 good morning good morning good morning my plan today is a one more time and crookie just to talk around various aspects of rigidity and necessity to the point where I hope we will all feel completely comfortable with these ideas and on Friday we will go on to Putnam's article meaning and reference which actually really is continuous with the Kripke and after Putnam will be going on to Evans and Putnam and Evans are really building on Kripke so all these ideas will keep coming back to from different angles so I want to start out by looking at what Kripke said about illusions of contingency why it's kind of a surprise to find that Hesperus is phosphorus is a necessary truth and then I want to come back to what we were talking about last time with the Strangler and different kind of names and so on because after last time's discussion a number of people made some very helpful comments about how I could have explained it better so I'm going to take another crack at it and then go on to review the definition of rigid designation and something about extending Kripke's approach beyond just ordinary proper names okay so let's start out looking at what Kripke says about Hesperus is phosphorus okay class Hesperus is phosphorus do we think that that is a necessary or be contingent is this rigid or flexible is this rigid or flexible is the whole thing necessary or contingent for a good class okay are you reasonably comfortable with that so far yeah because actually what we're going to do is just keep I'm going to do today just keep coming back at this from various angles but that's like the basic data we want to try and keep prodding away at okay the one objection Kripke considers you might have to say that's necessary it's a little after all couldn't it have turned out that Hesperus was not phosphorus I mean presumably there was a point in human history when nobody knew whether Hesperus was phosphorus I mean lots of these informative identities are like that right you it was a surprise to find out they were true but if it could have turned out that Hesperus was not phosphorus well doesn't that mean there is contingent if Hesperus is phosphorus I mean this is one thing is though that this isn't just supposed to be an epistemic possibility it's perfectly all right for Kripke to say there was a time at which for all we knew Hesperus could have turned out not to be phosphorus but could it really have turned out that Hesperus and phosphorus were different things is that it's possible that Hesperus and phosphorus were different things then it can't be necessary that Hesperus is phosphorus so here we have Hesperus coming up over the morning in the Pacific and here we have Dural phosphorus in the evening they are the other as you can see they look rather different couldn't it have turned out that they were different things isn't it possible for those to be different things if that's right then that's a challenge to the idea that the identity is necessary well what Gripke says about this is that it really could have happened that you had a visual presentation like this of the heavenly body in the evening and a visual presentation like that sorry a visual presentation like this of the heavenly body in the morning and a visual presentation like this of the heavenly body in the evening and it could have been that these two visual presentations were presenting different objects that really is a possibility there's a possible world in which that happens. You get a presentation like this in the evening. You get a presentation like that in the morning. You get a presentation like this in the evening. And they're actually presentations. They're, in fact, presentations of different things. That's got to be possible. Yes? But the question is, are you describing, then, a situation in which Hesperus is not phosphorus? If you are describing a situation in which Hesperus is not phosphorus, then it's possible for Hesperus not to be phosphorus. So it can't be necessary that Hesperus is phosphorus. Follow me very closely here. But the argument is, this isn't really a situation. Although it's possible that there could be in different heavenly bodies, providing this presentation and that presentation, at least one, either this one wasn't Hesperus or that one wasn't phosphorus. It was something different that was presenting in that way. It was something different that looked like that. So what you've got is a situation in which there are two distinct bodies occupying the very positions occupied by Hesperus, phosphorus, venus. But these are different. One of them is not Hesperus or one of them is not phosphorus. So Kripke's general answer to this kind of objection is, any necessary truth, whether it's an episteriori-necessary truth or an a priori-necessary truth, could not have turned out otherwise. It could not have turned out that Hesperus was not phosphorus. That's not really possible. But in the case of some necessary episteriori truths like Hesperus is phosphorus, you can say that under appropriate, qualitatively identical, evidential situations, so the qualitatively identical means you're getting presentations like this and this. It seems just the same. Under appropriate, qualitatively identical, evidential situations, an appropriate corresponding qualitative statement might have been false. So in this situation, you might have used words like Hesperus and phosphorus here, actually. But you wouldn't have been talking about the same objects. So that statement and that situation would have been false. Under appropriate, qualitatively identical, evidential situations, an appropriate corresponding qualitative statement might have been false. So there is a kind of illusion of contingency there, because you could