davidson suggests that ‘X’ in my example, or ‘T’ in his, works best if it stands for ‘true’. In other words, a theory of meaning will do what we want of it if it gives instances of this schema, which is called the ‘T schema’:
Sentence ‘s’ is true if and only if p.
Perhaps the most trivial example is where the object language on the left is part of the same language used to state the whole condition. So
‘Snow is white’ is T iff snow is white.
Davidson calls this a ‘snowbound triviality’. Here ‘iff’ stands for if and only if and, very importantly we mention the sentence on the left by putting it in quotes but we use the sentence on the right. (I said ‘part of’ just now because the meta language needs to have two things that the object language doesn’t need to have: a way to mention sentences rather than things or properties (we use quotation marks) and the truth predicate.)
“What’s all this got to do with Trotsky?” asks Lottie impatiently.
“Tarski not Trotsky! Well, he was interested in giving a theory of truth. In fact, his aim was modest. He did not aim to tell us what truth is, whether it is some sort of special property of thoughts, for example, but to show how to generate a statement of the condition under which any sentence of any degree of complexity in a language is true, based on some finite axioms. It’s very easy to do that if you start with a list of whole sentences and the rules governing logical connectives such as AND, OR, IF-THEN etc. But Tarski’s approach showed how to do it for a language whose sentences can themselves be analysed more finely into objects and properties.”
“Oh” exclaims Lottie, surprising herself “Do you mean like naming and predicating?! Like Monday’s lesson?”
“Let’s see! For his purposes, Tarski was quite happy to assume the meaning of sentences in the object language because he was shedding light on something else: how their truth condition could be calculated from basic components. This included sentences saying: ‘there is at least one thing such that…’ and also ‘for everything…’ These are the two logical quantifiers of Frege’s logic represented as ∃x(f(x)) and ∀x(f(x)). The first says, there exists at least one x such that x is f. The second says that for all or any x, x is f. It would still be an achievement to have a truth-theory for English as an object language written in English as a meta-language. (Roughly!) It would still show how the truth condition for very complicated sentences was constructed from finite axioms. So Tarski assumed it was unproblematic for his purposes to assume and thus state a translation of any object language in one’s favourited meta language.
But Davidson’s aim is precisely to earn the right to that. So he assumes that truth is simple and we can use it to shed light on meaning by constructing theories with the same machinery as Tarski’s but used for the opposite purpose.”
Can an extensional theory capture meaning?
pTravis is now waving his pipe about distractedly trying get attention. It is a good thing he never lights the pipe. “Something’s been bothering me. It’s what you said earlier when you quoted Davidson. You said something about sweeping away the obscure ‘means that’ and treating the link between s and p extensionally. Now I may have forgotten what little philosophy I ever studied at school but doesn’t this mean that what works for Tarski cannot work for Davidson?”
Both Lottie and Masongill look blank and one of them thinks it is high time this lesson came to an end but Hipparchus merely gestures for pTravis to say some more.
“Well ‘extensional’ here must mean having to do with truth. And we have ‘swept sameness of meaning away’. But how about this:
‘Clark Kent is a bit nerdy’ is T iff Superman is a bit nerdy.
That’s a perfectly true example of the T schema. I can see that it would be fine for Tarski (not that you’ve really told us what’s going on under the surface of Tarski’s theory) but if this is the outcome for Davidson, it’s wrong. The second used sentence does not give the meaning of the first one, after all. How could this work? Meaning is more fine-grained than truth.”
“Very good” replies the tutor. “You haven’t said it yet but I think you were taught about the distinction between sense and reference. ‘Clark Kent’ and ‘Superman’ are two names for the same person. Much of the drama – such as it is – presupposes that we the viewers know that they are the same person but the other characters do not. So although all the sentences predicating properties of Clark Kent will be true if they are true of Superman, that extensional equivalence cannot be assumed to serve the purposes of a theory of meaning. According to Frege, the two names have the same referent or reference but different senses. The same goes for ‘Hesperus’ and ‘Phosphorus’ or the ‘Morning’ and ‘Evening’ stars’ which are both in fact the planet Venus, not that the ancient Greeks knew. But although you picked a good example to use as an objection, the real problem is more widespread. Let’s think about that and then return to sense and reference and then let’s let Lottie go off and play.
As I have said, Davidson replaces the intensional connective ‘means that’ with the extensional form ‘s is true if and only if p’. Clearly, however, the fact that the truth-values of the left- and right-hand sides of this conditional agree does not in itself ensure that the right-hand side provides an interpretation of the sentence mentioned on the left-hand side. They might concern utterly unrelated matters such as grass being green and snow being white (both equally true). For the overall sentence to be true, all that matters is that they have the same truth value (that is: true or false). In Tarski’s use of the T schema, it can simply be assumed or stipulated that the right-hand side provides an interpretation by being the same sentence as, or a translation of, the sentence mentioned on the left-hand side. Tarski helps himself to facts about meaning to show how to determine the conditions under which a truth-predicate applies to sentences of the object language. But Davidson has to earn the right to that claim.
Davidson’s response to this is to point out that instances of the T schema should not be thought of as interpretative in themselves. Rather, it is the fact that each instance can be derived from an overall theory for the language that also allows the derivation of many other instances of the T schema all with the correct matching of truth-values, that is interpretative. Only if the theory systematically correctly matches words on the left- and right-hand sides of T schema instances will it have a chance of generating all and only true instances. But if it does, that is very strong evidence for a match of meaning. Instances of the T schema play a role within the larger deductive structure of the meaning theory of a whole language. And linking back to the idea of radical interpretation, what an interpreter has to go on is an alien speaker’s assertion in the face of some truth that the interpreter can also judge. That is a pairing a sentence with a fact. So the formal theory helpfully dovetails with that.
A Tarskian theory of truth as a theory of sense
“Yes but that doesn’t help with my example. Clark Kent is Superman, after all. He is the same thing. It’s not just like saying that grass is green has the same truth value as snow being white. I can see how Davidson can eliminate that problem. A theory that is good enough to give the right truth conditions for sentences like ‘snow is white’, ‘snow is cold’, ‘sheep are white’ on the basis of some basic axioms might well be passing sufficient a test to be interpretative in those cases. That is, giving conditions that are true just when the object sentences are true (a weak test) across a wide range of sentences (a strong test) would be an achievement. But switching between the two names ‘Clark Kent’ and ‘Superman’ would never make a difference to the truth of the theory but it might matter to interpretation.”
“No you’re right. And for that, we need to go back to the context of this theory. It is supposed to encode the output of radical interpretation. In the quotation, Davidson sets out the form of the theory he proposes without assuming it will be based on truth. He wants a theory that will relate sentences such as to give the meaning of one set using another. There is already a constraint from radical interpretation here. The radical interpreter has to make rational sense of the subjects they study. Thus not every true Tarskian theory would be a theory of meaning. To be that, too, it has to pass the interpretative tests of radical interpretation and pair the right sentences. John McDowell argues that by passing this stricter test, although truth-based theories of meaning merely state extensional equivalents, they can express theories of sense.”
“But how does that cash out?”
“‘Cash out’! How vulgar! But, for example, to capture the rationality of the ancient Greeks – both their language and their beliefs – we cannot match ‘Phosphorus’ and ‘Hesperus’ with ‘Venus’. McDowell suggests that we have to neologise as far as English is concerned and even in the sentences we use on the right to capture the object language on the left, we will have to speak, differently, of Hesperus and Phosphorous.”
“Enough already, already, already” cries Lottie and makes a dash for the door and the lesson comes to a sudden end.