The philosophical method - logic and argument

Right. Well, I think we should get started. Welcome back, everyone. Nice to see you. That you haven't been frightened off. Today, I'm going to talk about something absolutely central to philosophy. And that's the methodology of philosophy, which is the methodology of logic and arguments. And just I think I said something last week about this, but it bears repeating. In science, people do experiments and experiments.

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. Well, knowledge, the true knowledge is not small, but the man in philosophy. We also do experiments, but the experience we do are not constrained by the laws of nature. And we don't do them in laboratories. They're not empirical experiments.

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. You can stay in the library. You don't have to get messed up with test tubes and things like that. You can just sit there and do it in your head. But in the same way as a scientist is constrained by the laws of nature. The philosopher is constrained by the laws of logic.

And that's why we can be fairly sure that when we have knowledge, when we think we've got something, we know we can be fairly sure we're right, especially if we corroborate what we think with other philosophers. Of course, third person corroboration is as important in philosophy as it is in science.

But what I'm going to be talking about staes is the arguments, that sort of logic that constrains our thought experiments. So that's what we're going to talk about, what logic is. It's not the sort of argument that your teenage children have. Okay. We all know that sort of argue. No, you didn't. Yes, I did. No, you didn't. Etc. It's nor is it the sort of argument that you laughed at on Monty Python.

You remember the arguments sketch? Probably. Instead, the argument is going to be a set of propositions which we call premises, which are put forward as reason to believe another proposition, which we call the conclusion. So here's an argument. I want to get to London by noon. I believe it's a necessary condition of getting to London by noon that I catch the 10 20 train. Therefore, give me the conclusion. I must catch the 10 20 train. So what you've got is you've got two propositions.

I want to get to London by noon and I believe it's a necessary condition to get into London by noon that I catch the 10 20. And together they combine. 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? And you all got it right. And that's because you are all rational animals. Actually, you do logic pretty well as well as I do.

What I can do that you can't do is tell you how you do logic, what it is that you're doing when you do logic. But as rational animals, you're doing logic all the time. You knew the answer to that reason you knew is because you do logic and logic is just the if you like,

the method by which you go from one set of thoughts to another thought. It's one way of acquiring knowledge, if you like. Okay, so that's that's what an argument is. Now there are different types of logic because there are different types of argument. So there are all sorts of different types of types as well. But one type of argument, for example, is dayon tech logic, the logic of moral discourse. So if I say to you, lying is wrong. Therefore, what conclusions are you going to give me?

Or I shouldn't lie or something. Yeah. Something to the effect. I should tell the truth. I shouldn't lie or whatever. 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. I shouldn't lie. But it's interesting because Kant says that's what's peculiar about de Ontake. Logic is you go straight from a statement to the effect that something's wrong. To the conclusion that you shouldn't do it.

And Kant thinks that's a very peculiar thing about morality, because for everything else, you would need a desire in there as well. So if you look again at the first argument, I want to get slammed by noon. It's a necessary condition of getting London to London. Da da da da da da. Therefore, I need to leave on the 10 20. If you took away the desire, would you have a good argument left? No, you just say it's a necessary condition of getting to London by noon, that I catch the 10 20.

Well, so what? You know, unless you want to get to London by noon. That doesn't entail anything, does it? You can do anything you like consistently with that. But once you've added that, you've got something that requires an action, haven't you? So it would be irrational to have that desire and that belief a not to believe. I must catch the 10 20. Wouldn't it? Okay. Have another way. That's true. But I have said the necessary condition here. So if I'd taken that, hold your rights.

But I think as I've put that in, anticipating that somebody might say something like. Sorry. You've only said, I believe. That's true. But if it's a matter of action, my belief would be sufficient to, wouldn't it? Because even if I was wrong about that, I would still think it's Russia. 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? OK, but if you look at this one. Do you need a desire in there?

