 Well I think we should get started. Welcome back everyone. Nice to see you haven't been frightened off. Today I'm going to talk about something absolutely central to philosophy, and that's the methodology of philosophy, which is the methodology of logic and argument. I think I said something last week about this, but it bears repeating. Felly, oes ychydig, rydych chi'n ei hunwn. Rhefn wrth gwrs, rwy'n meddwl eu ffaisfodau y mnog, os ymgyrraedd nhw'n meddylo, a'r rhefn ai'r meddwl ei gynwylltu'n meddwl rhywbeth. Mae'r rhefn wedi'u meddwl rhywbeth yn hyn. Felly, mae meddwl mewn meddwl, maen nhw'n meddwl ei ddweud i ddweud, maen nhw'n meddwl ei ddweud i meddwl mewn meddwl. experience. Instead, we do thought experiments. So it's very nice being a philosopher because you don't have to leave the comfort of your armchair. You can stay in the library. You don't have to get messed up with test tubes and things like that. You can just sit there and do it in your head. But in the same way as a scientist is constrained by the laws of nature, the philosopher is constrained by the laws of logic, and that's why we Mae'n tynnu'n gyfnwys gwirio ydych chi'n gwirio. Dyn ni'n fyddenim ni'n gwrs oherwydd oedd yw'n gweithio'n gwirio'n gwirio'n gwirio'n gwirio'n gwirio, ac ei gynnig i ni'n gallu bod fynd i chi'n gwirio'n ymddangos addai'r hyn sy'n arlyfawr i'ch bethau ymarferlain arir y cyflosifau a'r cyflosfi wneud. Roedd y gallwn i chi'n dod i'n gawsihon ychydig am ydych chi, yn y cyflosifiydd gwaith ymddangos a'r lleidio'n ymddangos. First of all, we're going to talk about what logic is. It's not the sort of argument that your teenage children have. We all know that sort of argument. No, you didn't. Yes, I did. No, you didn't, etc. Nor is it the sort of argument that you laughed at on Monty Python. You remember the argument sketch probably. Instead, the argument is going to be a set of propositions which we call premises, which are put forward as reason to believe another proposition which we call the conclusion. So, here's an argument. I want to get to London by noon. I believe it's a necessary condition of getting to London by noon that I catch the 1020 train. Therefore, give me the conclusion, I must catch the 1020 train. So, what you've got is you've got two propositions. I want to get to London by noon, and I believe it's a necessary condition of getting to London by noon that I catch the 1020, and together they combine, and you all knew immediately what the conclusion had to be, because there's only one conclusion that's entailed by these two, isn't there? And you all got it right. That's because you are all rational animals. Actually, you do logic pretty well as well as I do. What I can do that you can't do is tell you how you do logic, what it is that you're doing when you do logic. But as rational animals, you're doing logic all the time. You knew the answer to that, and the reason you knew is because you do logic. Logic is just the method by which you go from one set of thoughts to another thought. It's one way of acquiring knowledge, if you like. Okay, so that's what an argument is. Now, there are different types of logic because there are different types of argument. And there are all sorts of different types of types as well. But one type of argument, for example, is deontic logic, the logic of moral discourse. So, if I say to you, lying is wrong, therefore, what conclusion are you going to give me? Or I shouldn't lie or something to the effect I should tell the truth or I shouldn't lie or whatever. Notice that's a different kind of argument because you haven't got two premises there, but you have got a premise again and a conclusion I shouldn't lie. But it's interesting because Kant says that what's peculiar about deontic logic is you go straight from a statement to the effect that something's wrong to the conclusion that you shouldn't do it. Kant thinks that that's a very peculiar thing about morality because for everything else, you would need a desire in there as well. So, if you look again at the first argument, I want to get to London by noon. It's a necessary condition of getting to London da da da da da. Therefore, I need to leave on the 10.20. If you took away the desire, would you have a good argument left? No, you'd just say it's a necessary condition of getting to London by noon that I catch the 10.20. Well, so what? Unless you want to get to London by noon, that doesn't entail anything, does it? You can do anything you like consistently with that. But once you've added that, you've got something that requires an action, haven't you? So, it would be irrational to have that desire and that belief and not to believe I must catch the 10.20, wouldn't it? That's true, but I have said a necessary condition here. So, if I've taken that out, you're right, but I think as I put that in, anticipating that somebody might say something like that. Sorry? You've only said I believe it. That's true, but if it's a matter of action, my belief would be sufficient, wouldn't it? Because even if I was wrong about that, I would still think it's rational. And what's more, I'd still be rational to catch the 10.20, wouldn't I? If I believed that, even if in fact I was wrong, okay? But if you look at this one, do you need a desire in there? Kant would say no, lying is wrong, therefore I mustn't lie. Do you need I don't want to do the wrong thing or I do want to do the right thing? Kant would say no, because he'd say if you think that you need to add and I want to do right, you just don't understand what it is to do something wrong. Okay, think about that for a second. If you entertain the possibility that you need to add I want to do what's right, you're implying that you might not want to do what's right, and Kant would think that that would show that you didn't actually understand what right means. Are you with me? No, but Kant would say they don't understand what's right. I understand that 10-year-olds go around making sweets from shops, because their understanding of right at the moment is if anyone finds out, I'll get into trouble. Wrong is mummy will find out and I'll get a smack or something like that. Ooh, how old-fashioned. Oops, it's illegal nowadays, isn't it? Anyway, whatever. It isn't. Okay, well at least I haven't said anything legal but immoral maybe. So if you're thinking that for something to be wrong is if I get caught I'll be punished, you haven't yet got the concept of right and wrong, have you? What you've got is a prudential concept that may cause you to act in some of the same ways, but I bet if I leave my purse here when I go out, as I may well do, you wouldn't not pinch it because you might be found out. No, you would have other reasons for not pinching it, mainly because you'd think it was wrong. Probably wouldn't occur to you, but you'd also, if it did occur to you, you'd think it's wrong. So there are different ways. If you think about it, do you think you could think that lying is wrong, but there's no reason why you shouldn't lie? So of course, let's say somebody says to you, your builder says to you or your solicitor says to you, well of course lying's wrong, but that doesn't mean I, it doesn't mean we shouldn't lie here. Isn't there something wrong with that? Isn't that a contradiction? Thank you. Yeah, that's different. We're saying if you believe that lying is wrong, then you're going to think you shouldn't lie. I mean, if you don't think lying is wrong, then there's no reason not to lie, is there? But if you do think lying is wrong, could you all, could you consistently believe, let's, all right, let's say if you believe this lie is wrong, could you consistently believe that there's no reason for you not to lie? I have defined lying in saying you think this lie is wrong, so it's not a white lie. I'm just saying that there are times when you don't lie. Yeah, but a white lie, we call them white lies because we don't really think they're wrong, do we? Well they are, because if you're saying that you're... Right, no, let's not get too away from the topic. If we believe that lying is wrong or that this particular lie is wrong, even if it's a white lie or not, doesn't matter, could you consistently think, never mind, that doesn't mean I shouldn't do it? Right. Yeah, okay, I'm going to leave this, because maybe Deontic logic was a bad idea. Okay, Kant would say that if you believe that, you have got to think I shouldn't lie. If you think that lying is wrong, you might not, but if you do, then you're going to think you shouldn't lie, because you cannot think lying is wrong, but that there is no reason for you not to lie, because for some things to be wrong, is itself a reason for you