The philosophical method - logic and argument

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Right. Well, I think we should get started. Welcome back, everyone. Nice to see you.

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That you haven't been frightened off. Today, I'm going to talk about something absolutely central to philosophy.

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And that's the methodology of philosophy, which is the methodology of logic and arguments.

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And just I think I said something last week about this, but it bears repeating.

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In science, people do experiments and experiments.

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They do a constrained by the laws of nature, which is why there is some confidence that their experiments are going to give them true knowledge.

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Well, knowledge, the true knowledge is not small, but the man in philosophy.

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We also do experiments, but the experience we do are not constrained by the laws of nature.

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And we don't do them in laboratories. They're not empirical experiments.

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Instead, we do somewhat experiments. So it's very nice being a philosopher because you don't have to leave the comfort of your armchair.

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You can stay in the library. You don't have to get messed up with test tubes and things like that.

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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.

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The philosopher is constrained by the laws of logic.

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And that's why we can be fairly sure that when we have knowledge, when we think we've got something,

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we know we can be fairly sure we're right, especially if we corroborate what we think with other philosophers.

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Of course, third person corroboration is as important in philosophy as it is in science.

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But what I'm going to be talking about staes is the arguments, that sort of logic that constrains our thought experiments.

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So that's what we're going to talk about, what logic is.

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It's not the sort of argument that your teenage children have.

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Okay. We all know that sort of argue. No, you didn't. Yes, I did. No, you didn't. Etc.

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It's nor is it the sort of argument that you laughed at on Monty Python.

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You remember the arguments sketch? Probably. Instead, the argument is going to be a set of propositions which we call premises,

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which are put forward as reason to believe another proposition, which we call the conclusion.

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So here's an argument. I want to get to London by noon.

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I believe it's a necessary condition of getting to London by noon that I catch the 10 20 train.

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Therefore, give me the conclusion. I must catch the 10 20 train.

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So what you've got is you've got two propositions.

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I want to get to London by noon and I believe it's a necessary condition to get into London by noon that I catch the 10 20.

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And together they combine.

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And you knew immediately what the conclusion had to be, because there's only one conclusion that's entailed by these two, isn't there?

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And you all got it right. And that's because you are all rational animals.

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Actually, you do logic pretty well as well as I do.

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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.

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But as rational animals, you're doing logic all the time.

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You knew the answer to that reason you knew is because you do logic and logic is just the if you like,

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the method by which you go from one set of thoughts to another thought.

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It's one way of acquiring knowledge, if you like.

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Okay, so that's that's what an argument is. Now there are different types of logic because there are different types of argument.

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So there are all sorts of different types of types as well.

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But one type of argument, for example, is dayon tech logic, the logic of moral discourse.

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So if I say to you, lying is wrong.

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Therefore, what conclusions are you going to give me?

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Or I shouldn't lie or something. Yeah. Something to the effect. I should tell the truth.

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I shouldn't lie or whatever.

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That's not 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.

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I shouldn't lie. But it's interesting because Kant says that's what's peculiar about de Ontake.

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Logic is you go straight from a statement to the effect that something's wrong.

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To the conclusion that you shouldn't do it.

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And Kant thinks that's a very peculiar thing about morality, because for everything else, you would need a desire in there as well.

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So if you look again at the first argument, I want to get slammed by noon.

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It's a necessary condition of getting London to London. Da da da da da da.

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Therefore, I need to leave on the 10 20. If you took away the desire, would you have a good argument left?

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No, you just say it's a necessary condition of getting to London by noon, that I catch the 10 20.

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Well, so what? You know, unless you want to get to London by noon.

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That doesn't entail anything, does it? You can do anything you like consistently with that.

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But once you've added that, you've got something that requires an action, haven't you?

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So it would be irrational to have that desire and that belief a not to believe.

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I must catch the 10 20. Wouldn't it? Okay.

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Have another way. That's true.

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But I have said the necessary condition here. So if I'd taken that, hold your rights.

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But I think as I've put that in, anticipating that somebody might say something like.

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Sorry. You've only said, I believe. That's true.

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But if it's a matter of action, my belief would be sufficient to, wouldn't it?

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Because even if I was wrong about that, I would still think it's Russia.

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And what's more, I'm still being rational to catch the 10 20, wouldn't I, if I believe that even if, in fact I was wrong?

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OK, but if you look at this one. Do you need a desire in there?

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Kant would say no. Lying is wrong. Therefore, I mustn't lie. Do you need I?

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I don't want to do the wrong thing or I do want to do the right thing.

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Kant would say no because he'd say, if you think that you need to adds and I want to do right.

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You just don't understand what it is to do something wrong. OK.

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Think about that for a second. If you if you entertain possibly that, you need to add.

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I want to do what's right. You were implying that you might not want to do what's right.

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And Kant would think that that would show that you didn't actually understand what right means.

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You with me? No, but and Kant would say they don't understand what's right.

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If you think I understand that 10 year olds go around nicking sweets from from shops

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because they understand you of right at the moment is is if anyone finds out,

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I'll I'll get into trouble. Okay. I did it wrong is Mummy will find out and I'll get smacked or something like that.

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How old fashioned hoops is legal.

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That isn't it. Anyway, whatever it is, it isn't.

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Okay. Well at least I haven't said anything illegal, but immoral maybe.

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So if you're thinking that for something to be wrong is if I get caught, I'll be punished.

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You've got that. You haven't yet got the concept of right and wrong. Have you?

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What you've got is a prudential concept that may cause you to act in some of the same ways.

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But I bet if I leave my purse here when I go out, as I may well do.

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You wouldn't not pinch hit because you might be fine.

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Found out. No. You would have other reasons for not pinching it, mainly because you'd think it was wrong.

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Probably wouldn't occur to you, but you'd also, if it did occur to you, you'd think it's wrong.

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And so there are different ways.

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And if you think about it, can do you think you could think that lying is wrong, but there's no reason why you shouldn't lie.

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So, of course, I'd say let's say somebody says to you, your builder says to you or you or your solicitor says to you.

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Well, of course lying's wrong. But that doesn't mean I you know, I mean, it doesn't mean we shouldn't lie here.

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Isn't there something wrong with that? Isn't that a contradiction? Thank you.

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Yeah. That's different. We're saying if you believe that lying is wrong, then you're going to think you shouldn't lie.

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I mean, if you don't think lying is wrong, then there's no reason, not lies.

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But if you do think lying is wrong, could you also could you consistently believe.

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Let's. All right. Let's say if you believe this lie is wrong.

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Could you consistently believe that there's no reason for you not to lie?

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I have to find lying and saying you think this lie is wrong. So it's not a white lie.

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Would you say that? Yes. Not yet.

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But a white lie. We call them white lies because we don't really think they're wrong, do we?

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Right. Right. Then then let's let's not get too far away from the topic.

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If we believe that lying is wrong or that this particular lie is wrong, even if it's a white lie or not.

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Doesn't matter. Could you consistently think. Never mind.

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That doesn't mean I shouldn't do it. But he came up last time with torture.

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Torture is wrong. Right.

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Yeah. OK. I'm going to leave this because maybe De Ontake logic was a bad idea.

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OK. Carrots would say that if you believe that, you have got to think I shouldn't lie.

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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.

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Lying is wrong. But there is no reason for you not to lie.

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Because for some things to be wrong is itself a reason for you not to do.

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It may not be the final reason. It may not be conclusive, but it is a reason not to do it.

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And that's De Ontake logic, because you've begun got a premiss and a conclusion, and the premise gives you reason to believe the conclusion.

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So that's what's down here. We've got a set of propositions or one proposition.

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A premise put forward is reason to believe another. Here's another type of argument.

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This is Moodle logic and I'm sorry, it's a bad example, but I'm lousy at thinking of examples.

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It's not possible for Vixen's to be male. That's because Vixen's are defined to be female.

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Therefore, that Viksten is not male.

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Okay. If you believe that, you're going to believe that. And that's because if something is not possible, then it can't be actual, can it?

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Okay, so. So if it's not possible for me to be mailed and then it can't be the case that I am male.

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So you're recognising that something's not possible.

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It will cause you to believe immediately that nor is it Hatchell because it couldn't be not possible and actual.

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So that's Moodle logic, the logic and modality, the logic of necessity.

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And then another type of logic is the logic conditionals. So you've probably all heard the saying, if it's gold, I'm a Dutchman.

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Okay. That means, as we all know, that it's not gold, doesn't it?

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How do you know that? Well, you'll just have to believe me, take it on authority.

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But that's because, you know, the logic of conditionals.

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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.

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You would see that if it's gold, I'm a Dutchman has to be true.

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And therefore, it has to be false that. It's gold.

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So I'm not going to go into that.

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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.

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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.

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Okay. Finally baffled, are you? Yes. All the different worlds.

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Well, some people say that a different possible world is nothing more than a different situation.

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There's a philosopher called Krip Key, very famous philosopher, still alive.

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Or if he isn't, he's only just. It was today or yesterday, and I'm very sorry about it.

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He believes that you in order to explain the truth of conditionals, like, okay, if Germany had won the war, we would be speaking German.

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Now, some of you may think that's true and some of you may think it's false.

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We could argue about this. We could give reasons for different sides.

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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.

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That's a counterfactual conditional. And so we think of conditionals, even counterfactual conditionals, as true and false all the time.

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And some logicians believe that in order to explain the truth of counterfactual conditionals, you've got to postulate other possible worlds.

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Now, of course, there are other reasons in physics for postulating possible worlds in mathematics.

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There are reasons for postulating possible worlds. And what is a possible world?

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Well, Chriqui thinks it is literally another place, just like all worlds, like our universe, rather than like our earth.

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But there's no causal interaction between one world and another.

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But you can say, okay, is there a possible world in which Marianne's wearing jeans?

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Tell me the answer, yes. Is that a possible world in which Marianne is male issue for you?

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Does anyone think that might be nine, Marianne?

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No, no, no, no. We're asking a question here. Could Matt. Could I have been male?

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Could I have been male? In other words, if I.

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If I had to. No one would.

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No. An X and Y chromosome instead of two X's. Would I still have been Marianne?

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Would I still exist? OK. Lots of people think no.

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It's an open question. Some people think no on that. Some people think yes.

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But notice, we do think there's a truth value to it.

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We can ask that question and we can argue about the answer.

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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.

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But not by perception. Do you see what I mean?

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We can see this world. We can touch it. We can hear it there.

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You heard part of it. But you can't see or touch a possible world.

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But you know, they're there because you argue about conditionals.

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Isn't there a world in which I'm male? Well, some of you think, yes, some of you think no.