have got a situation that was, for all the world seemed just like the situation we actually have, and in that situation, what you'd have expressed by Hesperus is phosphorus would have been false. But really, you wouldn't have been talking about Hesperus and phosphorus there. You'd have been talking about some different object. Because if that one really was Hesperus and that one really was phosphorus, they'd have been the same thing. Here ends the first lesson. So it can look like Hesperus is phosphorus is contingent, but that's just a mistake. Once you know all the facts, you realize that the identity is both true and necessary. Yes? The dubbing, yes, yes, you say, I dub the Hesperus and I dub the phosphorus. Yep. Well, isn't the photograph good enough? I mean, I'm trying to show the quality of the evidential situation by using the photograph. You could have a situation that seemed just like this. You have the same pixels, even though it's a different object at the other end. Yes? Fixing of the object is done by dubbing, sure. The dubbing is what? That's right. That's right. Not supposedly, we are fixing the reference by that dubbing. Yeah. That couldn't have happened. That's right. But that's not the supposition. The point is rather you could have a situation, you could have a qualitative situation that's qualitative like this and you say, I dub the phosphorus. You could have another situation that was qualitatively just like this one, but it was actually a different object you were looking at and you say, I dub the phosphorus and it's actually a different thing you've dubbed. I mean, it could happen with dubbing a person, right? You say, I dub the Balthazar and then a qualitatively identical situation. You've got the identical twin and you're saying, I dub the Balthazar. These are two different dubbings, the dubbings of different objects, but they're qualitatively very similar, yeah. So the point is that in the actual, given that what really happened, we actually did dub the same object twice over and once that's in place, the identity is necessary. But you can make sense of the hypothesis of a qualitatively similar situation in which you had dubbed different objects twice over, yeah. That's the thing that makes sense. That's where you get the illusion of contingency. That's why you might mistakenly think that phosphorus was phosphorus was not necessary. Last call, if you can formulate it as a question and raise it, yep, yes? The way you'd establish a truth here is by something of a spatial temporal location, which, yeah, it is important to distinguish all these different factors, you're right. But the simple idea here is you're taking one object, Hesperus, and you're saying all of it, phosphorus, there is one in the same. So if it's one in the same object in this world, how could it, here is something like this is what really is intuitively driving Kripke's thing. If it's one in the same object in this world, how could it somehow split apart in another possible world? I mean, if it's split apart in another possible world where you have two objects and in fact, you only have one in this world, how does that even make sense? If there are two in some other possible world, they can't both be identical to the original one. Do you see what I mean? Because they're two different things. So it really is kind of commonsensical. If Hesperus really is phosphorus, then it must be necessary. You can't make sense of it splitting up in different worlds. How could you split with yourself in a different part? I mean, somehow with yourself actually, it's so tempting almost to imagine, well, maybe I could be in two different places or many different places, wouldn't that be grand? But really, it doesn't make any sense. Yeah, because which one's you? So there's that, but at the same time, you have to try and do justice to the sense that, well, after all, there are things that could have turned out otherwise here. And that's what this is trying to do, is saying that you can't envisage a situation which is for all the world like the actual situation. But actually, you were talking about two different objects when you said Hesperus and phosphorus. So you're actually envisaging here a situation in which it wouldn't even be true that this one is that one. Yeah, there were always two objects, if you see what I mean. That's right, the illusion of contingency, but ultimately it's really a thing about epistemic possibility and not proper possibility, metaphysical possibility. Yeah, yep, yep, yep. No, I'm just looking for people who hadn't asked a question, but no, it doesn't explain why the designation is rigid. Okay, that's our next topic. Okay, are we reasonably comfortable with that? Okay, so let's go back to this thing about descriptions and names. So, okay, class, the inventor of the wheel is that, so that designates an object, all right, but we can make sense of talking about that as a designating an object, the one and only one person who invented the wheel. All right, does that designate the same object in every possible world? No, so that is a flexible designator. Consider the actual inventor of the wheel. Is that, that designates someone, all right? Does that designate the same person in every possible world? Yes, because every time it designates someone, you have to keep tracking back. For every possible world, when you wanna know who the actual inventor of the wheel designates in any possible world, you have to look back at the actual world and find out who in the actual world invented the wheel and then look at what that person's up to in this world. Yes? So, the inventor of the wheel is flexible, the actual inventor of the wheel is rigid. Yes? Nixon, yeah? Uh-huh. If we do have