not to do it. It may not be the final reason, it may not be conclusive, but it's a reason not to do it. And that's Deontic logic, because you've again got a premise and a conclusion, and the premise gives you reason to believe the conclusion. So that's what's down here, we've got a set of propositions or one proposition, a premise put forward as reason to believe another. Here's another type of argument, this is modal logic. And I'm sorry, it's a bad example, but I'm lousy at thinking of examples. It's not possible for Vixens to be male, that's because Vixens are defined to be female, therefore that Vixen is not male. If you believe that, you're going to believe that, and that's because if something's not possible, then it can't be actual, can it? So if it's not possible for me to be male, then it can't be the case that I am male. So you're recognising that something's not possible will cause you to believe immediately that nor is it actual, because it couldn't be not possible and actual. So that's modal logic, the logic of modality, the logic of necessity. And then another type of logic is the logic of conditionals. So you've probably all heard the saying, if it's gold, I'm a Dutchman. That means, as we all know, that it's not gold, doesn't it? How do you know that? Well, you'll just have to believe me, take it on authority, but that's because you know the logic of conditionals. And if I were to write the truth table up here for conditionals, a truth table gives you the truth of a conditional in every possible world, you would see that if it's gold, I'm a Dutchman, has to be true. And therefore, it has to be false that it's gold. So I'm not going to go into that. I'm just going to tell you, you know what that means, because you know the logic of conditionals, because you're a rational animal. What you don't know is what I know, which is how to draw the truth tables and how to show that that means it's not gold. Okay? Firely baffled, are you? Yes? All the different worlds. Well, some people say that a different possible world is nothing more than a different situation. There's a philosopher called Kripke, a very famous philosopher, still alive, or if he isn't, he's only just... It was today or yesterday, and I'm very sorry about it. He believes that in order to explain the truth of conditionals like if Germany had won the war, we would be speaking German. Now, some of you may think that's true and some of you may think it's false. We could argue about this. We could give reasons for different sides. But I'll tell you what doesn't make it true, namely that the Germans won the war and we are speaking German, because they didn't. That's a counterfactual conditional. And so we think of conditionals, even counterfactual conditionals, as true and false all the time. And some logicians believe that in order to explain the truth of counterfactual conditionals, you've got to postulate other possible worlds. Now, of course, there are other reasons in physics for postulating possible worlds. In mathematics there are reasons for postulating possible worlds. What is a possible world? Well, Kripke thinks it is literally another place just like our worlds, like our universe rather than like our Earth. But there's no causal interaction between one world and another. But you can say, okay, is there a possible world in which Marianne's wearing jeans? Tell me the answer? Yes. Is there a possible world in which Marianne is male? No. Are you sure? Does anyone think there might be? No, no, no, no. We're asking a question here. Could I have been male? Or could I have been male? In other words, if I had to... No, hang on. No, an X and a Y chromosome instead of two Xs. Would I still have been Marianne? Would I still exist? Okay, lots of people think no. It's an open question. Some people think no on that. Some people think yes. But notice we do think there's a truth value to it. We can ask that question and we can argue about the answer. And it's possible that in order to do that we've got to postulate the existence of possible worlds. Of other worlds that we know about by reason but not by perception. Do you see what I mean? We can see this world. We can touch it. We can hear it. There, you heard part of it. But you can't see or touch a possible world but you know they're there because you argue about conditionals. Is there a world in which I'm male? Well, some of you think yes, some of you think no. And the more you look at the logic the more you might be able to come up with you're absolutely right it is, no, the answer. Or you're absolutely right it is, yes, or whatever. But that's what philosophers are doing is that sometimes I talk about it as spinning the possible worlds in order to find out what the limits of possibility are. Because if you think of what a scientist is doing they're looking to see what the limits of actuality are. What is the case in this world? Whereas what philosophers are looking for is what could be the case. Okay? Not just in this world but in any world. Could there be, could time travel be possible, for example? It looks as if time travel isn't possible. We know time travel isn't possible at the moment. Could it be? Is there a world in which it's possible? And if so, could this be a world in which it is? So, we're expanding the worlds and asking, okay, we know there are possible worlds. We know there isn't a world in which there are square circles, don't we? Is there a world in which circles are square? Could there be? Could a circle be square? Exactly. It's the concept, isn't it? If something's a circle, it could not be a square. End of story. So, we know that there's no possible world in which circles are square. That's not a possible world. Whereas the world in which Marianne is male, maybe that is a possible world. The world in which Marianne's wearing jeans is definitely a possible world. So, we're trying to limit the possibilities. What possible worlds are there and which aren't there? Yes, but what we're asking is, is Marianne necessarily female? Or is it just a contingent fact that I'm female in the same way it's a contingent fact that I'm wearing a dress? I might have put jeans on this morning. Might I have been male? We know that Vixen can't be female because in the same way we know that a bachelor can't be married because it's part of the definition of being a bachelor or part of the definition of being Vixen. Is it part of the definition of Marianne, of me, the time female? Well, some people do think so, but others think not. You thought not. So, there are different views on this one. And I could give you other ones where we're not sure. What's important is there are some cases where it's definite there is such a world, some cases where it's definite there isn't such a world, some cases that we don't know about. And the job of a philosopher is to find out about those. So, that's modal logic. And I looked at the logic of conditionals. But there are two main generic forms of argument. These are looking at particular types of discourse and the logic of that sort of discourse. So, as moral agents, you understand something about deontic logic even if you've never heard about it before. You also understand something of the logic of modality and the logic of conditionals. But here are two very broad sorts of argument, deductive arguments and inductive arguments. Now, I want you to ignore the ones under the dotted lines at the moment and just look at the ones on the top. Now, I know you're all reading the ones underneath the dotted line at the moment. Stop it! Okay, let's look at this one. If it snows, the male will be late. It is snowing, therefore, the male will be late. The nice thing about deductive arguments is that they give us certainty. They don't give us unconditional certainty, sadly. If the premises of the argument are true, then the conclusion must be true. Okay? So, have a look at these premises there and tell me if that's a deductively valid argument. If it snows, the male will be late. It is snowing, therefore, the male will be late. Could it be that these premises are true and the conclusion false? No, okay. Some people are thinking about it. Let's let them think. Yeah, but why do we want to do that? Because I'm giving you an example of a deductive argument and if I change that will to might, then I haven't got a deductive argument, have I? Because then the premises could be false without the conclusion being true. The particular thing about this one is I wanted an example of a deductively valid argument. What I hope I've got is that if these premises are true, the conclusion must be true. There is absolutely no logical possibility of those premises being true and