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And the more you look at the logic, the more you might be able to come up with.

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You're absolutely right. It is no the answer or you're absolutely right.

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It is. Yes. Or whatever. That's what philosophers are doing, is there?

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Sometimes I talk about it as spinning the possible worlds in order to find out what the limits of possibility are.

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Because if you think of what a scientist is doing, they're looking to see what the limits of actuality are.

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What is the case in this world? Whereas what philosophers are looking for is what could be the case.

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Okay. Not just in this world, but in any world. Could there be could time travel be possible, for example?

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Mean it looks as if time travel isn't possible? Well, we know time travel isn't possible at the moment.

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Could it be? Is there a world in which it's possible? And if so, could this be a world in which it is?

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So we're expanding the worlds and asking, okay.

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We know there are possible worlds. We know there isn't a world in which there are square circles, don't we?

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It's a world in which circles of square. Could could there be could a circle be square?

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Exactly. It's the concept, isn't it? If something is a circle, it could not be a square.

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End of story. So we know that there is no possible world in which circles are square.

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That's not a possible world. Whereas the world in which Marianne is male, maybe that is a possible world.

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The world in which Marianne's wearing jeans is definitely a possible world. So we're trying to limit the possibilities.

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Which possible worlds are there and which aren't there. Yes.

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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?

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It's a contingent fact that I'm wearing a dress. I mean, I might have put jeans on this morning.

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Might I have been male? OK,

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we know a Viksund cannot be female because in the same way we know that a bachelor

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can't be married because it's part of the definition of being a bachelor,

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that you're part of a definition of being vixen. Is it part of the definition of Marijan of me, the time female?

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Well, some people do think so, but others think not. You do. You thought not.

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So there are there are different views on this one. And I could give you other ones that are where we're not sure.

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What's important is there are some cases where it's definite there is such a world, some cases where it's definite that there isn't such a world.

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And some cases that we don't know about. And the job of a philosopher is to find out about those.

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Okay, so that's modal logic. And I looked at the logic of conditionals, but there are two main generic forms of arguments.

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OK. These are these are looking at particular types of discourse and the logic of that sort of discourse.

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So as moral agents, you understand something about day on tick logic, even if you've never heard about it before.

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You also understand something of the logic of modality and the logic of conditionals.

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But here are two very broad sorts of argument, deductive arguments, an inductive arguments.

196
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Now I want you to ignore the ones under the dotted lines at the moment and just look at the ones on the top.

197
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Now, I know you're all reading the ones underneath the dotted line at the moment. Stop it.

198
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Okay, let's look at this one. If it snows, the mail would be late.

199
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It is snowing. Therefore, the mail will be late. The nice thing about deductive arguments is that they give us certainty.

200
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They didn't give us unconditional certainty. Sadly, if the premises of the argument are true, then the conclusion must be true.

201
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Okay, so have a look at these premises there and tell me if that's a deductively valid argument.

202
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If it snows, the mail will be late. It is snowing. Therefore, the mail will be date.

203
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Could it be that these premises are true? And the conclusion false?

204
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No. OK. Some people are thinking about it. Let's let's let them think. But yeah, but why do we want to do that?

205
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Because I'm giving you an example of a deductive argument. And if I change that will to my right, then I haven't got a deductive argument.

206
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Have I? Because then the premises could be false. Without that.

207
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So it could be true without the conclusion being true. And the particular thing about this one is I wanted an example of a deductively valid argument.

208
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And what I hope I've got is that if these premises are true, the conclusion must be true.

209
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There is absolutely no logical possibility of those premises being true and that conclusion being false.

210
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Is that right? Yeah. Okay, that's great.

211
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So we've got certainty in a deductive argument, conditionally upon the truth of the premises and the validity of the argument.

212
00:21:42,190 --> 00:21:47,740
Now, here's an invalid deductive argument. If it snows, the mail will be late.

213
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The mail is late. Therefore, it's snowing. OK.

214
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Now, there's something wrong with that argument, isn't there? What's wrong with it?

215
00:21:58,420 --> 00:22:05,920
Good. Give me another reason. Yes, but can you tell me.

216
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Give me a reason. In which puncher. Good. You can't hear people looking at you.

217
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Oh, okay. I'm good.

218
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I've got to say. Okay, well, I'll repeat what was said there. If you've got an an invalid argument,

219
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what you be able to find or at least what you'll be able to to say that there is you may not be able to find one,

220
00:22:31,500 --> 00:22:36,280
because if you're like me, your lousy examples. If it snows, the mail will be late.

221
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The mail is late. Therefore, it's snowing. You should be able to find a counterexample.

222
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In other words, a situation where the premises are true and the conclusions false.

223
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OK, so let's say the mailman had a puncture. OK?

224
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If it snows, the mail will be late. The mail is late. Therefore, it's Snowbell.

225
00:22:58,480 --> 00:23:05,560
No, you know, it's actually the mailman's had a puncture instead or he got up drunk or, you know, whatever happens there.

226
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All sorts of reasons why the mail might be late. In addition to it's snowing.

227
00:23:11,020 --> 00:23:19,840
So we can't go from the comfort, from the affirmation of the antecedent, to the affirmation of the conclusion,

228
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whereas we can go from this one to that conclusion presupposes some causal relationship between Snowy,

229
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which goes in one direction, whereas the second one causations does not.

230
00:23:41,570 --> 00:23:47,680
Well, it doesn't go in the right direction. Exactly.

231
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But the fact is, if you have any argument of that form, you will have a valid argument.

232
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Whereas if you have any argument of that form, you won't. Let's. I'll show you what I mean by that.

233
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Hang on. I'll have to find one I haven't written on. And then I might be able to find where I am.

234
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So you'll have to wait by. If P then Q p therefore.

235
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Q Okay. Can you see that that's a formalisation of this argument.

236
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What does P stand for here? Sorry, not the premise.

237
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No, not at all. Sorry if P then Q formalises the whole premise, doesn't it?

238
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What does P stand for? Now you're all too clever.

239
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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.

240
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Thank you. It is snowing or it snows. Yes.

241
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So, Piers, it snows. So if it snows, then the mail will be late.

242
00:25:00,540 --> 00:25:05,340
Exactly. So you say you've got it now. You didn't know you could all do logic, therefore.

243
00:25:05,340 --> 00:25:10,620
Sorry, P. So this says it is snowing. Notice I should probably put it.

244
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If it is snowing then the mail will be late and I didn't. But ok. It is snowing.

245
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Therefore the mail will be late.

246
00:25:18,330 --> 00:25:34,710
Thank you. OK then we've got if p then Q q therefore p and noticed that whereas every all arguments that form it

247
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doesn't matter what you put in there that would be valid and it doesn't matter what you put in here,

248
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it wouldn't be valid would it. So if we, if we make P let's change the interpretation.

249
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So if I do this, if you are a student doing this, you would have to and you gave me these arguments.

250
00:25:53,580 --> 00:25:58,080
So I'd say, where's your interpretation? And if you hadn't provided one, you would lose marks.

251
00:25:58,080 --> 00:26:03,880
Okay, so let's give an interpretation, Piers. It is snowing.

252
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And Q is the male. We'll be late.

253
00:26:09,670 --> 00:26:17,740
Who's going to try it actually try? Now try and give me another interpretation of those sentence letters.

254
00:26:17,740 --> 00:26:21,730
OK, so forget about snow in the mail. Give another interpretation.

255
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Think about Marianne lecturing or Marianne wedding dresses or it's being Monday all.

256
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Do you know what you're doing? You're all looking very. Okay. You're just looking serious.

257
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Good. It's serious stuff. Shush.

258
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Don't yell out. You're all trying it. I'll tell you what, when you've got one.

259
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Put your hand up. And just keep it up till I. OK.

260
00:26:52,420 --> 00:27:12,460
So you're looking for another sentence for P. And another sentence for Q, which gives you a an argument.

261
00:27:12,460 --> 00:27:20,410
OK, gentlemen, back there. What have you got? Yeah.

262
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Well, you don't need the F because the interpretation is only four P, so P is.

263
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No, not if just Obama wins. Do you see what I mean?

264
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Because if is a logical word here. Yes.

265
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That's right. Okay. Q Is the Democrats. Democrats will be pleased.

266
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So if we pull that in here, we've got. If Obama wins, then the Democrats will be pleased.

267
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Obama actually got a problem here, haven't we? Because notice we've got 10 said, which immediately causes a problem.

268
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But let's forget that for a minute, shall I say. Obama wins.

269
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Therefore, the Democrats will be pleased. Okay, here we go.

270
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If Obama wins, then the Democrats will be pleased. The Democrats are pleased.

271
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Therefore, Obama won. I mean, there must be something else that would please them, wouldn't it?

272
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Okay. How about someone else? Let's have just one more.

273
00:28:25,140 --> 00:28:35,590
Okay. You want to have a go? Hang on, what's P.

274
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Milkman arrives. Okay. And queue is my dog barks.

275
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Okay, so if the milk that arrives in the morning, then the dog pops the milk there arrived, therefore the dog barks.

276
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If the milkman arrives, then the dog barks. The dog barks.

277
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Therefore, the milkman has arrived. You can see what's going on, can't you?

278
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Any argument to this form means that because the thing is p maybe a sufficient condition for Q but is not a necessary condition for Q is it.

279
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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.

280
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And this fallacious argument here suggests it is a necessary condition.

281
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And that's why it's never gonna work. Okay. Well, you see, you're all doing logic and that's what you're all doing.

282
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Formal logic immediately. Fantastic. Okay.

283
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So that's deduction. And the nice thing about deduction is it gives you certainty if the premises are true.

284
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The conclusion must be true. But of course, that that's quite a big if, isn't it?

285
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If the premises are true, the conclusion must be true. Often we may not know whether the premises are true or not.

286
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And therefore, we won't know whether the conclusions true. But the fact that we know the argument is valid is nevertheless useful, isn't it?

287
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Because the validity will preserve the truth of the conclusions.

288
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So well then if we can show by scientific methods or whatever that the conclusion the premises are true, we will know that the conclusion is true.

289
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And if we can show by empirical means or whatever that the premise that the conclusion is false, then what do we know?

290
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Good. One of the premises is false. Exactly. So we learn a lot from a valid argument that has a false conclusion.

291
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We learn that one of the premises must be false. We say, yes, you can at least one of the premises because it needn't be more than one,

292
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just one false premises quite sufficient to to show that the conclusion might be false.

293
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Not not is false, but might be false. Okay, good.

294
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Fantastic. In fact, shame about the day Ontake logic, wasn't it?

