 Today is Davidson again on instrumentalism about reference, and we'll skip class on Wednesday by popular demand, and we'll meet again in a week, I guess, because Wednesdays are often Friday. So Monday is, and we'll look at Politions stuff then. Politions are the experimental psychologist, but his stuff on reference is some of the, well, I think it's where the subject is today, with Politions kind of approach to reference. Not so much the details of what he says about that type of approach. So let me just repeat, we will not have a lecture on Wednesday, and we'll take up again on Monday. Okay, so I want to just go over what Davidson says about truth theories, and then look again at what it means to say that reference drops out as Davidson puts it. We don't need an account of reference in explaining the relation between truth and reality, between language and reality. So remember the idea of a meta-language. Meta-language has, you're going to state the truth theory in a meta-language. And the meta-language has to have an aim for every sentence in your object language, and a translation or a copy of every sentence in your object language. That's plain enough? Yep. Okay. And it came up briefly last time. I just want to pause in this a little bit, because there is a whole subject area here. But the meta-language usually does not contain the word true. For our purposes, we'll usually consider cases in which the meta-language does not contain the word true. And that's kind of intuitive, because true is a word that you're used to comment on sentences in your object language, when you're saying this one's true, or that one's true. You see what I mean? If you say this is a very long sentence, that's a way of commenting on a characteristic of the sentence in the object language, saying this is a very true sentence is also a way of commenting on the sentence in the object language. The basic reason for this was set out by Tarski. When I say meta-language, I was using a convention familiar in the thread whereby when I say meta-language, I mean object language. Let me rephrase that. Lucky this isn't being recorded. Do you like that better? Should I take that from the top? True is a term of the meta-language used to comment on object language sentences. Is that now perfectly clear? The basic reason for this is Tarski pointed out that if you take sentences like this sentence is not true, is that sentence true? Put out your hand if you think it's true. It is not true? It's not true. This is the lie of paradox, going back to antiquity. If you say it's true, well, it must be false because if it's true, then it can't be right to say it's not true. If it's not true and it says it's not true, then that's true. So it's not true. No, wait a minute. Suppose it's not true, right? Suppose it's false, in fact. If it's false, then what it's saying is that it's not true. So that's right. So it is true. But if it's true, then it's not true. So which is it? So really desperate methods are often resorted to to try and explain what's going on here. Tarski gave a fairly simple, yes? It means that very sentence on the board. See, from the one quotation mark, from the left quotation mark to the right quotation mark, call that sentence S, right? Yes? No, no. Call that sentence from the left, from the T to the U to the E, I mean. Who should I skip today? From the T to the U, right? Call that sentence. Sorry? A, blast it. Right, from the T to the E, call that sentence S. Yes? That's a good name. Okay. So we say this sentence, that is referring to S. Okay. And that's the question, is that sentence S true or not true? You can't figure that out. Yeah, yeah. I mean, you get a contradiction whichever you assume. So Tarski said, what's going wrong here is that true here is being used as a term, both of the object language and the meta language, is being used to comment on the whole sentence. So is a term of the meta language and is a term of the object language, just as a constituent of the sentence that you're commenting on. Yeah? Yep? The meta language is true. It contains every assertive statement. Does the phrase say the sky is blue is the same thing as saying the sky is blue is true? Anyone has to acknowledge that there's something very similar about saying the sky is blue and saying the sky is blue is true. Yep. This is like a syntactic restriction that you're not getting a proper sentence here. So the sky is blue is true is, well, it's just syntactically different to the sky is blue. Yeah? So the idea is you're not, you're just syntactically, this is this bad grammar to have true in both ways. That's consistent with saying that thing about saying it's a meaning. Yeah? They're not quite the same in meaning anyhow, but that's a separate point. Okay, so you can block this kind of paradox by saying that you can't have true in the object language. Yep. That makes sense? Okay. And of course, someone said last time, well, can't you have true in the object language and the meta language? And of course, once you've got your meta language, you could regard your meta language as itself an object to study. So you could have a meta-meta language in which you study your meta language, I think. Yes? Okay. So then you could have true in your meta language being studied by a meta-meta language in which you also have an ocean of true. And Tuske's point was, you can do that, but never have, you just have a hierarchy of true predicates, each one of which is used to comment on the language below it in the hierarchy. So the idea is, at no level do you get to say this sentence is not true and have the true truth predicate tucked inside the sentence you're commenting on and being the predicate you're using to comment on it. That's the argument for saying that you should separate out truth as a term of the meta language because truth is a term of the object language. It gives you a very simple