that conclusion being false. Is that right? Yeah. Okay, that's great. So, we've got the certainty in a deductive argument conditionally upon the truth of the premises and the validity of the argument. Now, here's an invalid deductive argument. If it snows, the male will be late. The male is late, therefore, it's snowing. Okay? Now, there's something wrong with that argument, isn't there? What's wrong with it? Good. Give me another reason. Yes, but can you tell me, give me a reason in which? Puncture. Puncture. Good. You can't hear. Ah, okay. Good. I'm glad to say. Okay, well, I'll repeat what was said there. If you've got an invalid argument, what you'll be able to find, at least what you'll be able to say that there is, you may not be able to find one, because if you're like me, you're lousiest example. If it snows, the male will be late. The male is late, therefore, it's snowing. You should be able to find a counter example. In other words, a situation where the premises are true and the conclusions false. Okay? So, let's say the male man had a puncture. Okay? If it snows, the male will be late. Well, it's late. Therefore, it's snowing? Well, no. You know, it's actually the male man's had a puncture instead, or he got up drunk, or he, you know, whatever happens. There are all sorts of reasons why the male might be late, in addition to it's snowing. So, we can't go from the confirmation, the affirmation of the antecedent to the affirmation of the conclusion. Whereas we can go from this one to that conclusion. There's some sort of causal relationship between snowing and the male will be late, which goes in one direction. Otherwise, it wouldn't always hold if there wasn't a causation. Whereas the second one, the causation simply isn't going to work. There's nothing that causation doesn't, in the first statement, doesn't go in the right direction for that to apply. Exactly. But the fact is, if you have any argument of that form, you will have a valid argument. Whereas if you have any argument of that form, you won't. Let's, I'll show you what I mean by that. Hang on, I'll have to find one I haven't written on. And then I won't be able to find where I am. So, you'll have to wait while I... If P, then Q, P, therefore Q. Okay, can you see that that's a formalisation of this argument? What does P stand for here? Sorry? Not the premise, no. Sorry, if P, then Q formalises the whole premise, doesn't it? What does P stand for? You're all too clever, you're all too clever, no. Have a look at that premise and tell me what I've taken out and replaced with a sentence letter. Thank you. It is snowing, or it snows. Yup, so P is, it snows. So, if it snows, then the mail will be late, exactly. So, you see, you've got it now. You didn't know you could all do logic. Therefore... Sorry, P, so this says... It's snowing. It is snowing. Notice I should have probably put it, if it is snowing, then the mail will be late and I didn't. Okay, it is snowing, therefore... Q, the mail will be late. The mail will be late, thank you. Okay, then we've got if P, then Q. Q, therefore P. And notice that, whereas every argument of that format, it doesn't matter what you put in there, that would be valid. And it doesn't matter what you put in here, it wouldn't be valid, would it? So, if we make P, let's change the interpretation. So, if I do this, if you were a student doing this, you would have to, and you gave me these arguments, so I'd say, where's your interpretation? And if you hadn't provided one, you would lose marks. Okay, so let's give an interpretation. P is, it is snowing. And Q is, the mail will be late. Who's going to try... Actually, all try now. Try and give me another interpretation of those sentence letters. Okay, so forget about snow in the mail. Give another interpretation. Think about Marianne lecturing, Marianne wearing dresses or... It's being Monday or... Do you know what you're doing? You're all looking very... Oh, okay, you're just looking serious. It's serious stuff. Shh! Don't yell out, you're all trying it. I'll tell you what, when you've got one, put your hand up. And just keep it up, till I... Okay, so you're looking for another sentence for P and another sentence for Q, which gives you an argument. Okay, gentlemen, that there. What have you got? Well, you don't need the if, because the interpretation is only for P. So P is... No, not if, just Obama wins. Do you see what I mean? Because if is a logical word here. Yep, that's right. Okay, and Q is, Democrats will be pleased. So if we pull that in here, we've got... If Obama wins, then the Democrats will be pleased. Obama...actually we've got a problem here, haven't we? Because notice we've got tense seed, which immediately causes us a problem. But let's forget that for a minute. Shall I say Obama wins? Therefore the Democrats will be pleased. Okay, here we've got... If Obama wins, then the Democrats will be pleased. The Democrats are pleased. Therefore Obama won. I mean, there must be something else that would please them, wouldn't it? Okay. How about someone else? Let's have just one more. Okay, do you want to have a go? Hang on, what's P? Milkman arrives, okay. And Q is... My dog barks. My dog barks. Okay, so if the Milkman arrives in the morning, then the dog barks, the Milkman arrived, therefore the dog barks. If the Milkman arrives, then the dog barks, the dog barks, therefore the Milkman has arrived. You can see what's going on, can't you? Any argument of this form means that... Because the thing is P may be a sufficient condition for Q, but it's not a necessary condition for Q, is it? So it's a sufficient condition of the male being late that the snow... that it's snowing, but it's not a necessary condition. And this fallacious argument here suggests it is a necessary condition, and that's why it's never going to work. Okay? Well, you see, you're all doing logic, and what's more, you're all doing formal logic immediately. Fantastic. Okay, so that's deduction, and the nice thing about deduction is it gives you certainty. If the premise is a true, the conclusion must be true. But of course, that's quite a big if, isn't it? If the premise is a true, the conclusion must be true. Often, we may not know whether the premise is a true or not, and therefore we won't know whether the conclusion is true. But the fact that we know the argument is valid is nevertheless useful, isn't it? Because the validity will preserve the truth of the conclusion. So, well then, if we can show by scientific methods or whatever that the premises are true, we will know that the conclusion is true. And if we can show by empirical means or whatever that the conclusion is false, then what do we know? Good. One of the premises is false. Exactly. So, we learn a lot from a valid argument that has a false conclusion. We learn that one of the premises must be false. Can we say at least one of the premises? Yes, you can. At least one of the premises, because it needn't be more than one. Just one false premise is quite sufficient to show that the conclusion might be false. Not is false, but might be false. Okay, good. Fantastic, in fact. Shame about the deontic logic, wasn't it? We might have to go back to that and bring yourself to be so good at logic. Okay, let's have a look at induction. Now, induction is different. Inductive arguments don't give us certainty. What they give us is more or less probability. So, probability is a matter of degree in a way that validity isn't. Validity isn't either or matter. Either an argument is valid or it isn't. Whereas induction gives us probability that's a matter of degree. You can have strong probability or weak probability. So, if we look at this argument here, every day in history, the sun has risen. Therefore, the sun will rise again. I should have put tomorrow in that, but tomorrow. Okay, that's a pretty strong inductive argument, isn't it? In fact, we're all pretty well relying on it. Anyone who's got a lunch appointment tomorrow, for example, is relying or a dentist's appointment or anything else. But, of course, it's not. It doesn't give us certainty, does it? Because we might be wrong. Tomorrow might be the day when the laws of nature are just going to change. The fact that it's always been like that in the past doesn't mean that it's always going to be like that in the future. The fact that the laws of nature have always been the same in the past doesn't mean that they're always going to be the same in the future. I'm the one who pointed out that, as a matter of fact, it just could be that, however strong your deductive argument is, it's not going to give you certainty. Russell talked about the chicken who every day in the whole of