295
00:31:08,430 --> 00:31:13,250
We might have to go back to that as you're proving yourself to be so good at logic.

296
00:31:13,250 --> 00:31:20,770
Okay. Let's have a look at induction now. Induction is different. An inductive argument is don't give a certainty.

297
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What they give us is more or less probability. So probability is a matter of degree in a way that validity isn't.

298
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Validity is an either all matter, either an argument is valid or it isn't.

299
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Whereas induction gives this probability and that's a matter of degree.

300
00:31:40,130 --> 00:31:49,090
Okay. You can have strong probability or weak probability. So if we look at this argument here every day in history, the sun has risen.

301
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Therefore, the sun will rise again. I should have put tomorrow in that.

302
00:31:52,420 --> 00:31:58,630
But tomorrow. Okay. That's a pretty strong inductive argument, isn't it?

303
00:31:58,630 --> 00:32:00,940
In fact, we're all pretty well relying on it.

304
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Anyone who's got a lunch appointment tomorrow, for example, is relying on a dentist's appointment or anything else.

305
00:32:08,680 --> 00:32:13,390
But of course, it's not. It doesn't give us certainty, does it?

306
00:32:13,390 --> 00:32:19,630
Because we might be wrong, tomorrow might be the day when the laws of nature are just going to change,

307
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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.

308
00:32:25,810 --> 00:32:32,620
The fact that the laws of nature, of always being the same in the past doesn't mean they're always going to be the same in the future.

309
00:32:32,620 --> 00:32:40,730
It was Hume who pointed out that, as a matter of fact, I mean, it just could be that the.

310
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Hi, this strong your deductive argument is it's not going to give you certainty.

311
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Russell talked about the chicken who every day and the whole of his life.

312
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The farmer had come out and given him food and the chicken.

313
00:32:54,260 --> 00:32:59,030
Here comes the farmer. And he thought, Oh, good. Him food's coming. Course, he got his neck wrong.

314
00:32:59,030 --> 00:33:04,910
Now, how do we know that we're not in that position with respect to the sun rising tomorrow?

315
00:33:04,910 --> 00:33:12,350
And what Hume said is we don't. There is nothing you can do to show that there's anything more than probability here.

316
00:33:12,350 --> 00:33:17,930
Because that argument rests on the idea that nature is uniform.

317
00:33:17,930 --> 00:33:20,320
Why do you believe that nature is uniform?

318
00:33:20,320 --> 00:33:27,170
In other words, that the future will be like the past because the future always has been like the past, hasn't it?

319
00:33:27,170 --> 00:33:32,870
Well, that's no argument, because that is itself an inductive argument, isn't it?

320
00:33:32,870 --> 00:33:55,810
Why is the future, not the past? It always has been like the past. You know, there's this now, it's like trying to hop around on one leg here cause.

321
00:33:55,810 --> 00:34:02,110
No. It's certainly true that that's in induction.

322
00:34:02,110 --> 00:34:10,450
You're going from something observed or something that has happened to your REM.

323
00:34:10,450 --> 00:34:15,230
What's the word? Mind's gone blank.

324
00:34:15,230 --> 00:34:22,190
No. When you project into the future, extrapolate.

325
00:34:22,190 --> 00:34:26,360
Whoever said as traveller. That's what I meant. You're extrapolating into the future, aren't you?

326
00:34:26,360 --> 00:34:31,910
So, for example, here's another inductive argument. I think you'll agree it's not a terribly strong one.

327
00:34:31,910 --> 00:34:35,390
Every time you've seen me, I've been wearing earrings. That's probably true. Is it?

328
00:34:35,390 --> 00:34:41,270
Especially if you've only seen me last week and this week. And next time you see me, I'll be wearing earrings.

329
00:34:41,270 --> 00:34:44,420
Now, that is an inductive argument, isn't it?

330
00:34:44,420 --> 00:34:51,540
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,

331
00:34:51,540 --> 00:34:57,740
it might be as I'm going out to get the paper in the morning before I even put clothes on.

332
00:34:57,740 --> 00:35:03,060
Dressing gown on something. I don't wear earrings with my dressing gown.

333
00:35:03,060 --> 00:35:10,100
And anyway, we know too much about human beings, too. To assume that that's a good inductive argument.

334
00:35:10,100 --> 00:35:16,430
So in deduction, you get certainty and it doesn't need to be about the past or the future.

335
00:35:16,430 --> 00:35:23,340
It can be about anything at all with induction. You are extrapolating from not the story of the past.

336
00:35:23,340 --> 00:35:31,370
You could easily extrapolate from the present to something else. So all the chairs in this lecture room are blue.

337
00:35:31,370 --> 00:35:36,130
Therefore, the chairs in the next lecture room are going to be blue. Now, there's no time element in that, is there?

338
00:35:36,130 --> 00:35:40,430
There's just a you know. Is that a good inductive argument?

339
00:35:40,430 --> 00:35:46,110
Well, it's sort of.

340
00:35:46,110 --> 00:35:50,720
No, it's not very good, is it? Certainly, no, it's not as good as that one.

341
00:35:50,720 --> 00:35:53,990
OK. So these are two types of argument.

342
00:35:53,990 --> 00:36:01,160
And when you've got De Ontake logic or conditional, logical, modal, logical, whatever, you'll get arguments of this kind.

343
00:36:01,160 --> 00:36:05,480
For example, the argument I was trying to convince you of lying is wrong.

344
00:36:05,480 --> 00:36:11,950
Therefore, you shouldn't lie. Kant believe that's a deductive argument.

345
00:36:11,950 --> 00:36:18,950
Okay. Because the premise entails the conclusion. If the premise is true, the conclusion can't be false.

346
00:36:18,950 --> 00:36:29,950
Now, some people disagree with Kant, in which case that wouldn't be a deductive argument, wouldn't obviously be a an inductive one either, instantly.

347
00:36:29,950 --> 00:36:40,300
There are other types of argument. Those are. This is where I'm told that one, haven't we?

348
00:36:40,300 --> 00:36:45,090
And we've had that one of those arguments by analogy.

349
00:36:45,090 --> 00:36:53,710
Anyone tell me what one of those is? Give me a very famous one, perhaps to do with watches.

350
00:36:53,710 --> 00:37:02,620
Anyone read Dawkins book The God Delusion? He talks about a very famous argument from an analogy.

351
00:37:02,620 --> 00:37:06,570
Can anyone tell me what it is? The Blind Watchmaker.

352
00:37:06,570 --> 00:37:11,320
Exactly. So. So the universe is like a watch. A watch has a maker.

353
00:37:11,320 --> 00:37:18,130
Therefore, the universe has a maker. OK. Dawkins thinks that's an appalling argument and he's probably right.

354
00:37:18,130 --> 00:37:27,250
But it's an argument from analogy. What do you do with an object from analogies is you find something that's like something else.

355
00:37:27,250 --> 00:37:32,260
And so if A you've got A is P okay.

356
00:37:32,260 --> 00:37:40,540
Has this property P, A is like B or B is like A, therefore B has P as well.

357
00:37:40,540 --> 00:37:46,270
Okay, so A. has this property B is like A therefore B has this property too.

358
00:37:46,270 --> 00:37:55,360
And of course there the, the premise of similarity is absolutely crucial because if you haven't got the similarity there then you can't,

359
00:37:55,360 --> 00:38:00,520
you haven't got the conclusion either. And of course there are arguments from causation.

360
00:38:00,520 --> 00:38:05,380
If A causes B, then you don't get an A without a B.

361
00:38:05,380 --> 00:38:13,060
Okay. And the reason that that's a valid argument is that you assume that causation brings correlation.

362
00:38:13,060 --> 00:38:23,060
If A cause is B and you get any without a B, then that shows you that A doesn't cause B because an A isn't sufficient for a B.

363
00:38:23,060 --> 00:38:26,270
Okay. Right. Well, let's let's move on from there.

364
00:38:26,270 --> 00:38:32,090
Those are the types of arguments and what's important about any argument,

365
00:38:32,090 --> 00:38:39,830
whatever sort of arguments it is, is that if you want to evaluate it, you've got to ask two questions.

366
00:38:39,830 --> 00:38:46,730
And the question is, you've got to ask, are these all the premises true? And is the argument valid?

367
00:38:46,730 --> 00:38:57,530
And in the 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?

368
00:38:57,530 --> 00:38:58,760
OK. That's what you're asking.

369
00:38:58,760 --> 00:39:08,000
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?

370
00:39:08,000 --> 00:39:14,900
So how strong a reason to the premises providers to believe the conclusion?

371
00:39:14,900 --> 00:39:18,230
So those are the the two questions you've got to ask.

372
00:39:18,230 --> 00:39:26,060
It doesn't matter what the argument is, if you're reading Descartes or you're reading the leader in today's newspaper.

373
00:39:26,060 --> 00:39:30,170
What you've got to do is try and firstly analyse the argument.

374
00:39:30,170 --> 00:39:36,440
In other words, set it out. Logic, books, style, identify. The first thing you go for is a conclusion.

375
00:39:36,440 --> 00:39:40,760
Identify what it is this person is arguing for. Okay.

376
00:39:40,760 --> 00:39:46,660
That's the conclusion. And then find out what he's using as his reasons.

377
00:39:46,660 --> 00:39:51,980
And once you've identified those, you've got the premises. So you should be able to set it out.

378
00:39:51,980 --> 00:39:59,570
Premise one premise to conclusion. And then you ask, okay, what do I think of these premises?

379
00:39:59,570 --> 00:40:03,470
Are they good premises? What do I think of this argument?

380
00:40:03,470 --> 00:40:07,190
Is is it valid? In other words, if the premises were true,

381
00:40:07,190 --> 00:40:14,540
would the conclusion have to be true or do the premises provide me with at least good reason to believe the conclusion?

382
00:40:14,540 --> 00:40:17,820
And if either of the answers to the question, too, I'm sorry,

383
00:40:17,820 --> 00:40:25,490
the court answer to either of these questions is no, then you don't have a good argument.

384
00:40:25,490 --> 00:40:32,660
If the answer to both those questions is yes, you might have a good argument.

385
00:40:32,660 --> 00:40:41,960
It's not sufficient. Let me give you an argument that satisfies both of these.

386
00:40:41,960 --> 00:41:05,810
Get lost again. OK. Now is the promise.

387
00:41:05,810 --> 00:41:09,690
OK, here's the premise. Here's the conclusion. OK.

388
00:41:09,690 --> 00:41:14,610
It's the premise of this argument. True. Okay.

389
00:41:14,610 --> 00:41:20,790
It says whales are mammals. Therefore, whales are mammals.