something like this in any possible world. Yes. Right. Yeah, the idea is the picture is, you might not think this is satisfactory, but the picture is we're designating a particular object and then it gets up to lots of different stuff in different possible worlds. And if you say, what makes it the same object, the answer, Kripke's answer is, there is no plainer English than that. It's the same thing, what more do you wanna know? If you keep shifting like that. I agree, that is, when Kripke talks about the telescope view of possible worlds, yeah, he's talking about a picture in which you got one possible world here, you got another possible world there. You look at all the, what's going on here, you look at what's going on here, and then you say to yourself, now which of these here is identical to which objects over here? That is really puzzling. And Kripke is trying not to get into that kind of problem. Yeah, he's trying to say, look, the whole way you specify a possible world is by saying, this one's getting Nixon in it, and that one's getting Nixon in it. And you just, you use the name to guarantee the sameness of the object across the worlds. Yeah, but that does lead to some pretty murky consequences. Like, if you don't mind me taking you and your neighbor as examples, right? In this, there's a possible world in which, okay, you're wearing a hat, and your neighbor is not wearing a hat. I mean, I hope you don't mind me doing this, right? But you're wearing a hat. So there's a world in which your neighbor is wearing the hat, and you're not wearing the hat, right? So there's a world in which you swap hats. There's a world in which you swap clothes. There's a world in which you swap many of your temperamental characteristics. I mean, presumably, if you go like this, you know, if your name is A and your name or his name is B, right? There's a world in which B gets all of A's characteristics and A gets all of B's characteristics. Yeah? I mean, that seems to make sense in Kripke's picture. There could be a world in which everybody in the room kind of shuffles around, yeah, takes on everybody else's characteristics, and you just stipulate that so. You say imagine the world in which A's got the hat, and you see what I mean? And the whole idea of your question, well, what makes it the same is to say, well, I don't know that that really makes sense. If you describe a world in which it's just like this one, the class looks just like this one, but everybody's shuffled round. You think, well, what makes it the case that it's the same? What makes it the case that it's the same person here who's sitting in this chair or is sitting in that chair in the other class? You don't know, looks just the same as this class. It looks like everybody's sitting in just the same chair. You see what I mean? So that seems kind of mysterious, but it is a consequence of Kripke's picture. Yeah, yes, yes, that's right. Yes, right. So the idea is that some objects do have essential properties, and they can't vary them in different worlds. But, and so then you have to get into the question, well, what characteristics of an object are essential to it? Yeah, and the trouble is there are some characteristics of an object that seem to be essential to it, like being a person, right? If I say, well, okay, it's one thing for everybody if you're shuffling around, what in the class? What about a world in which you're made of wood? You're actually a chair. You see what I mean? You might think, well, where do you go too far? Shuffling around is one thing, but actually being a chair or being a frog or being a wave out at sea. Yeah, that's not really possible. But the trouble is that's kind of intuitive, but the trouble is are you going to be able to amp that up, that doctrine of essential properties to such an extent that you can stop people shuffling around? You see what I mean? It's not that it seems completely hopeless, but it doesn't seem obvious either, and you could do that, yeah. So there is a puzzle for how you stop the shuffle. If you can just stipulate as Nixon and another, you're talking about in another possible world, and then go to speculate as to wherever might be going on with him in that world, it seems like it could be just anything. Well, or at any rate, the essential properties are not going to put that much of a dampen up on what you speculate might be happening in that world. Yep, yes, yes, right, that's right. Yes, yeah, ah, ah, current is interesting, but it is, I read current, if you put in current, the current president of the United States, yeah, I read that as flexible, yeah, because if Al Gore is looking at Obama, say, and saying that could have been me, he doesn't mean he could have been Obama, you see what I mean? He means he could have been the current president of the United States. So he's thinking that's flexible. Yes. That's, I mean, I don't mean that said in store, you know, God told me, but so far as straight off, my feeling is that it's only when you put in an actual that you get this effect, yeah. There are interesting analogies between time and possible worlds. You can think of time analogously to possible worlds, and you can think of descriptions, designators that vary, have different references at different times, as opposed to designators that designate the same thing relative to all times, yeah. And when you think about that, current is really kind of analogous to actually, but it's only an analogy, it's not the same thing, yeah. Okay, is this all right about the inventor of the wheel and the actual inventor of the wheel? Yeah, that's all right. Okay, now I think what happened last time was, I said, okay, I'm going to introduce a name bright for the inventor of the wheel. And