his life, the farmer had come out and given him food. And the chicken, here comes the farmer and he thought, oh, good, food's coming. Of course, he got his neck rung. Now, how do we know that we're not in that position with respect to the sun rising tomorrow? And what Hume said is we don't. There is nothing you can do to show that there's anything more than probability here, because that argument rests on the idea that nature is uniform. Why do you believe that nature is uniform? In other words, that the future will be like the past, because the future always has been like the past, hasn't it? Well, that's no argument, because that is itself an inductive argument, isn't it? Whereas the future has been like the past, it always has been like the past. You know, it's like trying to hop around on one leg here. Can I ask you a question? Of course, no. It's certainly true that in induction, you're going from something observed or something that has happened to your, oh, what's the word? Mine's gone blank. No, when you project into the future, extrapolate, whoever said extrapolate, that's what I meant. You're extrapolating into the future, aren't you? So, for example, here's another inductive argument, so I think you'll agree it's not a terribly strong one. Every time you've seen me, I've been wearing earrings. That's probably true, is it? Especially if you've only seen me last week and this week. Next time you see me, I'll be wearing earrings. Now, that is an inductive argument, isn't it? There's some probability there, but I think you'd agree it's not as strong as that one, because next time you see me, it might have been as I'm going out to get the paper in the morning before I even put clothes on, the dressing gown on or something. I don't wear earrings with my dressing gown. Anyway, we know too much about human beings to assume that that's a good inductive argument. So, in deduction, you get certainty, it doesn't need to be about the past or the future. It can be about anything at all. With induction, you are extrapolating from, not necessarily the past, you can extrapolate from the present to something else. So, all the chairs in this lecture room are blue. Therefore, the chairs in the next lecture room are going to be blue. Now, there's no time element in that, is there? There's just a, you know, and is that a good inductive argument? Well, it's sort of, no, it's not very good, is it? Certainly, no, it's not as good as that one. Okay, so these are two types of argument and whether you've got deontic logic or conditional logic or modal logic or whatever, you'll get arguments of this kind. For example, the argument I was trying to convince you of, lying is wrong, therefore you shouldn't lie. But Kant believes that's a deductive argument. Okay, because the premise entails the conclusion. If the premise is true, the conclusion can't be false. Now, some people disagree with Kant, in which case that wouldn't be a deductive argument. Wouldn't obviously be an inductive one either. Instantly, there are other types of argument. There's, ah, this is where I'm, haven't we? And we've had that one. Okay, there's arguments by analogy. Anyone tell me what one of those is? Give me a very famous one perhaps to do with watches. Anyone read Dawkins' book, The God Delusion? He talks about a very famous argument from an analogy. Can anyone tell me what it is? The blind watchmaker, exactly. So the universe is like a watch. A watch has a maker, therefore the universe has a maker. Okay, Dawkins thinks that's an appalling argument, and he's probably right. But it's an argument from analogy. What you do with an argument from analogy is, you find something that's like something else, and so if A, you've got A is P, okay, A has this property P, A is like B or B is like A, therefore B has P as well. Okay, so A has this property, B is like A, therefore B has this property too. And of course there, the premise of similarity is absolutely crucial, because if you haven't got the similarity there, then you haven't got the conclusion either. And of course there are arguments from causation. If A causes B, then you don't get an A without a B. Okay, and the reason that that's a valid argument is that you assume that causation brings correlation. If A causes B and you get an A without a B, then that shows you that A doesn't cause B, because an A isn't sufficient for a B. Okay? Right, well let's move on from there. Those are the types of arguments. What's important about any argument, whatever sort of argument it is, is that if you want to evaluate it, you've got to ask two questions. And the questions you've got to ask are these, are the premises true and is the argument valid? And in a case of a deductive argument, what you're asking is, is it the case that if the premises are true, the conclusion must be true? Okay, that's what you're asking if the argument is deductive. And if it's inductive, you're asking, is it the case that the premises provide good reason to believe the conclusion? So how strong a reason to the premises provide us to believe the conclusion? So those are the two questions you've got to ask. It doesn't matter what the argument is, if you're reading Descartes, or you're reading the leader in today's newspaper, what you've got to do is try and first to analyze the argument, in other words, set it out logic book style, identify the first thing you go for is the conclusion. Identify what it is this person is arguing for. Okay, that's the conclusion. And then find out what he's using as his reasons. And once you've identified those, you've got the premises. So you should be able to set it out premise one, premise two, conclusion. And then you ask, okay, what do I think of these premises? Are they good premises? What do I think of this argument? Is it valid? In other words, if the premises were true, would the conclusion have to be true? Or do the premises provide me with at least good reason to believe the conclusion? And if either of the answer to either of these questions is no, then you don't have a good argument. If the answer to both those questions is yes, you might have a good argument. It's not sufficient. Let me give you an argument that satisfies both of these. So I'll get lost again. Now, is the premise... Okay, here's the premise. Here's the conclusion. Okay, is the premise of this argument true? Oh, sorry. It says whales are mammals. Therefore whales are mammals. Okay, the premise is true? Okay, is there any possible situation in which the premise is true and the conclusion false? There isn't, is there? How could there be? The conclusion is the same as the premise. That is a circular argument. All circular arguments are valid. How could they not be? If the conclusion is amongst the premises, then there can't be any situation in which the premises are true and the conclusion false. So that's a valid argument. But what's wrong with that is it's circular. You're not going to learn anything from that argument. So the fact that you answer yes to both those questions isn't sufficient for it being a good argument, but it's certainly necessary. And that as a philosopher, those are the two questions that are... Well, actually as a philosopher, that's the one that bothers you. It's often scientists who are interested in that one. So, for example, every swan I've ever seen has been white. Therefore, all swans are white. Okay? Well, it may be true that every swan I've ever seen has been white. I need to find out now whether that's a sufficient reason for thinking that the swan in the next room is white. I mean, if it's true that all swans are white, the swan in the next room will be white, won't it? But my job is to go into the next room and see if it's white. And if it isn't, what do I know? Well, either that it isn't a swan, okay, or that it's not the case that all swans are white. And maybe we would say it isn't a swan. I mean, you must have heard when Mrs Thatcher in people saying she's the best man in the cabinet. Okay? Well, here's the argument. All women are passive. Mrs Thatcher is a woman. Therefore, Mrs Thatcher is passive. There's the argument. Well, Mrs Thatcher clearly isn't passive. Therefore, either she's not a woman or not all women are passive. But do you see how it works? Humor often depends on logic precisely because it tells us what we ought to think and then somehow confounds us. Are the same. Well, therefore, actually just marks the conclusion of an argument. It says I am, the thing about an argument is it's premises giving reasons for a conclusion. And we can give any premises as reasons for any conclusion. So, if I say Melbourne is in Australia, the sea is salt, therefore Paris is the