390
00:41:20,790 --> 00:41:29,910
Okay. The premise is true. Okay. Is there any possible situation in which the premise is true and the conclusion false?

391
00:41:29,910 --> 00:41:34,290
There isn't. Is that how could there be? The conclusion is the same as the premise.

392
00:41:34,290 --> 00:41:41,910
Okay, that is a circular argument. Circular circular arguments are valid.

393
00:41:41,910 --> 00:41:47,700
How could they not be. If the premise is amongst its sorry, if the conclusion is amongst the premises,

394
00:41:47,700 --> 00:41:53,250
then then there can't be any situation in which the premises are true and the conclusion false.

395
00:41:53,250 --> 00:41:57,540
So that's a valid argument. But what's wrong with that is it's circular.

396
00:41:57,540 --> 00:42:00,300
You're not going to learn anything from that argument.

397
00:42:00,300 --> 00:42:09,140
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.

398
00:42:09,140 --> 00:42:12,690
And that as a philosopher, those are the two questions that.

399
00:42:12,690 --> 00:42:20,370
Well, actually, as a philosopher. That's the one that bothers you. It's it's often scientists who are interested in that one.

400
00:42:20,370 --> 00:42:25,470
So, for example, every swane I've ever seen has been white.

401
00:42:25,470 --> 00:42:30,000
Therefore, all swans are white. Okay.

402
00:42:30,000 --> 00:42:34,410
Well, it may be true that every swan I've ever seen has been white.

403
00:42:34,410 --> 00:42:41,380
I need to find out now whether that's a sufficient reason for thinking that the swan in the next room is white.

404
00:42:41,380 --> 00:42:45,990
I mean, if it's true that all swans White Swan in the next room will be white, won't it?

405
00:42:45,990 --> 00:42:52,800
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?

406
00:42:52,800 --> 00:42:57,030
Well, either this isn't a swan, okay.

407
00:42:57,030 --> 00:43:02,580
Or that it's not the case that all swans white and maybe we would say it isn't a swan.

408
00:43:02,580 --> 00:43:07,600
I mean, you must have heard when Mrs Thatcher in people saying she's the best man in the cabinet.

409
00:43:07,600 --> 00:43:13,470
Okay, here's the argument. All women are passive. Mrs Thatcher is a woman.

410
00:43:13,470 --> 00:43:19,410
Therefore, Mrs Thatcher is passive. That is the argument. Well, Mrs Thatcher clearly isn't passive.

411
00:43:19,410 --> 00:43:23,340
Therefore, either she's not a woman or not.

412
00:43:23,340 --> 00:43:27,740
All women are passive, but you know them. Do you see how it works here?

413
00:43:27,740 --> 00:43:41,240
Often depends on logic. Precisely because it tells us what we ought to think and then somehow confounds us.

414
00:43:41,240 --> 00:43:57,000
Mm hmm. All the same.

415
00:43:57,000 --> 00:44:03,100
Yeah, well. Therefore, actually just marks the conclusion of an argument.

416
00:44:03,100 --> 00:44:09,120
It says I am. The thing about an argument is its its premises giving reasons for a conclusion.

417
00:44:09,120 --> 00:44:13,480
And we can give any premises as reasons for any conclusions.

418
00:44:13,480 --> 00:44:20,780
So if I say Melbourne is in Australia, the sea is salt.

419
00:44:20,780 --> 00:44:26,030
Therefore, Paris is the capital of France.

420
00:44:26,030 --> 00:44:30,560
Okay. Now that sounds like a really bad argument, doesn't it?

421
00:44:30,560 --> 00:44:34,220
But I could tell you a story about how here we are.

422
00:44:34,220 --> 00:44:39,980
We're all not only we all terribly ignorant, really very badly ignorance.

423
00:44:39,980 --> 00:44:47,720
And we have been told that these two sentences are such that if they are true, this third sentence is true.

424
00:44:47,720 --> 00:44:53,630
Okay. The first sentence is the sea is salt. The second sentence is Melbourne's in Australia.

425
00:44:53,630 --> 00:44:57,400
So I say, OK, you go off and find out where the sea is salt.

426
00:44:57,400 --> 00:45:00,020
OK. You go off and find out where the Melbourne is in Australia.

427
00:45:00,020 --> 00:45:05,600
So you scurry and you find the nearest encyclopaedia or dictionaries on you come back and say the sea is salt.

428
00:45:05,600 --> 00:45:11,900
You come back and say, Melbourne's in Australia. And I say, therefore, Paris is the capital of France.

429
00:45:11,900 --> 00:45:21,970
OK. 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.

430
00:45:21,970 --> 00:45:31,180
Isn't it? By providing a context, I could make those apparently completely irrelevant sentences an argument.

431
00:45:31,180 --> 00:45:39,160
So therefore just stands for a conclusion to say, I am saying that that is reason to believe that.

432
00:45:39,160 --> 00:45:46,300
Now, notice something else. If I had lots of other sentences in here.

433
00:45:46,300 --> 00:45:55,810
I'm going to change the fact that this argument's valid.

434
00:45:55,810 --> 00:45:59,680
Well, let's put it, it's not the case that mammals, whales are mammals.

435
00:45:59,680 --> 00:46:06,340
It's not the case. Not whales.

436
00:46:06,340 --> 00:46:11,790
All mammals. Whales are amongst them mammals.

437
00:46:11,790 --> 00:46:22,170
Therefore, whales are mammals. Now, is there any situation where both those premises are true and that conclusions false?

438
00:46:22,170 --> 00:46:26,610
Actually, that's a. They can't both be true.

439
00:46:26,610 --> 00:46:35,880
Can they? So is this argument valid? Yes, it is, because there's no possible situation in which the premises are true.

440
00:46:35,880 --> 00:46:43,220
So how can there be a possible situation in which the premises are true and the conclusion false?

441
00:46:43,220 --> 00:46:47,780
And I'm going to do a truth table here, which is probably asking for trouble.

442
00:46:47,780 --> 00:47:03,140
But let's let's do it, shall we? Let's. Okay.

443
00:47:03,140 --> 00:47:16,670
This is using the notion of possible worlds to explain something.

444
00:47:16,670 --> 00:47:22,700
OK, I've got it. Thank you. P therefore. Q No, I don't want that.

445
00:47:22,700 --> 00:47:50,040
Hold on. Sorry. I'm changing my mind. Let's try this, OK?

446
00:47:50,040 --> 00:47:54,000
Each of these each sentence can be either true or false.

447
00:47:54,000 --> 00:47:56,910
Can't it? OK. Most.

448
00:47:56,910 --> 00:48:03,000
I mean, let's assume for the moment, if you've got a sentence, the cat sat on the mat or Marion's wearing a dress or something like that.

449
00:48:03,000 --> 00:48:07,290
It could either be true or it can be false if it's contingence sentence.

450
00:48:07,290 --> 00:48:16,170
So this truth table represents every possible world with respect to the combination of truth values here.

451
00:48:16,170 --> 00:48:20,370
OK. So this is a world in which P is true and Q is true.

452
00:48:20,370 --> 00:48:27,300
Okay. This is the world in which. Tell me. Good.

453
00:48:27,300 --> 00:48:32,040
Okay. This is the world in which u.s. That's right.

454
00:48:32,040 --> 00:48:35,950
And this is the world in which they're both false. Absolutely.

455
00:48:35,950 --> 00:48:43,240
That you do. You're really doing well here. And they talked and undergraduates can't do that.

456
00:48:43,240 --> 00:48:51,390
And it's because they haven't separated the possible worlds because each these possible worlds is quite separate from me, from the other.

457
00:48:51,390 --> 00:49:01,460
Okay. Now, in the world where if we just take P here in the worlds where P is true, then the premise here is going to be true, isn't it?

458
00:49:01,460 --> 00:49:06,180
Okay. And in the world where P is true here, the premise is going to be true.

459
00:49:06,180 --> 00:49:13,180
Okay. And in the world by appears false. And false again.

460
00:49:13,180 --> 00:49:19,150
Exactly, so. OK. And that's going to be the same here because we've got exactly the same letter here.

461
00:49:19,150 --> 00:49:24,280
OK. Now, do we know whether this argument is valid? We'll look at a structure in turn.

462
00:49:24,280 --> 00:49:29,950
Is this a world in which the premise is true and the conclusions false?

463
00:49:29,950 --> 00:49:34,420
No. Okay, so that's OK. It's valid.

464
00:49:34,420 --> 00:49:41,300
There is this world where the premise is true and the conclusion false.

465
00:49:41,300 --> 00:49:49,720
Hang on. This is number two, the second world. Is this a world where the premise is true and the conclusion false?

466
00:49:49,720 --> 00:49:55,900
No, it isn't. That's okay. Is this a world where the premise is true and the conclusion false?

467
00:49:55,900 --> 00:50:00,280
No. And is this world where the premise is true and the conclusion false?

468
00:50:00,280 --> 00:50:06,880
No, I don't. Who said yes? Look, is this a world where the premise is true?

469
00:50:06,880 --> 00:50:11,290
And the conclusion false? No.

470
00:50:11,290 --> 00:50:17,350
So there's no possible world. Does each of these is a possible world and these are all possible worlds.

471
00:50:17,350 --> 00:50:22,670
And there isn't one where the premise is true and the conclusion false is the.

472
00:50:22,670 --> 00:50:27,050
This is a circular argument, so we know that this argument is valid.

473
00:50:27,050 --> 00:50:32,690
Now I'm going to add not pee in here, session's about it queue at all.

474
00:50:32,690 --> 00:50:36,860
I've just complicated things by adding you ignore it.

475
00:50:36,860 --> 00:50:41,180
That's not pee. OK, what's the truth? Value here is true.

476
00:50:41,180 --> 00:50:45,470
So in this world, not P is false.

477
00:50:45,470 --> 00:50:52,010
Good. So that's not that is not OK in this world.

478
00:50:52,010 --> 00:50:55,970
P is true. So not P is false.

479
00:50:55,970 --> 00:51:03,290
Again in this world P is false. So not P is true.

480
00:51:03,290 --> 00:51:08,570
You really do well. Okay. And in this world P is false. So not P is true.

481
00:51:08,570 --> 00:51:17,330
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.

482
00:51:17,330 --> 00:51:22,220
Okay, so this world, the world number one, we've got two premises.

483
00:51:22,220 --> 00:51:29,960
Is this a world where the premises are both true? And the conclusion false?

484
00:51:29,960 --> 00:51:34,280
No, because the premise is not both true. This one's false, isn't it?

485
00:51:34,280 --> 00:51:38,580
So, okay, this is valid. That's all right. Here's one. OK.