Kant would say no. Lying is wrong. Therefore, I mustn't lie. Do you need I? I don't want to do the wrong thing or I do want to do the right thing. Kant would say no because he'd say, if you think that you need to adds and I want to do right. You just don't understand what it is to do something wrong. OK. Think about that for a second. If you if you entertain possibly that, you need to add. I want to do what's right. You were implying that you might not want to do what's right.

And Kant would think that that would show that you didn't actually understand what right means. You with me? No, but and Kant would say they don't understand what's right. If you think I understand that 10 year olds go around nicking sweets from from shops because they understand you of right at the moment is is if anyone finds out, 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. How old fashioned hoops is legal.

That isn't it. Anyway, whatever it is, it isn't. Okay. Well at least I haven't said anything illegal, but immoral maybe. So if you're thinking that for something to be wrong is if I get caught, I'll be punished. You've got that. You haven't yet got the concept of right and wrong. Have you? What you've got is a prudential concept that may cause you to act in some of the same ways. But I bet if I leave my purse here when I go out, as I may well do.

You wouldn't not pinch hit because you might be fine. Found out. No. You would have other reasons for not pinching it, mainly because you'd think it was wrong. Probably wouldn't occur to you, but you'd also, if it did occur to you, you'd think it's wrong. And so there are different ways. 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.

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. 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. Isn't there something wrong with that? Isn't that a contradiction? Thank you. Yeah. That's different. We're saying if you believe that lying is wrong, then you're going to think you shouldn't lie.

I mean, if you don't think lying is wrong, then there's no reason, not lies. But if you do think lying is wrong, could you also could you consistently believe. Let's. All right. Let's say if you believe this lie is wrong. Could you consistently believe that there's no reason for you not to lie? I have to find lying and saying you think this lie is wrong. So it's not a white lie. Would you say that? Yes. Not yet.

But a white lie. We call them white lies because we don't really think they're wrong, do we? Right. Right. Then then let's let's not get too far away from the topic. If we believe that lying is wrong or that this particular lie is wrong, even if it's a white lie or not. Doesn't matter. Could you consistently think. Never mind. That doesn't mean I shouldn't do it. But he came up last time with torture.

Torture is wrong. Right. Yeah. OK. I'm going to leave this because maybe De Ontake logic was a bad idea. OK. Carrots would say that if you believe that, you have got to think I shouldn't lie. If you think that lying is wrong, you might not. But if you do, then you're going to think you shouldn't lie because you cannot think. Lying is wrong. But there is no reason for you not to lie. Because for some things to be wrong is itself a reason for you not to do.

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

So that's what's down here. We've got a set of propositions or one proposition. A premise put forward is reason to believe another. Here's another type of argument. This is Moodle logic and I'm sorry, it's a bad example, but I'm lousy at thinking of examples. It's not possible for Vixen's to be male. That's because Vixen's are defined to be female. Therefore, that Viksten is not male.

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? 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. So you're recognising that something's not possible. It will cause you to believe immediately that nor is it Hatchell because it couldn't be not possible and actual. So that's Moodle logic, the logic and modality, the logic of necessity.

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. Okay. That means, as we all know, that it's not gold, doesn't it? How do you know that? Well, you'll just have to believe me, take it on authority. But that's because, you know, the logic of conditionals. And if I were to write the truth table up here for conditionals, a truth table gives you the truth of a conditional in every possible world.

You would see that if it's gold, I'm a Dutchman has to be true. And therefore, it has to be false that. It's gold. So I'm not going to go into that. I'm just going to tell you, you know what that means because you know the logic of conditionals, because you're a rational animal. What you don't know is what I know, which is how to draw the truth tables and how to show that that means it's not gold. Okay. Finally baffled, are you? Yes. All the different worlds.

Well, some people say that a different possible world is nothing more than a different situation. There's a philosopher called Krip Key, very famous philosopher, still alive. Or if he isn't, he's only just. It was today or yesterday, and I'm very sorry about it. He believes that you in order to explain the truth of conditionals, like, okay, if Germany had won the war, we would be speaking German. Now, some of you may think that's true and some of you may think it's false.