response to the LIAR paradox. Yes? There are no more difference between them than I just stated. There are terms of different languages, so you can't put them into the same sentence. That's the key thing. Yeah? You can have a truth predicate in the language you're studying. But the meta language in which you're studying that language can't contain that very same truth predicate. Sorry, would what mean? Well, no. I don't understand the N minus 1. It doesn't matter what level N it is. You can't have this sentence as not true as a well-formed sentence. And then if you do that, you block the paradox. Yes? No, I don't see why. You can have the same truth predicate in a single meta language for both French and English. Well, not the same object language, but they just have the same predicates applicable to them. Like, a long or short could be used as terms in the meta language. Four sentences in English or French. Similarly, you could have true your meta language being used as a term applicable to sentences in English or French. Okay? This is not central to what we're doing here. I just want to set this up because it's a subject area in its own, this whole topic. Many people think that Tarski's approach is too restrictive that you do want to have proof in your object language and meta language. But what happens then? I mean, people do go for what seemed like really desperate solutions, saying that, for example, contradictions can be true, as, for example, in the Lyre sentence. I mean, Wigelstein talked somewhere about the superstitious fear and awe of mathematicians in the face of contradiction. You just have to get over that, but for those of us that have not gone over it, this is a very simple thing. Okay, so what's important for our concerns is we want to be able to say where s is the name of a sentence in the object language and where what replaces p is a translation or copy of that sentence in the meta language. Then we can say s is true if and only if p, and that's always going to come out right. That will always be correct if s is a name of a sentence that's translated by what replaces p. That's okay? So as long as we have that, so long as we can state that condition, we can say a truth theory is a theory that has a finite number of axioms and generates every instance of that s is true if and only if p. That's all right too? There's not very many of us here, you can pause me. It will include vague terms, yeah. If there's a vague term in s in your object language, there needs to be a corresponding vague term in your meta language. Very good. For a term like small elephant, it will not be trivial to state this because small for an elephant is not small for a mouse. So you need some way of articulating what that relativity is of small to the predicate it's been coupled with. You see what I mean? You need some explanation of what it is for s is a small f, for the blank is a small f to apply to something, and that will be relative to what your choice is for f. There's one very immediate way in which constructing a truth theory for a real language is much more complex than just what we're talking about, a language with two names and two predicates. It would be contained in the axioms from which you derive this theorem. The idea is that you state axioms from which you can derive all of these theorems. I meant to be playing back what you just said. Is that what you meant? You would know that p is, what's replacing p is just a sentence. So in my simple example, it will be something like Raleigh Smokes. So it will be if and only if Raleigh Smokes. You just have to know who, to understand it, you just have to know who Raleigh is and what smoking is. So the truth predicate, the idea isn't showing up on the right-hand side. The truth predicate is only showing up on the left-hand side. So once we've got that, just by the way, we might note that that will fix uniquely what are which sentences of your object language the word crew applies to. And what you want to know of a definition is, a basic thing you want to know of a definition is which things does this term apply to. So this will fix what which sentences crew applies to. There couldn't be two predicates that both met, two truth predicates, that both met the schema and apply to different sentences. And if you could crew one and true two and you said, well, one of them counts S as right and the other one doesn't count S as true. That couldn't be because S counts as true one or true two if and only if the cat is in the mat or whatever it is. So the truth predicates will apply. That fixes uniquely what the extension is of the truth predicate. You can't have two truth predicates that both meet this condition but apply to different sentences. Suppose you had S and you get true one and you get true two. And you say, true ones applies to S and true two doesn't apply to S. So they disagree as to which sentences count as true. Suppose that happened. There are just two terms that both meet this general condition. That S is T if and only if P. For each sentence S that we're talking about, it's true if and only if P. Well, what replaces P is a translation of the sentence S. That's right. My point is there can't be two truths. That fixes uniquely what you're talking about when you're talking about truth. Because suppose there were two truth, two predicates that disagreed on a sentence S. Well, then you have to ask, is P true or not? Is it so that P is P so or not? Because you know that they both apply if and only if P. Then if the cat is in the mat or whatever it is, then they stand to fall together. You just need to know that this applies to both of them, that this holds for both of them. If you know that this holds for a predicate, that's all you need to know to fix which sentences fall under it and which don't. We can go back to this. If you remember a language with two names and two predicates, remember