486
00:51:38,580 --> 00:51:44,980
Is this a world where the premises are both true and the conclusion false? No, it isn't, is it OK?

487
00:51:44,980 --> 00:51:49,310
Is this a world where the premises are both true and the conclusion false? No.

488
00:51:49,310 --> 00:51:55,430
And is this a world in which the premises both true and conditional? So is the argument valid?

489
00:51:55,430 --> 00:52:05,870
Yes, good, really good. I think the thing is you can at any premiss to a circular argument.

490
00:52:05,870 --> 00:52:13,740
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.

491
00:52:13,740 --> 00:52:15,420
So obviously not valid.

492
00:52:15,420 --> 00:52:24,770
Now, if I were a politician wanting to to kick sand in your face, the best way to do it would be to offer you a circular argument.

493
00:52:24,770 --> 00:52:28,880
But in the media, blind you with science, hide the premise.

494
00:52:28,880 --> 00:52:33,440
That is the conclusion in amongst lots of other premises.

495
00:52:33,440 --> 00:52:35,270
So you wouldn't see you.

496
00:52:35,270 --> 00:52:44,420
That therefore would sound fine to you then, because it looks as if you'd have an argument that actually it wouldn't change the validity, would it?

497
00:52:44,420 --> 00:52:53,440
You as a rational animal would recognise the validity. What you wouldn't recognise is that the argument is valid because it's circular.

498
00:52:53,440 --> 00:53:00,800
Are you with me? So circular arguments are jolly useful if you're trying to confuse someone.

499
00:53:00,800 --> 00:53:07,040
And the reason they're useful is because you, as rational animals, are validity detectors.

500
00:53:07,040 --> 00:53:13,040
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 such a good argument.

501
00:53:13,040 --> 00:53:17,660
Is she right? It's. You're asking yourself whether my argument is valid.

502
00:53:17,660 --> 00:53:26,500
You're setting yourself to validity detection node.

503
00:53:26,500 --> 00:53:33,080
Chris. If they if somebody. Mm hmm.

504
00:53:33,080 --> 00:53:39,450
Yeah. Yeah, yeah, yeah.

505
00:53:39,450 --> 00:53:45,890
You could use it. The thing about that is it's self-referential because the liar.

506
00:53:45,890 --> 00:53:52,880
If if I say I'm telling the truth and you don't know whether I'm lying or a liar or not.

507
00:53:52,880 --> 00:53:56,600
You don't know whether that sentence is true.

508
00:53:56,600 --> 00:54:05,590
But, yes, you could use truth tables for that. Yeah, yeah. Yeah.

509
00:54:05,590 --> 00:54:17,010
Two different answers. Still give you. I'm just a bit confused, my first one was that one.

510
00:54:17,010 --> 00:54:21,950
So you could keep that you could you could use that.

511
00:54:21,950 --> 00:54:29,400
Were you being confused by the fact I put you in there? Do you think or were you being confused by the fact I wrote that out?

512
00:54:29,400 --> 00:54:39,320
First you say. Well, a mammals, therefore, whales are not mammals.

513
00:54:39,320 --> 00:54:47,280
Yeah. Okay.

514
00:54:47,280 --> 00:54:53,540
Yeah. If you look at it, that that's truth table. I've just done exactly that argument.

515
00:54:53,540 --> 00:55:01,560
If we provide the interpretation that says P is whales are mammals.

516
00:55:01,560 --> 00:55:06,910
Do you see, because when you look at that, Piers, whales are mammals, not pee.

517
00:55:06,910 --> 00:55:11,650
Sorry. This is Piers, whales, mammals.

518
00:55:11,650 --> 00:55:16,570
This says it's not the case. The whales are mammals and this is whales are mammals.

519
00:55:16,570 --> 00:55:21,390
So that's the truth table for that argument.

520
00:55:21,390 --> 00:55:26,370
Yes. And I do that, and I then didn't do it because I realised it wasn't circular.

521
00:55:26,370 --> 00:55:32,410
But if I do the truth table for that one, what's going to happen?

522
00:55:32,410 --> 00:55:44,500
Does anyone recognise this argument? If P, then Q, p, therefore Q.

523
00:55:44,500 --> 00:55:59,880
He's not going to come out valid. It's not circular because the queue isn't a premiss, the queue is part of a premiss and that's different.

524
00:55:59,880 --> 00:56:07,500
That's okay. So that's not circular. If you had queue in here, it would be a circular argument and it would be valid for that reason.

525
00:56:07,500 --> 00:56:15,470
What's this argument? You've seen it today already. Or rather, this is a formalisation of an argument you've seen today.

526
00:56:15,470 --> 00:56:19,560
So thank you. Exactly. So if it's snowing in, the mail will be late.

527
00:56:19,560 --> 00:56:29,280
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 four.

528
00:56:29,280 --> 00:56:35,110
Uh. Whoops.

529
00:56:35,110 --> 00:56:46,960
Yes, that's right. Uh. OK, let's leave there for.

530
00:56:46,960 --> 00:56:51,820
Is this a world in which the premises are all true and the conclusion false?

531
00:56:51,820 --> 00:56:56,810
No. OK. So that's right. Is this a will that the premises are all true and the conclusion false?

532
00:56:56,810 --> 00:57:02,080
No. Is this one where the premises are all true and the conclusion false? Is this one?

533
00:57:02,080 --> 00:57:13,000
No. OK. So that argument is valid. But if I change this to a Q.

534
00:57:13,000 --> 00:57:52,400
Sorry, I'll get another pen, because it's a. Uh.

535
00:57:52,400 --> 00:57:57,050
Okay. Is this a world where the premises are all true?

536
00:57:57,050 --> 00:58:00,590
And the conclusion false? Okay.

537
00:58:00,590 --> 00:58:05,360
Is this a well with the premises rolled through and the conclusion false? No.

538
00:58:05,360 --> 00:58:12,170
Is this a world where the premises Royal Troon, the conclusion false? It is, isn't it?

539
00:58:12,170 --> 00:58:21,410
Okay. That is quite sufficient to show that this argument, any argument of that form is invalid,

540
00:58:21,410 --> 00:58:26,660
because here's a world just here's a possible world in which the premises are true and the

541
00:58:26,660 --> 00:58:32,080
conclusion falls and all the rest becomes irrelevant because you only need one counterexample.

542
00:58:32,080 --> 00:58:44,030
And we can even say what the counterexample is because that argument is invalid in the world where P is false.

543
00:58:44,030 --> 00:58:53,580
And Q is true. So if we put in the interpretation we had before, what was P?

544
00:58:53,580 --> 00:58:59,790
It's snowing and Q is the male is late.

545
00:58:59,790 --> 00:59:08,010
So in the world where P is false. In other words, it's not snowing, but the male is late because of that puncture.

546
00:59:08,010 --> 00:59:12,780
That's the counterexample to this argument. Do you see.

547
00:59:12,780 --> 00:59:18,280
Do you see how useful logic is? It's fantastic. And you say you're doing it now.

548
00:59:18,280 --> 00:59:26,010
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.

549
00:59:26,010 --> 00:59:32,160
The really difficult bit is the interpretation from English into formal logic.

550
00:59:32,160 --> 00:59:38,590
That's that's the really difficult bit. But this bit dead simple once you know how to do it.

551
00:59:38,590 --> 00:59:41,430
And this is formal logic. Okay. Right.

552
00:59:41,430 --> 00:59:48,690
Actually, that takes me quite neatly onto the next slide, because I wanted to point out that there are two sorts of logic.

553
00:59:48,690 --> 00:59:59,490
So far we've been looking at formal logic. But I also want say something about philosophical logic, because that's a bit different.

554
00:59:59,490 --> 01:00:03,620
But firstly, just to say something a bit more about formal logic.

555
01:00:03,620 --> 01:00:11,510
You've got to distinguish film from contents, the form of the argument from the content of the argument.

556
01:00:11,510 --> 01:00:18,860
So this is the form of the argument up here. The content is supplied by the interpretation.

557
01:00:18,860 --> 01:00:25,940
So you notice that you give this a completely different interpretation. But the form would still be the same.

558
01:00:25,940 --> 01:00:32,720
And that's actually very important because what that tells us is that logic is topic neutral.

559
01:00:32,720 --> 01:00:38,750
Once you know how to do logic, it doesn't matter what subject you're talking about.

560
01:00:38,750 --> 01:00:43,940
The logic will work for any subject at all. So let's look at this one.

561
01:00:43,940 --> 01:00:48,500
Let's look at here are two arguments. Sorry, I'll move this over.

562
01:00:48,500 --> 01:00:54,110
All men are mortal. Socrates is a man. Therefore, Socrates is mortal.

563
01:00:54,110 --> 01:01:01,490
All actions that produce the greatest happiness, the greatest number are right. That action produces the greatest happiness of the greatest number.

564
01:01:01,490 --> 01:01:09,530
Therefore, that action was right. Now, can you see that these two arguments, completely different subject matter only.

565
01:01:09,530 --> 01:01:14,660
This is about mortality. And Socrates. And that's about ethics.

566
01:01:14,660 --> 01:01:18,950
The greatest happiness is the greatest number, etc. But they've got the same form.

567
01:01:18,950 --> 01:01:24,320
And now I want you to practise your logic by telling me what the form of this argument is.

568
01:01:24,320 --> 01:01:29,810
Okay. Work it out for yourself and then put your hands up when you've got it without yelling it out.

569
01:01:29,810 --> 01:01:33,530
Work out what the form of that argument is.

570
01:01:33,530 --> 01:01:41,290
Remember that there are logical words and there are English words and it's the logical words you want to leave in.

571
01:01:41,290 --> 01:01:49,820
And the English word. Well, they're all English words, but these are logical words in provide an interpretation for the non logical words.

572
01:01:49,820 --> 01:02:04,700
Don't worry if you find this difficult. This is difficult stuff. Put up your hands if you think you've got it.

573
01:02:04,700 --> 01:02:39,340
Let me give you a tip that all is a word that you live in and is is a word that you'll leave in.

574
01:02:39,340 --> 01:02:48,790
Put up your hand if you think you've got knots of. Good.

575
01:02:48,790 --> 01:03:13,260
We're getting that. Symbolic logic because of the form is captured in symbols.

576
01:03:13,260 --> 01:03:20,910
Good. Okay. Good food, you want to have a go? Okay.

577
01:03:20,910 --> 01:03:31,640
Oh, no. Oh, surely somebody could invent something better than this.

578
01:03:31,640 --> 01:03:37,830
Do you think what a crayon.