We could argue about this. We could give reasons for different sides. But I'll tell you what doesn't make it true, namely that the Germans won the war and we are speaking German because they didn't. That's a counterfactual conditional. And so we think of conditionals, even counterfactual conditionals, as true and false all the time. And some logicians believe that in order to explain the truth of counterfactual conditionals, you've got to postulate other possible worlds.

Now, of course, there are other reasons in physics for postulating possible worlds in mathematics. There are reasons for postulating possible worlds. And what is a possible world? Well, Chriqui thinks it is literally another place, just like all worlds, like our universe, rather than like our earth. But there's no causal interaction between one world and another. But you can say, okay, is there a possible world in which Marianne's wearing jeans?

Tell me the answer, yes. Is that a possible world in which Marianne is male issue for you? Does anyone think that might be nine, Marianne? No, no, no, no. We're asking a question here. Could Matt. Could I have been male? Could I have been male? In other words, if I. If I had to. No one would. No. An X and Y chromosome instead of two X's. Would I still have been Marianne? Would I still exist? OK. Lots of people think no. It's an open question. Some people think no on that. Some people think yes.

But notice, we do think there's a truth value to it. We can ask that question and we can argue about the answer. And it's possible that in order to do that, we've got to postulate the existence of possible worlds of other worlds that we know about by reason. But not by perception. Do you see what I mean? We can see this world. We can touch it. We can hear it there. You heard part of it. But you can't see or touch a possible world. But you know, they're there because you argue about conditionals.

Isn't there a world in which I'm male? Well, some of you think, yes, some of you think no. And the more you look at the logic, the more you might be able to come up with. You're absolutely right. It is no the answer or you're absolutely right. It is. Yes. Or whatever. That's what philosophers are doing, is there? Sometimes I talk about it as spinning the possible worlds in order to find out what the limits of possibility are.

Because if you think of what a scientist is doing, they're looking to see what the limits of actuality are. What is the case in this world? Whereas what philosophers are looking for is what could be the case. Okay. Not just in this world, but in any world. Could there be could time travel be possible, for example? Mean it looks as if time travel isn't possible? Well, we know time travel isn't possible at the moment.

Could it be? Is there a world in which it's possible? And if so, could this be a world in which it is? So we're expanding the worlds and asking, okay. We know there are possible worlds. We know there isn't a world in which there are square circles, don't we? It's a world in which circles of square. Could could there be could a circle be square? Exactly. It's the concept, isn't it? If something is a circle, it could not be a square.

End of story. So we know that there is no possible world in which circles are square. That's not a possible world. Whereas the world in which Marianne is male, maybe that is a possible world. The world in which Marianne's wearing jeans is definitely a possible world. So we're trying to limit the possibilities. Which possible worlds are there and which aren't there. Yes. But what we're asking is, is Marianne necessarily female or is it just a contingent fact that I'm female in the same way?

It's a contingent fact that I'm wearing a dress. I mean, I might have put jeans on this morning. Might I have been male? OK, we know a Viksund cannot be female because in the same way we know that a bachelor can't be married because it's part of the definition of being a bachelor, that you're part of a definition of being vixen. Is it part of the definition of Marijan of me, the time female? Well, some people do think so, but others think not. You do. You thought not.

So there are there are different views on this one. And I could give you other ones that are where we're not sure. What's important is there are some cases where it's definite there is such a world, some cases where it's definite that there isn't such a world. And some cases that we don't know about. And the job of a philosopher is to find out about those. Okay, so that's modal logic. And I looked at the logic of conditionals, but there are two main generic forms of arguments.

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

So as moral agents, you understand something about day on tick logic, even if you've never heard about it before. You also understand something of the logic of modality and the logic of conditionals. But here are two very broad sorts of argument, deductive arguments, an inductive arguments. Now I want you to ignore the ones under the dotted lines at the moment and just look at the ones on the top. Now, I know you're all reading the ones underneath the dotted line at the moment. Stop it.