that? Can we just run through that? I say Rolly Smokes and you come back with Isaac Fish is very good. And I say, well, Rolly Fish is Isaac Smokes exactly. And then the long day is done. So if you have a language like that and none of this stuff about small, none of this tricky stuff, right? We've just got Smokes and Fish and Rolly and Isaac. Then we can have two axioms for the names. Rolly refers to Rolly, Isaac refers to Isaac. And Smokes applies to X. And Fish is applies to X. I haven't said it. Isaac's Fish is. So then we've done it. That is a Davis-Onion truth theory for our little language. Once you've explained how you put the predicate and the name together, so you know that the predicate coupled with the name gives you a sentence that is true if the predicate applies to what the name refers to. Okay, so that's a general idea of a truth theory. And you see that it's going to be complex to do it for particular areas of English. But the general thing seems quite perfectly feasible. And that is normal today. That is conventional today is how people think of doing theory of meaning. Is that okay? Is that reasonably clear what a truth theory is? This is your chance to complain if it's not. Okay, so here's Davidson explaining what's going on and giving up the concept of reference as basic to an empirical theory of language. Notions like the reference of a part or the reference of a name or what the predicate applies to. These are theoretical constructs whose function is exhausted in stating the truth conditions of sentences. The meaning theory assigns no empirical content directly to relations between names or predicates and objects. These relations are given a content indirectly when the theorems via s is true if and only if p sentences are. So when you have this s is true if and only if p thing, then that takes for granted the notion of meaning. It says that what replaces p should be a translation of the sentence s, have the same meaning. But the way we are to think of a truth theory being constructed is, well, suppose you are just parachuted into some foreign land. Suppose you're just parachuted into some valley deep in Papua New Guinea with a people speaking a language that has never been studied and it's never connected to English or French. So you don't have the same alphabet. Nothing is in common between that language and English. So your task now is to translate the signs of that language. What are you going to do? How do you go about it? Hold on. What would you do? With the locals, that's right. Point to a tree. Really just express puzzlement. Yes. I think that's right. I don't really see what else you could do. You just hang out with the locals and see what they say and you hope that they're going to be sufficiently helpful to say things like in local, that's a tree. Right. So the thing here is when you're doing that, what you're getting from the locals is always going to be something at the level of a sentence. You're going to hear them saying, oh, that's a tree. I'm going to say it in native and you translate that as that's a tree. Just because language always operates at the level of the whole sentence, you're never going to be able to interrogate them directly. And Davidson says you can start to articulate just what you'd be presupposing in translating the other. For example, if they point to the tree and say, what do you say? I'm a ravenchi in local. Then you don't suppose they're making a gratuitous mistake. You don't suppose they're pointing to the tree and saying, that's a badger. You see what I mean? You might try interpreting them as really remarkably stupid and imperceptive people who make random remarks without bearing no relation to the facts of the matter. But that just wouldn't be a good translation practice or good interpretive practice. What you do is you assume that the people you're dealing with are reasonable levels of the good and the true who basically express a certain sentence just when those sentences are, in fact, true. Or attenuate in conditions where it's reasonable to assert those sentences. You might allow that there are mistakes that they might naturally make, but you always have them coming out as broadly rational, broadly reasonable people. So that's what you do when you're trying to translate the foreign language into English and you don't have any prior history or dictionaries or anything like that to go on. So start out by interpreting them as holding true sentences that you also hold true, as being reasonable by your rights. And the thing is that those constraints on translating the other people, what you will do is you will try to make a manual in which you say for each term of the language what it refers to, but your evidence is always stuff at the level of the whole sentences. You're always trying to guess what a particular sentence meant. So in this view, if you get two manuals that both have the same sets of axioms, specifying references and satisfaction conditions for the predicates, then if they give you the same theorems, if it's true, if and only a p, then it would make no sense to wonder whether one is right and the other is wrong. All your translation manual is, all your interpretation manual is, is a concise way of generating all these truths about how to interpret particular sentences. Yeah, that's all you're doing. I mean, when you're out in the field, what you want to know is what some particular utterance meant, what some particular sentence meant. All you use, the set of axioms you've got for is generating the truth condition of that sentence. So if you get, it's just an abacus, it's just a calculating device to let you predict what the truth condition of any sentence of the language is going to be. So if you get two manuals, two sets of axioms that give you the same by conditionals here, then it's going to make no sense to wonder which set of axioms is the