579
01:03:37,830 --> 01:03:44,570
Yes. Yes. Would work, wouldn't it. All.

580
01:03:44,570 --> 01:03:48,960
All. A is B o, all A's, r, b.

581
01:03:48,960 --> 01:04:02,700
Can I. Can I change it? Yeah. Okay. All A's are B and C is A therefore give the girl a gold star.

582
01:04:02,700 --> 01:04:08,360
Fantastic. You said all A's r b.

583
01:04:08,360 --> 01:04:12,970
S isn't a therefore s is a B. A lot of us out there.

584
01:04:12,970 --> 01:04:18,170
Well, let's provide the interpretation for each of these arguments.

585
01:04:18,170 --> 01:04:23,670
Okay. So the interpretation says, what does a mean. What does he mean.

586
01:04:23,670 --> 01:04:28,050
And what does s mean. And we've got two arguments.

587
01:04:28,050 --> 01:04:35,680
So we need to provide two interpretations. This is a here.

588
01:04:35,680 --> 01:04:43,720
If you do decide if we do, the first argument first acts as a man is what it is,

589
01:04:43,720 --> 01:04:48,100
actually I'll put that in because these are projects is a man is a predicate.

590
01:04:48,100 --> 01:04:53,380
So you need to have a place holder. X is a man.

591
01:04:53,380 --> 01:04:57,330
B is. X is mortal.

592
01:04:57,330 --> 01:05:03,110
Yep. An s. Socrates.

593
01:05:03,110 --> 01:05:16,160
Well done. OK. The interpretation here A is X is a bit long winded, this one.

594
01:05:16,160 --> 01:05:24,640
A is an action, an action that produces the greater toughness. What's the gross number?

595
01:05:24,640 --> 01:05:28,510
And B is is right.

596
01:05:28,510 --> 01:05:34,610
X is right. Well done. And X is.

597
01:05:34,610 --> 01:05:41,360
Well done, well done, that action, because that action is a designator, isn't it?

598
01:05:41,360 --> 01:05:47,990
That action, it picks out one particular thing, in this case, an action in the same way that Socrates is a designator.

599
01:05:47,990 --> 01:05:54,710
It picks out one particular thing, Socrates. So we're saying the first one.

600
01:05:54,710 --> 01:06:01,520
Anything that's a man is mortal. So anything that has this property also has that property.

601
01:06:01,520 --> 01:06:07,440
Socrates has this property, the first one. Therefore, Socrates has the other one.

602
01:06:07,440 --> 01:06:13,210
OK. And we're saying exactly the same thing in that one, except we're talking about something completely different.

603
01:06:13,210 --> 01:06:19,070
We're talking about actions and whether they produce the great stuff in disgrace number or not.

604
01:06:19,070 --> 01:06:28,040
So do you see why logic is topic neutral? Once you've learnt logic, it doesn't matter what you're thinking about.

605
01:06:28,040 --> 01:06:30,120
You can think clearly about it.

606
01:06:30,120 --> 01:06:37,160
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.

607
01:06:37,160 --> 01:06:43,760
It really doesn't matter what you're talking about. There's a philosophy, a mind, a philosophy, a biology, a philosophy of chairs.

608
01:06:43,760 --> 01:06:52,010
Probably somebody was trying to persuade me to run a weekend school on the philosophy of accountancy yesterday.

609
01:06:52,010 --> 01:06:55,000
If anyone would like to do that, they can share it.

610
01:06:55,000 --> 01:07:02,990
No, actually, I'm sure that there is a philosophy of accountancy and actually, if there are, I'm sure, philosophical issues in there.

611
01:07:02,990 --> 01:07:14,000
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.

612
01:07:14,000 --> 01:07:18,500
And that's because logic is topic neutral. Okay, let's move on.

613
01:07:18,500 --> 01:07:23,600
So what we do in formal logic, as you've seen, is we strip an argument of its content.

614
01:07:23,600 --> 01:07:31,130
We're not interested in the content. We reveal its form and then we can test mechanically for validity.

615
01:07:31,130 --> 01:07:36,920
And you've seen me test mechanically for validity here.

616
01:07:36,920 --> 01:07:40,400
That's one way of testing mechanically for validity. Okay.

617
01:07:40,400 --> 01:07:46,670
Now, the trouble with that is what happens if I add another premise here.

618
01:07:46,670 --> 01:07:54,080
So I have an AR as well. It hurts to see it's going to get unwieldy, isn't it?

619
01:07:54,080 --> 01:08:03,150
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.

620
01:08:03,150 --> 01:08:11,840
And it's very, very boring to work it out. And then I show them that they can do this instead.

621
01:08:11,840 --> 01:08:20,780
I could find a. OK.

622
01:08:20,780 --> 01:08:25,470
Now, you'll just have to believe me that that arrow means if then.

623
01:08:25,470 --> 01:08:34,070
OK, so that that formula there means if P then Q And that little sign there means it is not the case.

624
01:08:34,070 --> 01:08:41,720
So that means not. Q And what I've done here, you remember the argument we had if P then cupie therefore.

625
01:08:41,720 --> 01:08:46,040
Q I've got the premise there, the first premise there.

626
01:08:46,040 --> 01:08:50,450
The second premise there. And I've negated the conclusion. Okay.

627
01:08:50,450 --> 01:09:03,140
Because the argument was if P than 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,

628
01:09:03,140 --> 01:09:08,840
a situation in which the premises are both true and the conclusions false.

629
01:09:08,840 --> 01:09:14,300
Let's see if I can find an argument like that or a situation like that.

630
01:09:14,300 --> 01:09:26,870
And I then apply completely mechanical rules that I could again teach you in a in an hour or so to get this.

631
01:09:26,870 --> 01:09:32,110
OK. That's the conditions under which that arch. That is true of that all true.

632
01:09:32,110 --> 01:09:35,740
That is true. Are there two situations? It's true. Just in case.

633
01:09:35,740 --> 01:09:42,880
Not P or Q and you can't. There is no possible worlds with both Q and not Q in it.

634
01:09:42,880 --> 01:09:48,430
So that's not a possible world. There is no possible world with not pee and pee in it.

635
01:09:48,430 --> 01:09:50,440
So that's not a possible world.

636
01:09:50,440 --> 01:10:01,240
There is no possible world in which the set consisting of the premises and the negation of the conclusion are true together.

637
01:10:01,240 --> 01:10:10,150
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

638
01:10:10,150 --> 01:10:18,280
how to do this so that all you have to do is any argument at all if you can translate it into symbols.

639
01:10:18,280 --> 01:10:23,080
And that's the biggest if if you can introduce it translated into symbols.

640
01:10:23,080 --> 01:10:27,430
There is a set of rules such that you can apply these rules and test it,

641
01:10:27,430 --> 01:10:34,310
just as I have done and say quite categorically, this is a situation in which, sorry, this is an argument is valid.

642
01:10:34,310 --> 01:10:39,730
And let's do the invalid one. Just see again how it works.

643
01:10:39,730 --> 01:10:44,900
The invalid one is if P then Q Q therefore P.

644
01:10:44,900 --> 01:10:53,040
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

645
01:10:53,040 --> 01:10:57,610
that sets consisting of the premises plus the negation of the conclusion.

646
01:10:57,610 --> 01:11:02,390
Well that's true. Just in case not P or Q again.

647
01:11:02,390 --> 01:11:12,080
But we don't have any contradictions here do we. See we've got not p, not P, q there's one possible world in which that set are all true.

648
01:11:12,080 --> 01:11:16,180
The sentences in that set are all true and we've got Q not P.

649
01:11:16,180 --> 01:11:24,460
Q So that's another world in which the sets consisting of the premises plus the negation of the conclusion are all true.

650
01:11:24,460 --> 01:11:35,270
So either of these, any situation in which Q are not P is true is a counterexample to that argument.

651
01:11:35,270 --> 01:11:39,950
And you go to your interpretation now, you find out what cures you find out what not P is.

652
01:11:39,950 --> 01:11:44,450
And you know what your counterexample is magic, isn't it?

653
01:11:44,450 --> 01:11:54,110
Well, yeah, p it is snowing. Q The male is linked.

654
01:11:54,110 --> 01:12:00,550
Do you see what I mean? I was just doing exactly the same example. Don't worry if you're getting confused that you don't know these rules.

655
01:12:00,550 --> 01:12:05,560
You have no idea why I've represented the truth.

656
01:12:05,560 --> 01:12:10,510
Conditions of that like that. And I would have to tell you that.

657
01:12:10,510 --> 01:12:16,330
And I'd also given that that's actually quite difficult to understand, I have to convince you that that is the case.

658
01:12:16,330 --> 01:12:19,450
But I would be able to do it. I promise you.

659
01:12:19,450 --> 01:12:28,600
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.

660
01:12:28,600 --> 01:12:35,830
And one, if if you showed it was invalid, you'd also be able to give me the counterexample because you would know which

661
01:12:35,830 --> 01:12:48,150
world is such that the premises are both true and the conclusion false is nice.

662
01:12:48,150 --> 01:13:03,290
It wasn't the case. He therefore paid. I understanding that as the therefore.

663
01:13:03,290 --> 01:13:09,850
You said P, therefore, Q Yeah. That's not a therefore it's it's an implication, not an entailment.

664
01:13:09,850 --> 01:13:19,330
That's saying if P, then Q not P, therefore. Q. I mean, don't worry too much about that.

665
01:13:19,330 --> 01:13:25,720
That would be. OK.

666
01:13:25,720 --> 01:13:29,260
So what I was asking was just would you be using. I'm just trying to get an idea.

667
01:13:29,260 --> 01:13:35,110
Yeah. Might use that kind of diagram. Is it because you're actually trying to challenge somebody and say, well, in fact.

668
01:13:35,110 --> 01:13:43,750
Yeah. And it's not the case. Well, what I'd be saying is if anyone made this argument, this is the argument they'd make.

669
01:13:43,750 --> 01:13:51,800
They'd be saying if P, then Q and P, then Q.

670
01:13:51,800 --> 01:13:58,280
So if these are true, then Q is true. So if it's if it's true that if it's snowing, the mayor will be late.

671
01:13:58,280 --> 01:14:03,110
And it's true that it's snowing. Then it must be the case of the male is late.

672
01:14:03,110 --> 01:14:07,370
And I would do this sort of diagram and I'd say, you know, you're right.

673
01:14:07,370 --> 01:14:15,710
That's absolutely right. But then if somebody tried the other argument. So as I'm reading Descartes, for example, and I think, okay,

674
01:14:15,710 --> 01:14:25,250
he what he's saying is that it's possible that all our beliefs about the external world are false.