Okay, let's look at this one. If it snows, the mail would be late. It is snowing. Therefore, the mail will be late. The nice thing about deductive arguments is that they give us certainty. They didn't give us unconditional certainty. Sadly, if the premises of the argument are true, then the conclusion must be true. Okay, so have a look at these premises there and tell me if that's a deductively valid argument. If it snows, the mail will be late. It is snowing. Therefore, the mail will be date.

Could it be that these premises are true? And the conclusion false? 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? 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. Have I? Because then the premises could be false. Without that.

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. And what I hope I've got is that if these premises are true, the conclusion must be true. There is absolutely no logical possibility of those premises being true and that conclusion being false. Is that right? Yeah. Okay, that's great.

So we've got certainty in a deductive argument, conditionally upon the truth of the premises and the validity of the argument. Now, here's an invalid deductive argument. If it snows, the mail will be late. The mail is late. Therefore, it's snowing. OK. Now, there's something wrong with that argument, isn't there? What's wrong with it? Good. Give me another reason. Yes, but can you tell me. Give me a reason. In which puncher. Good. You can't hear people looking at you. Oh, okay. I'm good.

I've got to say. Okay, well, I'll repeat what was said there. If you've got an an invalid argument, 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, because if you're like me, your lousy examples. If it snows, the mail will be late. The mail is late. Therefore, it's snowing. You should be able to find a counterexample. In other words, a situation where the premises are true and the conclusions false.

OK, so let's say the mailman had a puncture. OK? If it snows, the mail will be late. The mail is late. Therefore, it's Snowbell. No, you know, it's actually the mailman's had a puncture instead or he got up drunk or, you know, whatever happens there. All sorts of reasons why the mail might be late. In addition to it's snowing.

So we can't go from the comfort, from the affirmation of the antecedent, to the affirmation of the conclusion, whereas we can go from this one to that conclusion presupposes some causal relationship between Snowy, which goes in one direction, whereas the second one causations does not. Well, it doesn't go in the right direction. Exactly. But the fact is, if you have any argument of that form, you will have a valid argument.

Whereas if you have any argument of that form, you won't. Let's. I'll show you what I mean by that. Hang on. I'll have to find one I haven't written on. And then I might be able to find where I am. So you'll have to wait by. If P then Q p therefore. Q Okay. Can you see that that's a formalisation of this argument. What does P stand for here? Sorry, not the premise. No, not at all. Sorry if P then Q formalises the whole premise, doesn't it? What does P stand for? Now you're all too clever.

You're all too clever. No. Have a look at that premise and tell me what I've taken out and replaced with a sentence letter. Thank you. It is snowing or it snows. Yes. So, Piers, it snows. So if it snows, then the mail will be late. Exactly. So you say you've got it now. You didn't know you could all do logic, therefore. Sorry, P. So this says it is snowing. Notice I should probably put it. If it is snowing then the mail will be late and I didn't. But ok. It is snowing.

Therefore the mail will be late. Thank you. OK then we've got if p then Q q therefore p and noticed that whereas every all arguments that form it doesn't matter what you put in there that would be valid and it doesn't matter what you put in here, it wouldn't be valid would it. So if we, if we make P let's change the interpretation. So if I do this, if you are a student doing this, you would have to and you gave me these arguments.

So I'd say, where's your interpretation? And if you hadn't provided one, you would lose marks. Okay, so let's give an interpretation, Piers. It is snowing. And Q is the male. We'll be late. Who's going to try it actually try? Now try and give me another interpretation of those sentence letters. OK, so forget about snow in the mail. Give another interpretation. Think about Marianne lecturing or Marianne wedding dresses or it's being Monday all.

Do you know what you're doing? You're all looking very. Okay. You're just looking serious. Good. It's serious stuff. Shush. Don't yell out. You're all trying it. I'll tell you what, when you've got one. Put your hand up. And just keep it up till I. OK. So you're looking for another sentence for P. And another sentence for Q, which gives you a an argument. OK, gentlemen, back there. What have you got? Yeah. Well, you don't need the F because the interpretation is only four P, so P is.