right one. How about that? Is that okay? Yes? Yeah, if you point to a rabbit and then say, gava guys, it might be, you take them, you take them, you say, yes, lower rabbit, not lower badger, lower squirrel, lower truck. Yeah, take them as coming out right. Yeah? Well, if you just use that one word, rabbit, I take it that's equivalent to saying low a rabbit, if you see what I mean, or there goes a rabbit. There are extra words there. Well, the such a thing is a one word sentence. I mean, the way you're using rabbit there is as a cry with which rabbithood is greeted. You see what I mean? Yeah. And it can be right or wrong, depending on whether there's a rabbit there. It has a truth value. If it turns out, that wasn't a rabbit. Yeah. There's an old stage act of Sir Harry Lauderd, the great Scott split, whatever he was, where he's waiting for the girl he loves to come over the moors, and he keeps saying, it's her, it's her. No, it's a rabbit. Anyway. That's it, by the way. Okay, so you write the sentences that will be very helpful to you as entry points, will be one word sentences, but it's a single word being used as a whole sentence there, but it can't be right or wrong. Yep. Okay? So, consider now one theory. Remember we've got a little language with two names and two predicates, where we can keep a clear track of what's going on. Suppose you've got one set of axioms that says, Rolly refers to the place one mile west of Rolly. So this theory does not say Rolly refers to Rolly. This says, if this is Rolly, then the name Rolly refers to the place one mile west of them. Okay? Does that make sense? And now suppose you have the symbol of axiom for Isaac. It says, Isaac refers to the place one mile west of Isaac. So that's a different theory, right? It doesn't say Isaac refers to Isaac. It says Isaac is referring to this place. And suppose that for the predicates, you have smokes applies to a place if the person one mile east of that place smokes. And fishes applies to a place if the person one mile east of that place fishes. So if I say this place fishes, then the way you find out whether that's true or not is go one mile east, find the person who's there one mile east and see if that person fishes. So that's a different axiom to saying fishes apply to a person just in case they fish. Yes? But does this come out giving you the same theorems as our original theory? Well sure, consider the sentence Rolly smokes. What does it take for Rolly smokes to be true? Well, smokes applies to Rolly just if the person one mile east of Rolly smokes. I mean the thing designated by Rolly smokes. And what does Rolly refer to? Rolly refers to this place one mile west of Rolly. So just to, here we have the noble lord himself. Here we have the place one mile west. So Rolly refers to that place. So when I say Rolly smokes I refer to that place. And when I say, and when I apply the predicate smokes to that place I'm applying something that's true just in case the person one mile east of that place smokes. That is Rolly. Yes? So this will come out true, Rolly smokes is true just in case Rolly smokes. See that works. Should I do that again? Put your hand up if you'd like me to do that again. Okay, I would describe that as moderate enthusiasm. Okay, so here we have Rolly. Here we have the place one mile west. What does the name Rolly refer to? It refers to this place. Yep. What does it take for the predicate smokes to apply to that place? Well, it has to be the thing one mile east of that, namely Rolly smokes. So for Rolly smokes to be true, what it takes is for Rolly to smoke. Yep. Yes? It refers to this. No, I don't. Yeah. Aha, very good. Thank you. Okay. Yeah, in the object language I'm using it to refer to Rolly. The noble lord all the way through. Yeah. Okay, very good. Okay, so the conclusion from that is that we have got these two sets of axioms here. Rolly refers to the place one mile west of Rolly. Isaac refers to the place one mile west of Isaac. Smokes applies to X of the person. One mile east of X smokes. Fisheries applies to X of the person one mile east of X fishes. That's true if and only if Rolly smokes, okay? So if you say what's the difference between that and our original theory when the name Rolly refers to Rolly and Isaac refers to Isaac. Davidson's answer is there is no difference. These two theories are exactly the same. It's like Fahrenheit and centigrade. When you say Rolly refers to Rolly, that's correct in one system. When you say Rolly refers to the place one mile west of Rolly, that's also correct. They're both equally correct ways of formulating axioms for a little language. So even in our little language, there is no way of saying determinately which thing any of these signs is applying to. So it really is reference dropping out. You can't say what the reference of a sign is. All the way through the first few weeks of this class, we were taking it good or refers to a particular person, the morning star refers to a particular star. The general point here is that kind of assumption of determinacy is just a mistake. There is no saying determinately what any sign refers to. The hard facts are the facts about truth conditions at the level of sentences. It leads us to there being such a thing as the unique determinant reference of a sign. We didn't stipulate that, we discovered it. I mean, it's just true, right? One way will do as well as another. Saying it refers to Rolly is saying it refers to the place one mile west of Rolly. That's right, and the natural language that is being used is these facts about sentences that I look at this individual holding his pipe and I say, ah, Rolly smokes. So the hard facts are all these facts at the level of individual sentences. The facts that you discovered if you were parachuted into the community. And the trouble with this, it seems to me, is that this is completely incredible. I mean, one way to get