capital of France. Okay? Now, that sounds like a really bad argument, doesn't it? But I could tell you a story about how, here we are, we're all, not only are we all terribly ignorant, really very badly ignorant. We have been told that these two sentences are such that if they are true, this third sentence is true. Okay? The first sentence is the sea is salt and the second sentence is Melbourne's in Australia. So I say, okay, you go off and find out where the sea is salt, okay, you go off and find out where the Melbourne's in Australia. So off you scurry and you find the nearest encyclopedia or dictionary and so on. You come back and you say the sea is salt and you come back and say Melbourne's in Australia and I say, therefore, Paris is the capital of France. Okay? Do you see then there is an argument there? And what's made those premises provide us with reason for the conclusion is the context, isn't it? By providing a context, I could make those apparently completely irrelevant sentences an argument. So the therefore just stands for a conclusion to say I am saying that that is reason to believe that. Now notice something else. If I add lots of other sentences in here, am I going to change the fact that this argument's valid? Well, let's put in it's not the case that mammals, whales are mammals. It's not the case that whales are mammals. Whales are mammals, therefore whales are mammals. Now, is there any situation where both those premises are true and that conclusion's false? Actually, that's a... They can't both be true, can they? So is this argument valid? Yes it is, because there's no possible situation in which the premises are true. So how can there be a possible situation in which the premises are true and the conclusion false? I'm going to do a truth table here, which is probably asking for trouble, but let's do it, shall we? Okay. This is using the notion of possible worlds to explain something. Okay, I've got, if P then Q, P, therefore Q. No, I don't want that. Hold on, sorry, I'm changing my mind. Let's try this. Okay, each sentence can be either true or false, can't it? Okay, let's assume for the moment, if you've got a sentence, the cat sat on the mat or Marianne's wearing a dress or something like that, it can either be true or it can be false if it's a contingent sentence. So this truth table represents every possible world with respect to the combination of truth values here. Okay, so this is the world in which P is true and Q is true. Okay, this is the world in which, tell me. Good, okay, this is the world in which. That's right, and this is the world in which they're both false, absolutely. You're really doing well here. If your mate's heart and undergraduates can't do that, it's because they haven't separated the possible worlds, because each of these possible worlds is quite separate from the other. Okay, now in the world where, if we just take P here, in the world where P is true, then the premise here is going to be true, isn't it? Okay, and in the world where P is true here, the premise is going to be true. Okay, and in the world where P is false and false again, exactly. So, okay, and that's going to be the same here because we've got exactly the same letter here. Okay, now do we know whether this argument's valid? Well, looking at each structure in turn, is this a world in which the premise is true and the conclusion's false? No, okay, so that's okay, it's valid there. Is this a world where the premise is true and the conclusion's false? Hang on, this is number two, the second world. Is this a world where the premise is true and the conclusion's false? No, it isn't, that's okay. Is this a world where the premise is true and the conclusion's false? No, and is this a world where the premise is true and the conclusion's false? No, hang on, who said yes? Look, is this a world where the premise is true Yang's a dynion ffals. Nog. Felly nil eich bod nol ddim yn llyfru hwn ar ar-di, felly ti yn llyfru hwn. Dyn ni'r llyfru hwn mae'r llyfru hwn. A mae eich eich bod… Felly yna ddynion ffals, ac yn llyfrw hwn. Mae'r ffals yw'r blwyddyn rhagiriaid, ac mae'n ddynion yma ond mae'n gallu unrhyw ymddraeth. Yna fod yna bod nil chi'n golygu'r ffrwys yn ddim yn rhagiriaid. Felly nid ei wedi gweld dda chi yn brygau. I've just complicated things by adding Q. Ignore it. Let's add not P. Okay, what's the truth value here? P is true, so in this world, not P is false. Good. Sorry, that's a not. That is not. Okay, in this world, P is true, so not P is false again. In this world, P is false, so not P is true. You're really doing well. Okay, and in this world, P is false, so not P is true. Okay, so now we're looking at two premises and let's see if we can find a world in which the premises are true and the conclusion false. Okay, so this world, the world number one, we've got two premises. Is this a world where the premises are both true and the conclusion false? No, because the premises are not both true. This one's false, isn't it? So, okay, this is valid, that's all right. Here's one where, okay, is this a world where the premises are both true and the conclusion false? No, it isn't, is it? Okay, is this a world where the premises are both true and the conclusion false? No, and is this a world in which the premises are both true and the conclusion false? So, is the argument valid? Yes, good, really good. The thing is, you can add any premise to a circular argument and it remains valid. So, it may be that a circular argument, when I look at that, therefore, you think this isn't an argument, it's so obviously not valid. Now, if I were a politician wanting to kick sand in your face, the best way to do it would be to offer you a circular argument, but in the middle, blind you with science, hide the premise that is the conclusion in amongst lots of other premises, so you wouldn't see, you know, the therefore would sign fine to you then, because it looks as if you'd have an argument, but actually it wouldn't change the validity, would it? You, as a rational animal, would recognise the validity, what you wouldn't recognise is that the argument is valid because it's circular. Are you with me? So, circular arguments are jolly useful if you're trying to confuse someone, and the reason they're useful is because you, as rational animals, are validity detectors. That's what you do. You know, if we're in the pub and I'm giving you an argument, you're sitting there thinking, is that a good argument? Is she right? You're asking yourself whether my argument is valid. You're setting yourself to validity detection mode. The thing about that is it's self-referential because the liar, if I say I'm telling the truth, and you don't know whether I'm a liar or not, you don't know whether that sentence is true, but yes, you could use truth tables for that. You could use that. Were you being confused by the fact I put Q in there, do you think? Or were you being confused by the fact I wrote that out first? Wales is not mammals, therefore Wales are not mammals. If you look at it, that truth table I've just done is exactly that argument. If we provide the interpretation that says P is Wales are mammals, do you see? Because when you look at that, P is Wales are mammals, not P, sorry, this is, yes, P is Wales are mammals, this says, it's not the case of Wales are mammals and this says Wales are mammals. So that's the truth table for that argument. And I drew that and I then didn't do it because I realised it wasn't circular, but if I do the truth table for that one, what's going to happen? Does anyone recognise this argument? If P then Q, P therefore Q, is that going to come out valid? It's not circular because the Q isn't a premise. The Q is part of a premise and that's different, that's okay, so that's not circular. If you had Q in here, it would be a circular argument and it would be valid for that reason. What's this argument? You've seen it today already or rather this is a formalisation of an argument you've seen today. So, thank you, exactly so. If it's snowing, the mail will be late. It is snowing, therefore the mail will be late. And if I write out the truth table and you'll just have to take these for, oops, yes, that's right. Okay, there's the therefore. Is this a world in which the premises are all true and the conclusion false? Nope, okay, so that's all right. Is this a world where the premises are all true and the conclusion false? Nope, is this one where the premises are all true and the conclusion false? Nope, is this one? No, okay, so that argument's valid. But if I change this to a Q, sorry, I'll get another pen because it's okay. Is this a world where the premises are all true and the conclusion