675
01:14:25,250 --> 01:14:30,170
Okay. And one of his premises is this one of his premises is that one of his premises?

676
01:14:30,170 --> 01:14:37,040
Is this. Is it true that that conclusion really follows from those premises?

677
01:14:37,040 --> 01:14:42,710
So I would do the truth table. And I would say, no, it isn't true or yes, it is true.

678
01:14:42,710 --> 01:14:47,500
And that would enable or you could look at the reader and the leader in tonight's paper and say,

679
01:14:47,500 --> 01:14:52,210
okay, here's the argument, premise one premise to premise three.

680
01:14:52,210 --> 01:14:59,900
I'll now formalise the arguments. I'll strip the content out of it and formalise it, and then I'll apply the rules of the predicate.

681
01:14:59,900 --> 01:15:03,560
Calculus would probably be needed. This is the propositional calculus,

682
01:15:03,560 --> 01:15:12,240
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.

683
01:15:12,240 --> 01:15:16,070
Because what you're determining is that the argument is a good one or not.

684
01:15:16,070 --> 01:15:20,720
That still doesn't tell you whether the conclusion is true, does it?

685
01:15:20,720 --> 01:15:27,020
Why not? Exactly.

686
01:15:27,020 --> 01:15:33,120
It might be the fact that an argument is valid isn't telling you that the premises are true.

687
01:15:33,120 --> 01:15:37,920
So as a philosopher, what you're interested in is the validity of the argument.

688
01:15:37,920 --> 01:15:39,900
You're also interested in the truth of the premises.

689
01:15:39,900 --> 01:15:48,850
If it's a not if it's a philosophical argument, but it might be an empirical argument, in which case the truth of premises isn't your business.

690
01:15:48,850 --> 01:15:58,440
You know, we don't go around getting our hands dirty ideas.

691
01:15:58,440 --> 01:16:13,110
They do say, no, it doesn't work like that because firstly, you've got to be able to formalise an argument.

692
01:16:13,110 --> 01:16:21,120
And there there are huge problems. If this is the class of oral arguments in the world.

693
01:16:21,120 --> 01:16:30,940
OK, all arguments here. You can formalise.

694
01:16:30,940 --> 01:16:38,370
I mean, I'm making this up. But let's say you can formalise that many in the predicate calculus.

695
01:16:38,370 --> 01:16:44,040
You can formalise that many in the in day Ontake logic. You can formalise that many in modal logic.

696
01:16:44,040 --> 01:16:49,470
This lot. You can't formalise at all. And therefore, you can't apply the rules.

697
01:16:49,470 --> 01:16:55,610
Now, what we hope as formal logicians is that we will learn how to formalise those.

698
01:16:55,610 --> 01:17:00,420
And for example, the predicate calculus was developed only a couple of hundred years ago.

699
01:17:00,420 --> 01:17:07,390
Aristotle developed syllogistic logic. But it took Frager to develop predicate logic.

700
01:17:07,390 --> 01:17:12,030
And that was a huge leap forward. Modal logic has only been developed.

701
01:17:12,030 --> 01:17:17,260
Well, it's still being developed. The logic of probability. Ditto dialectic logic.

702
01:17:17,260 --> 01:17:22,800
We're still working on it. So, you know, you're right at the cutting edge here.

703
01:17:22,800 --> 01:17:31,530
I've given you the the knotty calculus. If you want to go and do it for yourself, you'll you'll have to do a lot more than I've given you here.

704
01:17:31,530 --> 01:17:35,880
But you know that. I mean. So, no, it's not the case.

705
01:17:35,880 --> 01:17:41,010
And of course, also the real skill is in translating the argument.

706
01:17:41,010 --> 01:17:49,410
And you'd know that if I if I made you do some, because it's really, really difficult to translate from English into a symbolic language.

707
01:17:49,410 --> 01:17:56,330
And there are lots of things left out. And it's very frustratingly inaccurate. And so there are there are real problems.

708
01:17:56,330 --> 01:18:03,970
But but we all do it all the time. Believe me, I sit in my study doing tables like that.

709
01:18:03,970 --> 01:18:12,760
It's much more interesting than you might think. I there are cases there may be more than one promise.

710
01:18:12,760 --> 01:18:22,750
Yeah. Well, I mean, there are more there's more than one premise in the arguments I've been doing, of course.

711
01:18:22,750 --> 01:18:28,600
That's one premise. That's another premise. And of course, there could be I mean, there could be 10 premises here.

712
01:18:28,600 --> 01:18:38,270
I could still apply these rules. No, no.

713
01:18:38,270 --> 01:18:49,540
You you only need one. That's false. And that's quite sufficient to show that the even if the arguments valid, the conclusion may be false.

714
01:18:49,540 --> 01:18:53,080
Yes. So the number of premises that's true is not very relevant.

715
01:18:53,080 --> 01:19:02,890
It's than if there's at least one that's false. He has a valid argument with a false conclusion.

716
01:19:02,890 --> 01:19:14,570
I think I wrote it down. I know I've written it here. If it's Tuesday, then Marianne isn't lecturing.

717
01:19:14,570 --> 01:19:18,590
It is Tuesday, therefore, Marianne isn't lecturing. Okay.

718
01:19:18,590 --> 01:19:22,340
Well, that's a valid argument, isn't it? You want to hear it again?

719
01:19:22,340 --> 01:19:26,930
If it's Tuesday, then Marianne isn't lecturing. It is Tuesday.

720
01:19:26,930 --> 01:19:33,790
Therefore, Marianne isn't lecturing. Now, if those premises were true, the conclusion would be true, wouldn't it?

721
01:19:33,790 --> 01:19:38,390
Okay. But the premises aren't true, are they? Neither is the conclusion.

722
01:19:38,390 --> 01:19:43,380
So you can have a valid argument with a false conclusion.

723
01:19:43,380 --> 01:19:49,160
If you know that the conclusion is false, of course you can go back and say one of the premises must be false.

724
01:19:49,160 --> 01:19:54,770
But there are often situations where we actually don't know whether the conclusion is true or false.

725
01:19:54,770 --> 01:20:05,180
And therefore, we don't know whether the premises are true or false. We know this is logic is in some ways the servant of science in other ways.

726
01:20:05,180 --> 01:20:14,040
Of course, science is the servant of logic. I mean, they they work together.

727
01:20:14,040 --> 01:20:20,610
Oh, yes. It tells you a lot. It tells you whether an argument is valid and you know that if.

728
01:20:20,610 --> 01:20:27,250
OK. Think of the difference between something's generating truth and something's preserving truth.

729
01:20:27,250 --> 01:20:32,680
Logic doesn't generate truth. If you haven't got truth in the premises, you won't have it in the conclusion.

730
01:20:32,680 --> 01:20:39,550
But if you have got truth in the premises, you preserve it in the conclusion by using a valid argument.

731
01:20:39,550 --> 01:20:44,620
And that's what you hope you, because there are things that we know about the world.

732
01:20:44,620 --> 01:20:52,160
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.

733
01:20:52,160 --> 01:21:01,810
And one of the ways of doing that is, is by using logic. If this is true and this is true, then this must be true.

734
01:21:01,810 --> 01:21:18,530
If this is true, yeah. Yeah.

735
01:21:18,530 --> 01:21:29,260
Well, let's say I'm a scientist and I say, well. If the Higgs bows on exists, then my building,

736
01:21:29,260 --> 01:21:38,800
this whacking Great Hadron Collider at a cost of millions and millions and millions of pounds might enable me to find it.

737
01:21:38,800 --> 01:21:41,950
Of course, if if the Higgs boson doesn't exist.

738
01:21:41,950 --> 01:21:48,640
I've wasted all that money, well, then, you know, they might may show me a few other things, but it won't tell me about the Higgs boson.

739
01:21:48,640 --> 01:21:54,070
So if statements are actually we use them all the time.

740
01:21:54,070 --> 01:22:03,340
I mean, if you think of any of your practical reasoning that says, okay, I want to do liver for supper tonight.

741
01:22:03,340 --> 01:22:13,390
Therefore, I need some onions or something like that. I haven't got any Anand's that you're using if statements to generate conclusions about

742
01:22:13,390 --> 01:22:22,390
actions or conclusions about knowledge or you can't you can't reason without if statements.

743
01:22:22,390 --> 01:22:27,770
This is. Yeah. I mean, it was when this was developed that computing became possible.

744
01:22:27,770 --> 01:22:32,440
Yeah. Yeah.

745
01:22:32,440 --> 01:22:37,120
Absolutely the same. Exactly. So. Yeah. Yeah. No.

746
01:22:37,120 --> 01:22:45,120
I mean what you're doing when you're doing, applying those truth tables and the Tablo rules is acting like a computer.

747
01:22:45,120 --> 01:22:58,630
You're making like a computer. There is a tendency towards a new ice age in the proceedings.

748
01:22:58,630 --> 01:23:02,820
Exactly. I mean, you might have two conflicting theories.

749
01:23:02,820 --> 01:23:07,150
Are you saying if this is true, then this will be the results? Let's see if this is the result.

750
01:23:07,150 --> 01:23:15,660
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 there is the correct one.

751
01:23:15,660 --> 01:23:26,470
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.

752
01:23:26,470 --> 01:23:30,940
I might not. I might need to go into the laboratory to see if and if statement is true.

753
01:23:30,940 --> 01:23:41,330
I wouldn't because there's no way laboratory could be. I think it will be because of our activities.

754
01:23:41,330 --> 01:23:52,130
But some people didn't say that. And they say it is a natural thing that's happened to.

755
01:23:52,130 --> 01:24:00,200
So do you see that now we have we have scope for going into the laboratory or the Arctic or wherever we go to find out.

756
01:24:00,200 --> 01:24:08,250
But without that bit of reasoning, first, you wouldn't even know what you were looking for.

757
01:24:08,250 --> 01:24:14,970
And the thing is, if logic can rule out something, then there's no point in going to the laboratory at all.

758
01:24:14,970 --> 01:24:25,890
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.

759
01:24:25,890 --> 01:24:33,270
Because why? Why should I fund him? Okay, moving on, because we've only got five minutes left.

760
01:24:33,270 --> 01:24:39,680
But that's all right because. OK. I was going to talk very briefly about philosophical logic.

761
01:24:39,680 --> 01:24:45,240
I've talked about formal logic, but philosophical logic is the philosophy of logic.

762
01:24:45,240 --> 01:24:50,730
I said there are philosophies of everything, including biology, accountancy, whatever.

763
01:24:50,730 --> 01:24:54,450
But the philosophy of logic is, as you can imagine,

764
01:24:54,450 --> 01:25:05,970
pretty damn important to philosophers because the philosophy of Lord of Logic looks at the notions without which logic can't work.