at it is to say, this whole approach here is depending on the idea that we want to have some system of axioms from, a finite system of axioms from which all these infinitely many theorems of the form s is true if and only if p can be derived. But why would you bother doing that? I mean, why not just say s is true if and only if p and really do without the notion of reference altogether? In fact, do without the notion of a part of a sentence altogether. Just treat sentences as the only significant units. The basic unit of meaning then would be the sentence. Forget words as having their own autonomous meanings at all. If I talk about that. I mean, it might be handy if you want to write down a manual or something. But since it's all just gas for generating the theorems, you could actually, I mean, we don't always, we don't generally use manuals to understand each other. Why not say, well, we can just dispense with the manuals. We can just dispense with these finite sets of axioms. I mean, the obvious reasons why we don't do that. One reason is that if you're trying to explain the extent of someone's understanding of their language, the way you do it, one basic thing you do is you explain what their vocabulary is. You list how many words they have in their vocabulary. The way you acquire a language is word by word. You learn a language by learning the individual words in it. I mean, you sometimes read things with titles like, it pays to increase your word power. And then you get the definition of some complicated word. And that's right. You just learn the definition of some complicated word. And now you can use a whole range of sentences that you couldn't do before. So when you're learning a language, you don't do it by learning sentences one by one. That's true for a relatively primitive level of language learning where you just got a phrasebook and you want some handy sentences like, help, where are the police? Can you lend me $20? Things like that. You just want to get by in a language. But if you're really learning a language so you can speak it proficiently, all you're doing is a word by word matter, without learning the meanings of signed sentence by sentence. And sadly, when you're losing your grasp of a language, when you just forget, then you do that word by word too. What I mean is, I used to know what a metamor is, but I was trying to remember the other day what a metamor was. I just had no idea. It's something to do with light and color. But more than that, I would know what to say. But that means that there's a whole collection of sentences, any sentence involving the word metamor that I now can't understand. So when you're learning your language and when you're losing your language, you do it word by word, not sentence by sentence. So we've gone, we should be able to explain what it is that your proficiency with an individual word comes to. And it should be important in explaining, to anyone encountering Davidson's picture for the first time, the idea that Rolly refers to this human is very natural. That's the natural idea. The idea that Rolly refers to this place one mile west of Rolly is absolutely crackers. I mean, why would you think that? Because we're supposed to be able to do Davidson's thing for the names of anyone in the class. We should be able to reinterpret your name as referring not to you, but to the place one mile west of you, or to the place two miles west of you, they're supposed to be equally good accounts of the reference of the name. But of course, we do not believe for a moment that they are equally good accounts of the reference of the name. And one reason we don't believe they're equally good accounts is when you're learning a name Rolly, the way you do it is by being, well, perhaps not in Rolly's case, but if anyone in the class is by being introduced to that person is by encountering the person. You don't do it by encountering the place one mile to their west. That notion of the encounter with the person really seems to be important. And when we're asking intuitively what we're referring to with particular terms, what matters is what you're perceiving, which object it is filling your field of vision, which object it is that you're attending to when you're learning the name. So it seems to me that something's gone wrong when we have a picture where the only empirical constraints on the account of meaning are at the level of the whole sentence. Because we just do, in fact, take it that our knowledge of what we mean by, our knowledge of what we mean by a sentence is deriving from knowledge of the meanings of individual words and when you're learning individual words, there are lots of basic cases in which what you're perceiving and what you're attending to are really important in fixing which thing it is that you're talking about, which thing it is that you understand the term as referring to. Okay. Any questions on that? Okay. Well, with that, we have, let's see, we've gone through Wittgenstein saying that we don't need the notion of truth conditions. We only need the use. And said, no, we do need the truth conditions. There's a big insight in Wittgenstein's picture, but we do need the notion of truth condition. We've gone through Davidson saying, we do need the notion of truth condition, but we don't need the notion of reference. Reference drops out. What I've just been briefly arguing is that we do need the notion of reference too. We need the notion of the references of the individual words of the language as what we grasp when we're understanding our language word by word. So at this point, we have won our way back to the picture of language that we started with. Isn't that good? And next week, next Monday, we'll go on to look at a politician's account of how simple terms like this and that refer how reference gets going in the first place. Okay. In the meantime, have a good Thanksgiving. Okay.