false? Okay, is this a world where the premises are all true and the conclusion false? No, is this a world where the premises are all true and the conclusion false? It is, isn't it? Okay, that is quite sufficient to show that this argument, any argument of that form is invalid because here's a world, just here's a possible world in which the premises are true and the conclusion false and all the rest becomes irrelevant because you only need one counterexample and we can even say what the counterexample is because that argument is invalid in the world where P is false and Q is true. So, if we put in the interpretation we had before, what was P? It's snowing and Q is the male is late. So, in the world where P is false, in other words it's not snowing but the male is late because of that puncture, that's the counter example to this argument. Do you see? Do you see how useful logic is? It's fantastic and you see you're doing it now. Okay, you've got a fair amount of help here but it wouldn't take me long to show you how to do this yourself. The really difficult bit is the interpretation from English into formal logic. That's the really difficult bit but this bit, dead simple once you know how to do it and this is formal logic. Okay, right, actually that takes me quite neatly on to the next slide because I wanted to point out that there are two sorts of logic. So far we've been looking at formal logic but I also want to say something about philosophical logic because that's a bit different but firstly just to say something a bit more about formal logic. You've got to distinguish form from content, the form of the argument from the content of the argument. So, this is the form of the argument up here. The content is supplied by the interpretation so you notice that you could give this a completely different interpretation but the form would still be the same and that's actually very important because what that tells us is that logic is topic neutral. Once you know how to do logic, it doesn't matter what subject you're talking about, the logic will work for any subject at all. So, let's look at this one and let's look at here are two arguments. Sorry, I'll move this over. All men are mortal. Socrates is a man therefore Socrates is mortal. All actions that produce the greatest happiness, the greatest number are right. That action produced the greatest happiness, the greatest number therefore that action was right. Now, can you see that these two arguments completely different subject matter, aren't they? This is about mortality and socrates and that's about ethics, the greatest happiness, the greatest number etc but they've got the same form and now I want you to practice your logic by telling me what the form of this argument is. Okay, work it out for yourself and then put your hands up when you've got it without yelling it out. Work out what the form of that argument is. Remember that there are logical words and there are English words and it's the logical words you want to leave in and the English word, well they're all English words but leave the logical words in, provide an interpretation for the non-logical words. Don't worry if you're finding this difficult, this is difficult stuff. Put up your hands if you think you've got it. Let me give you a tip that all is a word that you'll leave in and is is a word that you'll leave in. Put up your hand if you think you've got an answer. Good, we're getting there. Symbolic logic because the form is captured in symbols. Good, okay we've got a few, do you want to have a go? Okay, hold on. Surely somebody could invent something better than this, don't you think? What? It's called a crayon. A crayon, yes. Yes, it would work, wouldn't it? All a is b. All a is b. All a's are b. Can I change it? Yeah, okay. All a's are b. S is a. Therefore, give the girl a gold star. Fantastic, do you see it? All a's are b. S is an a, therefore S is a b. And what about up there? Let's provide the interpretation for each of these arguments. Okay, so the interpretation says what does a mean, what does b mean, and what does s mean? And we've got two arguments, so we need to provide two interpretations. What is a here? Oh, you're doing the same. If we do the first argument first. X is a man is what it is, actually. I'll put that in because these are predicates. X is a man is a predicate, so you need to have a placeholder. X is a man. B is x is mortal, yep. And s, socrates. Well done. Okay, and the interpretation here, a is x is, it's a bit long-winded this one. A is an action that produces the greatest happiness of the greatest number. And b is is right, x is right. Well done. And s is well done. Well done. That action, because that action is a designator, isn't it? That action, it picks out one particular thing, in this case an action, in the same way that Socrates is a designator, it picks out one particular thing, Socrates. So we're saying, the first one, anything that's a man is mortal, so anything that has this property also has that property. Socrates has this property, the first one, therefore Socrates has the other one. Okay, and we're saying exactly the same thing in that one, except we're talking about something completely different. We're talking about actions, and whether they produce the greatest happiness, the greatest number or not. So, do you see why logic is topic neutral? Once you've learned logic, it doesn't matter what you're thinking about, you can think clearly about it. And this is one of the joys of being a philosopher, as far as I'm concerned, because it means you can put your nose in anywhere. It really doesn't matter what you're talking about, there's a philosophy in mind, a philosophy of biology, a philosophy of chairs probably, somebody was trying to persuade me to run a weekend school on the philosophy of accountancy yesterday. If anyone would like to do that, they can share it. No, actually, I'm sure that there is a philosophy of accountancy, and actually if there are, I'm sure, philosophical issues in there. There is a philosophy of everything because of this. Logic is the methodology of philosophy, and it can be applied to any subject at all, and that's because logic is topic neutral. Okay, let's move down. So, what we do in formal logic, as you've seen, is we strip an argument of its content, we're not interested in the content, we reveal its form, and then we can test mechanically for validity. And you've seen me test mechanically for validity here. That's one way of testing mechanically for validity. Okay, now the trouble with that is, what happens if I add another premise here? So, I have an R as well. It's going to get unwieldy, isn't it? And just for fun, I always get undergraduates to do one with four or five premises in, so that their truth table goes on and on and on, and it's very, very boring to work it out. And then I show them that they can do this instead. Okay, now you'll just have to believe me that that arrow means if then. Okay, so that formula there means if p then q. And that little sign there means it is not the case, so that means not q. And what I've done here, you remember the argument we had if p then q, p therefore q. I've got the premise there, the first premise there, the second premise there, and I've negated the conclusion. Okay, because the argument was if p then q, p therefore q. And I'm saying, well, let's pretend that we've got if p then q, p and not q. In other words, a situation in which the premises are both true and the conclusion's false. Let's see if I can find an argument like that, or a situation like that. And I then apply completely mechanical rules that I could again teach you in an hour or so to get this. Okay, the conditions under which that is true, that is true, that is true. Are there two situations? It's true just in case not p or q. And you can't, there is no possible world with both q and not q in it, so that's not a possible world. There's no possible world with not p and p in it, so that's not a possible world. There is no possible world in which the set consisting of the premises and the negation of the conclusion are true together. Okay, now you won't have understood that, but I hope you can see that I know what I'm talking about and that it would be very easy to teach you how to do this, so that all you have to do is any argument at all, if you can translate it into symbols and that's the biggest if, if you can translate it into symbols, there is a set of rules such that you can apply these rules and test it just as I have done and say quite categorically, this is a situation in which, sorry, this is an argument that's valid. And let's do the invalid one, just to see again how it works. The