the way I hear that is when you enter, I mean, Kripke says names aren't typically descriptive, and that's all right, I'm not quarreling with our argument, but I just say, I'm going to dub that, I'm going to say whoever it is that invented the wheel, I'm going to call them bright, and that's a name. And I mean, Kripke can't stop me, right, I'll do what I like, yeah. I can call him bright or her bright if I want, yeah. And then the thing is, my ear is that when you say by bright, I shall mean the actual inventor of the wheel, the inventor of the wheel, you always, when it's a name, kind of sticking naturally so that really you're using bright as rigid, yeah. My ear says I can make sense of the supposition that bright might not have invented the wheel. Now the thing is that you guys quite rightly picked up on the possibility that bright could be used as actually strictly synonymous with this description, so then it would not be rigid but flexible. So there are two ways you could go, you could say bright means the actual inventor of the wheel, or you could say bright means the inventor of the wheel, and if you say bright means the actual inventor of the wheel, that's to say that it's rigid, whereas what you guys are saying, or many of you were saying was, if bright means just the inventor of the wheel, then that's flexible, yes? And I actually compounded the confusion by using the strangler as my example, because there it really is, well I still think my ear is, it's a little bit weird to use that as flexible. I mean, let me give an example, if you say the president, that really is flexible, right? I mean, Al Gore can say I could have been the president. You can meet, it specifies a role, if you meet an aged Jimmy Carter or a dinner in Washington somewhere, he might say to you plentifully, I used to be president, you know? My hearing of the strangler was not that it was flexible like that, but I think it's a possible interpretation that it's flexible. You could imagine someone saying, I used to be the strangler, I don't think much of the new guy, what do you think? You see what I mean, you could use the strangler as the name for a role, yeah? In the way you use the president as the name for a role, and I think that is how you were hearing it, it's the name for a role, and in that case it is flexible. Someone else could have been the strangler, just as someone else could have been the president, yes? But I wasn't hearing it like that, I was hearing it as, meaning the actual, whoever's actually done it, a particular person that we're then going to speculate about, but once you say that, I think that sorts it all out. Is that right? So if you interpret bright as meaning just the inventor of the wheel and that's flexible, but if you hear it the way I was hearing it as the actual inventor of the wheel and that's rigid, so then if you hear it the way I was hearing it and you say bright is the inventor of the wheel, then that's a priori, but it's not necessary. So there you go, I blew up the idea that a priori, throughs are all necessary. The nice thing about this example is it seems so clear to, so to see clear what's going on, yeah? Oh, this is the rigid use. So if you take the rigid use here, then this is rigid, this is flexible. So different possible worlds, this is picking out something different. This is always picking out the same thing, yeah? So if I say, well, bright could have been hit by an asteroid, then a bright wouldn't have invented the wheel. So I'm hearing it as rigid and then it's not necessary that bright invented the wheel because it could have been prevented. She could have been prevented, but it is a priori because if anyone invented the wheel it was bright, yeah? That's right, that's a priori, right? But not necessary. The actual inventor of the wheel is the inventor of the wheel, very good, yeah? Okay, so the thing this brings out is when you get something that is a sign having its reference fixed by a description, then it really could be rigid or flexible. That was really the model of the discussion last time. I was saying, I hear it when it's a name is always being rigid. You guys are saying, no, but it could be flexible. And that's right. And that's where someone had mentioned intention, right? You get a choice. If you're hooking up the name to the reference by means of a description, you get a choice as to whether it's rigid or flexible. That's all right, okay. But then think about, I mean, the whole point of a lot of Krupi's discussion is this is really an untypical case. Usually the connect between a name and an object is set up by a causal chain. And if it's a causal chain, they're setting up the name object connection. There's no role being specified that something different could be meeting in different possible worlds. If it's just a causal connection, setting up the connect between the name and the object, then it looks like that has to be rigid. You couldn't keep the meaning of the name constant but vary the object. What would it mean to keep the causal connection constant but vary the object? It doesn't, I mean, it's a bit like if you imagine having a telephone conversation with someone, you can say, well, I might not have had that conversation with that person. So there's you and the other person and this causal connection between you down the telephone line, but it hardly makes sense to say I could have been having that very same conversation but a different person there. A causal connection, if it's gonna be the same causal connection, it's gonna be the same things on both ends. So if it was a causal connection between the object and the sign, that it's making it true that the sign refers to the object, then you couldn't keep constant the meaning