No, not if just Obama wins. Do you see what I mean? Because if is a logical word here. Yes. That's right. Okay. Q Is the Democrats. Democrats will be pleased. So if we pull that in here, we've got. If Obama wins, then the Democrats will be pleased. Obama actually got a problem here, haven't we? Because notice we've got 10 said, which immediately causes a problem. But let's forget that for a minute, shall I say. Obama wins. Therefore, the Democrats will be pleased. Okay, here we go.

If Obama wins, then the Democrats will be pleased. The Democrats are pleased. Therefore, Obama won. I mean, there must be something else that would please them, wouldn't it? Okay. How about someone else? Let's have just one more. Okay. You want to have a go? Hang on, what's P. Milkman arrives. Okay. And queue is my dog barks. Okay, so if the milk that arrives in the morning, then the dog pops the milk there arrived, therefore the dog barks.

If the milkman arrives, then the dog barks. The dog barks. Therefore, the milkman has arrived. You can see what's going on, can't you? Any argument 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. So it's a sufficient condition of the male being late that the snow, that it's snowing, but it's not a necessary condition.

And this fallacious argument here suggests it is a necessary condition. And that's why it's never gonna work. Okay. Well, you see, you're all doing logic and that's what you're all doing. Formal logic immediately. Fantastic. Okay. So that's deduction. And the nice thing about deduction is it gives you certainty if the premises are true. The conclusion must be true. But of course, that that's quite a big if, isn't it?

If the premises are true, the conclusion must be true. Often we may not know whether the premises are true or not. 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? Because the validity will preserve the truth of the conclusions. 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.

And if we can show by empirical means or whatever that the premise that the conclusion is false, then what do we know? Good. One of the premises is false. Exactly. So we learn a lot from a valid argument that has a false conclusion. We learn that one of the premises must be false. We say, yes, you can at least one of the premises because it needn't be more than one, just one false premises quite sufficient to to show that the conclusion might be false.

Not not is false, but might be false. Okay, good. Fantastic. In fact, shame about the day Ontake logic, wasn't it? We might have to go back to that as you're proving yourself to be so good at logic. Okay. Let's have a look at induction now. Induction is different. An inductive argument is don't give a certainty. What they give us is more or less probability. So probability is a matter of degree in a way that validity isn't.

Validity is an either all matter, either an argument is valid or it isn't. Whereas induction gives this probability and that's a matter of degree. 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. Therefore, the sun will rise again. I should have put tomorrow in that. But tomorrow. Okay. That's a pretty strong inductive argument, isn't it? In fact, we're all pretty well relying on it.

Anyone who's got a lunch appointment tomorrow, for example, is relying on a dentist's appointment or anything else. But of course, it's not. It doesn't give us certainty, does it? Because we might be wrong, tomorrow might be the day when the laws of nature are just going to change, the fact that it's always been like that in the past doesn't mean that it's always going to be like that in the future.

The fact that the laws of nature, of always being the same in the past doesn't mean they're always going to be the same in the future. It was Hume who pointed out that, as a matter of fact, I mean, it just could be that the. Hi, this strong your deductive argument is it's not going to give you certainty. Russell talked about the chicken who every day and the whole of his life. The farmer had come out and given him food and the chicken.

Here comes the farmer. And he thought, Oh, good. Him food's coming. Course, he got his neck wrong. Now, how do we know that we're not in that position with respect to the sun rising tomorrow? And what Hume said is we don't. There is nothing you can do to show that there's anything more than probability here. Because that argument rests on the idea that nature is uniform. Why do you believe that nature is uniform?

In other words, that the future will be like the past because the future always has been like the past, hasn't it? Well, that's no argument, because that is itself an inductive argument, isn't it? 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. No. It's certainly true that that's in induction. You're going from something observed or something that has happened to your REM.