invalid one is if p then q, q, therefore p, so I'm negating p because that's the conclusion, and I want to see if there's a possible world in which these are all true together, the set consisting of the premises plus the negation of the conclusion. Well, that's true just in case not p or q again, but we don't have any contradictions here, do we? See we've got not p, not pq, there's one possible world in which that set are all true, the sentences in that set are all true, and we've got q not pq, so that's another world in which the set consisting of the premises plus the negation of the conclusion are all true. So either of these, any situation in which q and not p is true is a counter example to that argument, and you go to your interpretation now, you find out what q is, you find out what not p is, and you know what your counter example is. Magic isn't it? Well yeah, p it is snowing, q the mail is laying. Do you see what I mean? I was just doing exactly the same example. Don't worry if you're getting confused here that you don't know these rules, you have no idea why I've represented the truth conditions of that like that, and I would have to tell you that, and I'd also given that that's actually quite difficult to understand, I'd have to convince you that that is the case, but I would be able to do it, I promise you, and once I'd done it you would then be able to take any argument and show whether or not it's valid or invalid, and if you showed it was invalid you'd also be able to give me the counter example because you would know which world is such that the premises are both true and the conclusion false. Isn't it nice? Are you understanding that as the therefore? You said p therefore q. Yeah, that's not a therefore, it's an implication, not an entailment. That's saying if p then q, not p therefore q. I mean don't worry too much about that, the therefore would be, okay, well what I'd be saying is if anyone made this argument, this is the argument they'd make, they'd be saying if p then q and p then q, so if these are true then q is true, so if it's true that if it's known the mail will be late and it's true that it's snowing then it must be the case that the mail is late, and I would do this sort of diagram and I'd say, you know, you're right, that's absolutely right, but then if somebody tried the other argument, so as I'm reading Descartes for example and I think okay, what he's saying is that it's possible that all our beliefs about the external world are false, okay, and one of his premises is this, one of his premises is that, one of his premises is this, is it true that that conclusion really follows from those premises? So I would do the truth table and I would say no, it isn't true, or yes it is true and that would enable, or you could look at the reader and the leader in tonight's paper and say okay, here's the argument, premise one, premise two, premise three, I'll now formalise the argument, I'll strip the content out of it and formalise it and then I'll apply the rules of the predicate calculus, would probably be needed, this is the propositional calculus but you'd need a slightly more sophisticated one, predicate calculus, and you'd be able to determine whether the argument is a good one or not. Of course what you're determining is that the argument is a good one or not, that still doesn't tell you whether the conclusion is true, does it? Why not? Exactly, the fact that an argument is valid isn't telling you that the premises are true, so as a philosopher what you're interested in is the validity of the argument, you're also interested in the truth of the premises if it's a philosophical argument but it might be an empirical argument in which case the truth of premises isn't your business, we don't go around getting our hands dirty. No, it doesn't work like that because firstly you've got to be able to formalise an argument and there are huge problems, if this is the class of all arguments in the world, all arguments here, you can formalise, I mean I'm making this up but let's say you can formalise that many in the predicate calculus, you can formalise that many in the deontic logic, you can formalise that many in modal logic, this lot you can't formalise at all and therefore you can't apply the rules. Now what we hope as formal logicians is that we will learn how to formalise those and for example the predicate calculus was developed only a couple of hundred years ago, Aristotle developed syllogistic logic but it took Frager to develop predicate logic and that was a huge leap forward, modal logic has only been developed, well it's still being developed, the logic of probability ditto, deontic logic, we're still working on it, so you're right at the cutting edge here, I've given you the noddy calculus, if you want to go and do it for yourself you'll have to do a lot more than I've given you here but you'd know that, so no it's not the case and of course also the real skill is in translating the argument and you'd know that if I made you do some because it's really really difficult to translate from English into a symbolic language and there are a lot of things left out and it's very frustratingly inaccurate and so there are real problems but we all do it all the time, believe me I sit in my study doing tables like that, it's much more interesting than if you might think, yeah well I mean there's more than one premise in the arguments I've been doing of course, that's one premise that's another premise and of course there could be, I mean there could be 10 premises here, I could still apply these rules, no no you only need one that's false and that's quite sufficient to show that even if the argument's valid the conclusion may be false yeah so the number of premises that's true is not very relevant it's the if there's at least one that's false, so here's a valid argument with a false conclusion, hang on I've written it here, if it's Tuesday then Marianne isn't lecturing, it is Tuesday therefore Marianne isn't lecturing, okay well that's a valid argument isn't it, do you want to hear it again, if it's Tuesday then Marianne isn't lecturing, it is Tuesday therefore Marianne isn't lecturing, now if those premises were true the conclusion would be true wouldn't it, okay but the premises aren't true are they, neither is the conclusion so you can have a valid argument with a false conclusion, if you then know that the conclusion is false of course you can go back and say one of the premises must be false but there are often situations where we actually don't know whether the conclusion is true or false and therefore we don't know whether the premises are true or false you know I mean this is, logic is in some ways the servant of science in other ways of course science is the servant of logic, I mean they work together, oh yes it tells you a lot it tells you whether an argument is valid and you know that if, okay think of the difference between something's generating truth and something's preserving truth, logic doesn't generate truth if you haven't got truth in the premises you won't have it in the conclusion but if you have got truth in the premises you preserve it in the conclusion by using a valid argument and that's what you hope because there are things that we know about the world and there are things that we want to know about the world so we want to extend our knowledge from what we already have to what we don't already have and one of the ways of doing that is by using logic, if this is true and this is true then this must be true, the if is, well let's say I'm a scientist and I say well um if the Higgs boson exists then my building this whacking great hadron collider at cost of millions and millions and millions of pounds might enable me to find it of course if the if the Higgs boson doesn't exist I've wasted all that money well you know it may show me a few other things but it won't tell me about the Higgs boson so if statements are actually we use them all the time I mean if you think of any of your practical reasoning that says okay I want to do liver supper tonight um therefore I need some onions or something like that um therefore I haven't got any and then you're using if statements to generate conclusions about actions or conclusions about knowledge or you can't you can't reason without if statements this is yeah I mean it was when this was developed that computing became possible yeah yeah absolutely the same exactly so yeah yeah no all I mean what you're doing when you're doing the applying those truth tables and the um tableau rules is is acting like a computer you're making like a computer exactly I mean you might have two conflicting theories and you're saying if