of the sign but vary the object. So that case of descriptive names is very unusual. Usually it's a causal connection that's fixing the reference of the sign and then the designator has always got to be rigid. The name has to be a rigid designator, yes? N is the number of cows in the field, yes, that's right, April, I'm a bit necessary, yeah. Yes. Almost, when you say, I can't remember if it was N or N, say it's N is the number of cows and the cows and the field, right? Then N is not there being used as a variable. I see why you say it's a variable but it isn't really being used as a variable. I mean, remember if you're doing this in a maths class, probably not very hard maths class but you're not there using it. You're there using it as a sign for a particular number and the task that you'd be set is find out what that number is. So its reference really has been fixed by this when you say N is the number of cows in the field, yeah. So it's standing for a definite number of cows. It's just unknown, that's right and you've got to find it out. That's right, there could have been a different number of cows in the field, yeah, but it's still April, I, that N is the number of cows in the field and anybody says, ah, but maybe you're wrong, maybe it's not N, that's just, you're making a joke if you say that, yeah. Well, really, okay, yeah, yeah. Yeah, right, well, this is the subtle thing with where the actually comes in. I mean, I realize I'm doing the same thing again. I'm assuming that once you make, once you have a name here, yeah, this is the number of cows that are actually in the field, yeah, you're not assuming that it varies depending on how many cows, oops, very, yeah, you can speculate had N not been the number of cows in the field, yeah, had there been more cows in the field, that makes perfect sense, it seems to me, yeah. But as with the Strangler, you can read it as a name as, you could read it, I think, as implying a role, but I do actually think it's a very, it's a kind of unnatural reading. If you don't mind my saying so, as with the Strangler, I'll be your Strangler tonight, you know. You can make sense of that way of talking, yeah, but it's a little bit weird, yeah, okay, okay, okay, well, let's see, one last bit of geeking out on rigid designation. So what is a rigid designator? Scribke's official definition is, we'll call something a rigid designator if in every possible world, it designates the same object. And of course, the same things kind of different names in other possible worlds, like came up earlier. You can make sense of saying, suppose Al Gore had not been called Al Gore, yes, we've got the actual world in which Al is called Al, and then we've got this other world in which his parents decided to call him something different. Yep, that makes perfect sense. You could have had a different name. People sometimes complain about their names. If only, well, actually, I'm gonna give some examples, but there may be some people of this name in the class, so I wouldn't do that. You can think of your own, right? Okay, that makes perfect sense. In every possible world, it designates the same object. That's what a rigid designator is. But of course, there are gonna be some possible worlds in which the object doesn't exist. I mean, people sometimes say God exists necessarily, or numbers exist necessarily, but you and I, presumably, don't exist necessarily. I mean, if your parents had never met, you would not have existed, yeah? So suppose you consider the possibility in which Al Gore doesn't exist. Relative to that possibility, does the name designate anything? Well, you could say it's a rigid designator if in every possible world in which the object exists, we're only gonna consider the worlds in which the object exists, and relative to those worlds, the name always designates the same thing, yeah? Or what about the worlds where the object doesn't exist? Does the name designate anything relative to such a world? Well, you could say, with hispirus and phosphorus, you could say in any possible world in which hispirus exists, it refers to the same thing. In any possible world in which phosphorus exists, it's always referring to the same, the name's always referring to the same thing. So in any possible world in which these, relative to which these two terms are designating something, the statement's necessary. I mean, it doesn't really get an evaluation with respect to a world in which hispirus doesn't exist. I mean, if the planets had been formed in a different way, then hispirus might never have come into existence. Right, that makes sense. So relative to that world, is it true that hispirus is phosphorus? In that world, is hispirus phosphorus? Hard to say? No, right, it's a little bit strange. Yes, it's hard to know quite what to say about that case, yeah. So you could say it's weakly necessary in the sense that it's not that it's true in every possible world, it's just that it's true in every world in which that planet exists, yeah. It's true in every world in which Venus exists. So that'd be a little bit weaker than saying it's true in absolutely every world in which, in every world, in any world at all. Or he could have a stronger definition of rigid designator. This is just like a homework question. I mean, it's not really clear, it seems to me, which way to go on this. You could say I'm gonna have a stronger definition. In every possible world, the name designates the same object, whether or not the object exists in that world. Yeah, isn't that weird? But suppose you consider an example like, if Hitler had never been born, the world would have been a better place, okay. Well, if you wanna consider that possibility, okay, I'm using the name here to specify