765
01:25:05,970 --> 01:25:09,720
So we've talked about truth a lot today, haven't we?

766
01:25:09,720 --> 01:25:15,750
I've drawn truth tables. I've drawn truth trees. I've said if this is true, that's true.

767
01:25:15,750 --> 01:25:20,490
So the notion of truth is absolutely central. Well, what is truth?

768
01:25:20,490 --> 01:25:24,860
Gone. Tell me you've all sat there looking intelligence as we've talked about truth.

769
01:25:24,860 --> 01:25:33,640
So I assume you understand the word. Tell me, what is truth?

770
01:25:33,640 --> 01:25:38,830
Something is correct, what's correct, then? I mean, you're just giving me a synonym there, aren't you?

771
01:25:38,830 --> 01:25:46,730
Whoever it was. Okay, so what? Okay, what is false then?

772
01:25:46,730 --> 01:25:52,020
No. No. Okay. But that doesn't tell me what either are.

773
01:25:52,020 --> 01:25:55,770
It's true. You can't have truth without falsehood. You can't have falsehood without truth.

774
01:25:55,770 --> 01:26:00,030
But what is truth? A fact. Okay.

775
01:26:00,030 --> 01:26:04,620
What's a fact? Let's let's.

776
01:26:04,620 --> 01:26:10,170
What is a fact? Certain knowledge is it is knowledge of fact.

777
01:26:10,170 --> 01:26:14,490
I mean, there's the knowledge that I'm wearing a dress. And there's the fact I'm wearing a dress.

778
01:26:14,490 --> 01:26:20,900
Are they the same thing? No, because there are facts of which we know nothing out there.

779
01:26:20,900 --> 01:26:32,660
So so facts are nothing to do with knowledge, but reality sounds like a synonym for truth here.

780
01:26:32,660 --> 01:26:38,080
A fact is actually something that makes a true sentence true.

781
01:26:38,080 --> 01:26:45,820
Isn't it? Think about it. What and what is a fact? You know, there are facts you can't prove.

782
01:26:45,820 --> 01:26:51,010
I mean, are there three consecutive sevens in the decimal expansion of PI?

783
01:26:51,010 --> 01:26:54,490
If there aren't, then you can't prove it. I'm told there are.

784
01:26:54,490 --> 01:27:01,060
By the way. So that's out of date. But just imagine the decimal expansion of PI is an infinite expansion.

785
01:27:01,060 --> 01:27:07,360
If there aren't three consecutive sevens, there's no way we're to be able to prove it.

786
01:27:07,360 --> 01:27:14,900
But it would still be a fact, wouldn't it? So knowledge of a fact and a fact are two quite different things.

787
01:27:14,900 --> 01:27:20,350
And what is a fact? A fact is something that makes a true sentence true.

788
01:27:20,350 --> 01:27:24,130
So talking about facts doesn't tell me anything about truth. So come on.

789
01:27:24,130 --> 01:27:32,000
Come on. You you've all been dealing with truth. What is it? You.

790
01:27:32,000 --> 01:27:37,830
So then how do we know we do not need to know it at all?

791
01:27:37,830 --> 01:27:44,160
No, you're all confusing. Not all of you may be epistemology and metaphysics here.

792
01:27:44,160 --> 01:27:49,020
Epistemology is what we know and metaphysics is what is the case.

793
01:27:49,020 --> 01:27:53,980
And there are two quite separate things. What are you going to know?

794
01:27:53,980 --> 01:28:00,230
Because a belief is usually to do with knowledge rather than because there might be facts about which we have no beliefs.

795
01:28:00,230 --> 01:28:07,410
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.

796
01:28:07,410 --> 01:28:19,920
How do you know whether I have one? Okay, but there's still a fact about my middle name.

797
01:28:19,920 --> 01:28:28,170
Irrefutable is to do with proof again, isn't it? Yeah, no, that's again to do with the pistol ology.

798
01:28:28,170 --> 01:28:35,340
The fact is, truth is a very, very difficult. You mentioned correspondence. There are two key theories about truth.

799
01:28:35,340 --> 01:28:41,820
Actually, here's another one. There's some belief that true truth is nothing, that the truth is completely redundant.

800
01:28:41,820 --> 01:28:49,220
Because if I say P is true, I'm not saying anything more than PMI.

801
01:28:49,220 --> 01:28:55,560
If I say peer's true onto my saying anything more than pee.

802
01:28:55,560 --> 01:29:04,710
Would you say not? I'm not not I'm saying not not pee on sight.

803
01:29:04,710 --> 01:29:10,070
Because if if pee is true, then then not pee is false.

804
01:29:10,070 --> 01:29:17,170
So if if, if I'm saying pee I'm saying not not pee, not pee.

805
01:29:17,170 --> 01:29:21,950
You two can do this eventually. Is truth demonstrable?

806
01:29:21,950 --> 01:29:34,160
Not always. No, no. Definitely not moral regard such as factual.

807
01:29:34,160 --> 01:29:40,970
Well, I think there are facts about values. So. So I don't think there's any opposition between fact and value.

808
01:29:40,970 --> 01:29:48,300
So I think there are moral truths and that what make a moral truth is that there are moral facts.

809
01:29:48,300 --> 01:29:56,210
You know, you can sing, you preach proof again. The proof is to do with knowledge anyway.

810
01:29:56,210 --> 01:30:01,520
One one people some people think there's no more to truth than coherence.

811
01:30:01,520 --> 01:30:06,890
What makes one believe true is that it coheres with your other beliefs.

812
01:30:06,890 --> 01:30:11,840
Other people think, well, hang on, I can have a set of beliefs here, all of which are coherence.

813
01:30:11,840 --> 01:30:16,040
And then if I negate the more that will be another set.

814
01:30:16,040 --> 01:30:21,570
All of which are coherence, won't it? But which is true.

815
01:30:21,570 --> 01:30:28,080
So coherence can't be the right theory. Well, no, because truth.

816
01:30:28,080 --> 01:30:36,240
Truth seems to be a property of sentences and beliefs, doesn't it?

817
01:30:36,240 --> 01:30:42,600
Well, reality isn't a property of your beliefs, is it, or of your sentences.

818
01:30:42,600 --> 01:30:45,960
Exactly. But truth seems to be a prop.

819
01:30:45,960 --> 01:30:53,420
If there weren't any beliefs in this world, there wouldn't be any sentences with the sentences, express beliefs.

820
01:30:53,420 --> 01:30:58,890
OK, if I believe that that your what's your name? Deirdre is wearing red.

821
01:30:58,890 --> 01:31:04,560
I just expressed that belief in saying Dajarra is wearing red. If there were no beliefs, there'd be no sentences.

822
01:31:04,560 --> 01:31:14,880
If there were neither beliefs nor sentences, there would be no truth, but they'd still be reality.

823
01:31:14,880 --> 01:31:29,800
Semantics means truth or means truth conditions. Yeah.

824
01:31:29,800 --> 01:31:35,350
That's because you're thinking of what makes things true.

825
01:31:35,350 --> 01:31:39,460
But, of course, truth is still the property of the sentence that you've uttered.

826
01:31:39,460 --> 01:31:46,270
I mean, what's true is the sentence. The reality is what makes it true.

827
01:31:46,270 --> 01:31:52,390
This is this is really difficult stuff here. Just talk about semantics and syntax at the moment.

828
01:31:52,390 --> 01:32:00,100
If we look at one of the truth trees, again, I have stripped the semantics out of the arguments there.

829
01:32:00,100 --> 01:32:07,210
I've left the syntax. All I've left is the shape. If I want to put the meaning back in.

830
01:32:07,210 --> 01:32:10,480
I've got to put semantics back in and inputting semantics back in.

831
01:32:10,480 --> 01:32:19,390
What I'm putting in is conditions of truth and falsehood. That's what semantics is, and that's that's what meaning is.

832
01:32:19,390 --> 01:32:33,250
Anyway, we've done it now. That's logic. That's your lot on logic. Oh, okay.

833
01:32:33,250 --> 01:32:38,430
Correspondence. Correspondence. So you've actually we've already looked at that.

834
01:32:38,430 --> 01:32:43,270
Truth is, correspondence between a sentence and a fact.

835
01:32:43,270 --> 01:32:48,610
But what's wrong with that is, is what is a fact of often something that makes a true sentence true.

836
01:32:48,610 --> 01:32:54,730
And therefore, that's just a secular definition. It gets you absolutely nowhere.

837
01:32:54,730 --> 01:33:01,390
Oh, goodness. It's lots of people. Yeah, A.J., I would certainly be one of them, I think.

838
01:33:01,390 --> 01:33:07,750
So what is truth answer? I don't know. I know more than you do, obviously.

839
01:33:07,750 --> 01:33:11,350
But I don't know because this is still an ongoing question.

840
01:33:11,350 --> 01:33:16,240
What is truth? That's what philosophical logic looks at. We also I mean, validity.

841
01:33:16,240 --> 01:33:21,550
I gave you one of the paradoxes of entailment two minutes ago, and you weren't very happy with it.

842
01:33:21,550 --> 01:33:33,960
Here's another two. Well, it would be if I can find them.

843
01:33:33,960 --> 01:33:42,610
We're running over our time. If anyone wants to go, they're most welcome. Um.

844
01:33:42,610 --> 01:33:47,080
No, I'm not going to be able to find it if I say the grass is green.

845
01:33:47,080 --> 01:33:54,910
Therefore, two plus two equals four. That's a valid argument because there's no possible situation which that conclusion is false.

846
01:33:54,910 --> 01:33:59,290
So how could there be a possible situation in which the premise is true? And the conclusion false?

847
01:33:59,290 --> 01:34:03,580
There couldn't be. That's one of the paradoxes of entailment.

848
01:34:03,580 --> 01:34:11,680
And one of the things that philosophical traditions would like to know is why is our definition of entailment faulty in that way?

849
01:34:11,680 --> 01:34:18,520
Because that surely that argument isn't valid. And yet our definition of valid makes it valid.

850
01:34:18,520 --> 01:34:25,980
So there's something wrong with our definition of validity. And yet somehow we can run computers that run Large Hadron Collider.

851
01:34:25,980 --> 01:34:31,750
And find the Higgs suppose on on our logic. So our logic isn't totally wrong.

852
01:34:31,750 --> 01:34:34,960
How do we do with it? Okay, we're going to stop right there.

853
01:34:34,960 --> 01:34:45,057
You know nothing about identity, but that's what I am sure we can talk about that some other time.