this is true then this will be the result let's see if this is the result but if this is true this will be the result and if we can find out whether it's this or that then I know which theory is the correct one do you see all reasoning you cannot do without if statements and I can tell you under exactly what conditions if statements would be true I might not I might need to go into the laboratory to see if an if statement is true actually I wouldn't because there's no way a laboratory can tell me that's a wonderful example because of our activities but some people don't so uh and they're saying they're there this is a natural thing that's happening in the world history of our history so do you see that now we have we have scope for going into the laboratory or the article wherever we go to find out but without that bit of reasoning first you wouldn't even know what you were looking for um and and the thing is if logic can rule out something then there's no point in going to the laboratory at all I mean if I can show an argument is invalid then any scientist who's trying to get funding on the back of that argument is is in serious trouble because you know why should I fund him okay moving on because we've only got five minutes left but that's all right because um okay I was going to talk very briefly about philosophical logic um I've talked about formal logic but philosophical logic is the philosophy of logic I said there are philosophies of everything including biology accountancy whatever but the philosophy of logic is as you can imagine pretty damn important uh to philosophers because the philosophy of logic um looks at the notions without which logic can't work so we've talked about truth a lot today haven't we I've drawn truth tables I've drawn truth trees I've said if this is true that's true so the notion of truth is absolutely central well what is truth go on tell me you've all sat there looking intelligence as we've talked about truth so I assume you understand the word tell me what is truth something that's correct what's correct then I mean you're just giving me a synonym there aren't you whoever it was okay so what in this case opposite of false okay what's false then no okay but that doesn't tell me what either are it's true you can't have truth without falsehood you can't have falsehood without truth but what is truth a fact okay what's a fact hang on let's let's what is a fact certain knowledge is it is knowledge a fact I mean there's the knowledge that I'm wearing a dress and there's the fact I'm wearing a dress are they the same thing no because there are facts of which we know nothing aren't there so so facts are nothing to do with knowledge but reality sounds like a synonym for truth here a fact is actually something that makes a true sentence true isn't it think about it what what is a fact no there are facts you can't prove I mean are there three consecutive sevens in the decimal expansion of pi if there aren't then you can't prove it I'm told there are by the way so that's out of date but just imagine the decimal expansion pi is an infinite expansion if there aren't three consecutive sevens there's no way we'd be able to prove it but it would still be a fact wouldn't it so knowledge of a fact and a fact are two quite different things and what is a fact a fact is something that makes a true sentence true so talking about facts doesn't tell me anything about truth so come on come on you you've all been dealing with truth what is it it has to be something or something we know then how do we know it it may not be sense experience no we don't need to know it at all no you're all confusing not all of you maybe epistemology and metaphysics here epistemology is what we know and metaphysics is what is the case and and they're two quite separate things what were you going to no because a belief is usually to do with knowledge rather than because there might be facts about which we have no beliefs i mean you have no beliefs about my middle name i shouldn't think you don't even have the belief that i have one how do you know whether i have one okay but there's still a fact about my middle name irrefutable is to do with proof again isn't it yep no that's again to do with epistemology no the fact is truth is a very very difficult you mentioned correspondence there are two key theories about truth actually here's another one there's some belief that truth is nothing that truth is completely redundant because if i say p is true i'm not saying anything more than p am i if i say p is true aren't i am i saying anything more than p no i'm not i'm saying not not p aren't i because if if p is true then then not p is false so if if i'm saying p i'm saying not not p not p you too can do this eventually is truth demonstrable not always no no definitely not moral as opposed to factual well i think there are facts about values so so i don't think there's any opposition between fact and value so i think there are moral truths and that what make a moral truth is that there are moral facts no you can think you prove proof again thing proof is to do with knowledge anyway one one people some people think that there's no more to truth than coherence what wakes one belief true is that it cohears with your other beliefs other people think well hang on i can have a set of beliefs here all of which are coherent and then if i negate them all that'll be another set all of which are coherent won't it but which is true so coherence can't be the right theory uh well no because truth truth seems to be a property of sentences and beliefs doesn't it well reality isn't a property of your beliefs is it or of your sentences exactly but truth seems to be a property if there weren't any beliefs in this world there wouldn't be any sentences would there sentences express beliefs okay if i believe that that your what's your name dear dear is wearing red i just expressed that belief in saying dear dear is wearing red if there were no beliefs there'd be no sentences if there were neither beliefs nor sentences there would be no truth but there'd still be a reality semantics means truth or it means truth conditions yeah yeah that's because you're thinking of what makes things true but of course truth is still the property of the sentence that you've uttered i mean what's true is the sentence the reality is what makes it true this this is really difficult stuff here um just talking about semantics and syntax at the moment if we look at one of the truth trees again um i have stripped the semantics out of the arguments there i've left the syntax all i've left is the shape if i want to put the the meaning back in i've got to put semantics back in and in putting semantics back in what i'm putting in is conditions of truth and falsehood that's what semantics is and that's that's what meaning is anyway we've done it now that's logic that's your lot on logic um i oh okay correspondence um correspondence so you've actually we've already looked at that truth is um correspondence between a sentence and a fact but what's wrong with that is is what is a fact other than something that makes a true sentence true and therefore it that's just a circular definition it gets you absolutely nowhere um oh goodness it's lots of people yeah not aje would certainly be one of them i think um so what is truth answer i don't know uh i know more than you do obviously but i don't know because this is still a an ongoing question what is truth that's what philosophical logic looks at we also i mean validity i gave you one of the paradoxes of entailment a minute ago um and you weren't very happy with it here's another two um well it would be if i can find them um we're running over our time if anyone wants to go they're most welcome um no i'm not going to be able to find it if i say um the grass is green therefore two plus two equals four that's a valid argument because there's no possible situation in which that conclusion is false so how could there be a possible situation in which the premise is true and the conclusion false there couldn't be that's one of the paradoxes of entailment and one of the things that philosophical logicians would like to know is why is our definition of entailment faulty in that way because that surely that argument isn't valid and yet our definition of valid makes it valid so there's something wrong with our definition of validity and yet somehow we can run computers that run large hadron colliders and find the higgs boson on our logic so our logic isn't totally wrong how do we deal with it okay we're going to stop right there you know nothing about identity but that's all right i'm sure we can talk about that some other time