the possible world, yeah. So I use the name and I specify this world. This is the world in which it's true that Hitler was never born, yeah. But if it's true in that world that Hitler was never born, then the name Hitler must be designating something relative to that world, right? Is it, is designating? Well, you can't, well, no, it's not designating an absence, it's designating a person. It just happens not to be there in that world. Just think how you make sense of this. If Hitler had never been born, I'm referring to a particular person, Hitler, and I'm specifying this possibility, he was never born. So how should you say you load the name up? Into the proposition you're considering, sorry, you load the object up, you load Hitler up into the proposition you're considering, and then you take it around the possible worlds and you look at what's happening in each possible world, and some of those Hitler is there and some of those he isn't. You see what I mean? But you seem to need to think about it in that way because if you say if Hitler had never been born, well, I wouldn't have known who you were talking about. That doesn't seem the right answer. Yeah, it seems perfectly clear that this is true. Well, I mean, yeah, there's nothing controversial about that. It seems perfectly clear that that's true. Yeah, yeah. Very good, yes. Yes. It's very hard to know what to say about the unicorns in this kind of picture because how does the term have meaning? In the actual world, there are no unicorns, yeah? So there's nothing to be causing the use of the term unicorn. So it must be descriptive, yeah? And whatever has a horn, something that has a horn. Is that right? I'm not sure if that's right. It's hard to know how it's got meaning the term unicorn. I mean, how does it have, how come I know what you're talking about when you say unicorn? Because there's nothing that I'm causally connected to, yeah? You're referencing the concept, yeah. That's not what you mean. The concept doesn't have a horn, right? You mean the unicorn's got a horn, not the concept of unicorns got a horn. Right, well, yeah, it's very hard to know how to, I find it hard to know how to evaluate the kind of claim is necessary that unicorns have horns. I mean, after all, if you take cows, I mean, cows, I mean, bulls, something that I'm not very sure moose, no, they have had flowers. Rums, rums of horns, right? Anyway, so rums of horns, that's true in this world, right? Is it necessarily true? Well, I guess not. I mean, after all, rums could have had horns bred out of them, could have happened thousands of years ago. There could have been some genetic mutation a couple of thousand years ago or tens of thousands of years ago, as a result of which rums never got horns. You can make sense of that. How does it go with unicorns? I mean, I don't know, I mean, how do you find out about the genetics of the unicorn? You see what I mean, it's very hard to know how to evaluate these statements about unicorns. And there's something, so the causal theory says it's hard to know how to interpret a statement about, the causal theory has difficulty interpreting statements about unicorns, but I actually suspect that you and I do too. As you see it, I mean, if you really pushed us on what we're talking about when we're talking about unicorns and what's true about unicorns and what's necessary, it's not that clear anyway. I think, yeah, yeah. Yep. Individual names say Hitler, you know, you might be referring to, That's the one, yes, sorry. Yeah, but I mean, I'm sure there are other people in Germany that unfortunately have that name. So you could be referring to somebody else, so it doesn't really seem like just a word has meaning. I told you, and you know, it doesn't, don't, you have to, is it meaning really just a property of statements or a language as a whole? Well, if you're going to talk about truth or falsity of individual statements, it's hard to see how a meaning can be just a characteristic of the language as a whole, because then you couldn't talk about the truth or falsity of an individual statement, yeah. So long as we're able to talk about a particular statement being true or false, then it does seem like we must be able to explain how the components of the statement are contributing to that truth or falsity. Yeah, that's that notion of semantic value. And the only, really the only way of explaining what a name is bringing to a statement being true or false is its reference. You could throw that out and say, I don't believe there's any such notion of truth, yeah. We only evaluate the totality of statements made in a culture or something. That totality is right or wrong, but it's a really wild view that, yeah. I mean, people have held just about any possible view here, but it really is not commonsensical. You don't know what it means to make of inference in such a case, yeah, because inference is taking you from true statements to true statements if it's correct, yeah. Okay. Okay, so you could say Hesperus is phosphorus is strongly necessary in that it's true in any world whether or not Venus exists in that world. Even in worlds in which Hesperus and a phosphorus don't exist, it's still true that Hesperus is phosphorus. So these are two different definitions of rigidity. In every possible world in which the object exists, the term designates that same object. And in every possible world in which, in every possible world, whatever, the term is still designating the same object. Whether or not the object exists in that world, that's the point of the Hitler example. Okay, I think we'll leave it there for geeking out on rigidity and necessity. Okay, we will move on to Putnam on Friday. Okay, thanks. Thanks for the discussion.