What's the word? Mind's gone blank. No. When you project into the future, extrapolate. Whoever said as traveller. That's what I meant. You're extrapolating into the future, aren't you? So, for example, here's another inductive argument. I think you'll agree it's not a terribly strong one. Every time you've seen me, I've been wearing earrings. That's probably true. Is it? Especially if you've only seen me last week and this week. And next time you see me, I'll be wearing earrings.

Now, that is an inductive argument, isn't it? There's some probability there. But I think you'd agree it's not as strong as that one, because next time you see me, it might be as I'm going out to get the paper in the morning before I even put clothes on. Dressing gown on something. I don't wear earrings with my dressing gown. And anyway, we know too much about human beings, too. To assume that that's a good inductive argument.

So in deduction, you get certainty and it doesn't need to be about the past or the future. It can be about anything at all with induction. You are extrapolating from not the story of the past. You could easily extrapolate from the present to something else. So all the chairs in this lecture room are blue. Therefore, the chairs in the next lecture room are going to be blue. Now, there's no time element in that, is there? There's just a you know. Is that a good inductive argument?

Well, it's sort of. No, it's not very good, is it? Certainly, no, it's not as good as that one. OK. So these are two types of argument. And when you've got De Ontake logic or conditional, logical, modal, logical, whatever, you'll get arguments of this kind. For example, the argument I was trying to convince you of lying is wrong. Therefore, you shouldn't lie. Kant believe that's a deductive argument.

Okay. Because the premise entails the conclusion. If the premise is true, the conclusion can't be false. Now, some people disagree with Kant, in which case that wouldn't be a deductive argument, wouldn't obviously be a an inductive one either, instantly. There are other types of argument. Those are. This is where I'm told that one, haven't we? And we've had that one of those arguments by analogy. Anyone tell me what one of those is? Give me a very famous one, perhaps to do with watches.

Anyone read Dawkins book The God Delusion? He talks about a very famous argument from an analogy. Can anyone tell me what it is? The Blind Watchmaker. Exactly. So. So the universe is like a watch. A watch has a maker. Therefore, the universe has a maker. OK. Dawkins thinks that's an appalling argument and he's probably right. 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. And so if A you've got A is P okay.

Has this property P, A is like B or B is like A, therefore B has P as well. Okay, so A. has this property B is like A therefore B has this property too. And of course there the, the premise of similarity is absolutely crucial because if you haven't got the similarity there then you can't, you haven't got the conclusion either. And of course there are arguments from causation. If A causes B, then you don't get an A without a B.

Okay. And the reason that that's a valid argument is that you assume that causation brings correlation. If A 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. Okay. Right. Well, let's let's move on from there. Those are the types of arguments and what's important about any argument, whatever sort of arguments it is, is that if you want to evaluate it, you've got to ask two questions.

And the question is, you've got to ask, are these all the premises true? And is the argument valid? 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? OK. That's what you're asking. If the argument is deductive and if it's inductive, you're asking, is it the case that the premises provide good reason to believe the conclusion? So how strong a reason to the premises providers to believe the conclusion?

So those are the the two questions you've got to ask. It doesn't matter what the argument is, if you're reading Descartes or you're reading the leader in today's newspaper. What you've got to do is try and firstly analyse the argument. In other words, set it out. Logic, books, style, identify. The first thing you go for is a conclusion. Identify what it is this person is arguing for. Okay. That's the conclusion. And then find out what he's using as his reasons.

And once you've identified those, you've got the premises. So you should be able to set it out. Premise one premise to conclusion. And then you ask, okay, what do I think of these premises? Are they good premises? What do I think of this argument? Is is it valid? In other words, if the premises were true, would the conclusion have to be true or do the premises provide me with at least good reason to believe the conclusion?

And if either of the answers to the question, too, I'm sorry, the court answer to either of these questions is no, then you don't have a good argument.

If the answer to both those questions is yes, you might have a good argument. It's not sufficient. Let me give you an argument that satisfies both of these. Get lost again. OK. Now is the promise. OK, here's the premise. Here's the conclusion. OK. It's the premise of this argument. True. Okay. It says whales are mammals. Therefore, whales are mammals. Okay. The premise is true. Okay. Is there any possible situation in which the premise is true and the conclusion false?

There isn't. Is that how could there be? The conclusion is the same as the premise. Okay, that is a circular argument. Circular circular arguments are valid. How could they not be. If the premise is amongst its sorry, if the conclusion is amongst the premises, then then there can't be any situation in which the premises are true and the conclusion false. So that's a valid argument. But what's wrong with that is it's circular. You're not going to learn anything from that argument.

So the fact that you answer yes to both those questions isn't sufficient for it being a good argument, but it's certainly necessary. And that as a philosopher, those are the two questions that. Well, actually, as a philosopher. That's the one that bothers you. It's it's often scientists who are interested in that one. So, for example, every swane I've ever seen has been white. Therefore, all swans are white. Okay. Well, it may be true that every swan I've ever seen has been white.

I need to find out now whether that's a sufficient reason for thinking that the swan in the next room is white. I mean, if it's true that all swans White Swan in the next room will be white, won't it? But my job is to go into the next room and see if it's white. And if it isn't, what do I know? Well, either this isn't a swan, okay. Or that it's not the case that all swans white and maybe we would say it isn't a swan.

I mean, you must have heard when Mrs Thatcher in people saying she's the best man in the cabinet. Okay, here's the argument. All women are passive. Mrs Thatcher is a woman. Therefore, Mrs Thatcher is passive. That is the argument. Well, Mrs Thatcher clearly isn't passive. Therefore, either she's not a woman or not. All women are passive, but you know them. Do you see how it works here? Often depends on logic. Precisely because it tells us what we ought to think and then somehow confounds us.

Mm hmm. All the same. Yeah, well. Therefore, actually just marks the conclusion of an argument. It says I am. The thing about an argument is its its premises giving reasons for a conclusion. And we can give any premises as reasons for any conclusions. So if I say Melbourne is in Australia, the sea is salt. Therefore, Paris is the capital of France. Okay. Now that sounds like a really bad argument, doesn't it? But I could tell you a story about how here we are.

We're all not only we all terribly ignorant, really very badly ignorance. And we have been told that these two sentences are such that if they are true, this third sentence is true. Okay. The first sentence is the sea is salt. The second sentence is Melbourne's in Australia. So I say, OK, you go off and find out where the sea is salt. OK. You go off and find out where the Melbourne is in Australia.

So you scurry and you find the nearest encyclopaedia or dictionaries on you come back and say the sea is salt. You come back and say, Melbourne's in Australia. And I say, therefore, Paris is the capital of France. 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. Isn't it? By providing a context, I could make those apparently completely irrelevant sentences an argument.

So therefore just stands for a conclusion to say, I am saying that that is reason to believe that. Now, notice something else. If I had lots of other sentences in here. I'm going to change the fact that this argument's valid. Well, let's put it, it's not the case that mammals, whales are mammals. It's not the case. Not whales. All mammals. Whales are amongst them mammals. Therefore, whales are mammals. Now, is there any situation where both those premises are true and that conclusions false?

Actually, that's a. They can't both be true. Can they? So is this argument valid? Yes, it is, because there's no possible situation in which the premises are true. So how can there be a possible situation in which the premises are true and the conclusion false? And I'm going to do a truth table here, which is probably asking for trouble. But let's let's do it, shall we? Let's. Okay. This is using the notion of possible worlds to explain something.

OK, I've got it. Thank you. P therefore. Q No, I don't want that. Hold on. Sorry. I'm changing my mind. Let's try this, OK?

Each of these each sentence can be either true or false. Can't it? OK. Most. 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. It could either be true or it can be false if it's contingence sentence. So this truth table represents every possible world with respect to the combination of truth values here. OK. So this is a world in which P is true and Q is true. Okay. This is the world in which. Tell me. Good.

Okay. This is the world in which u.s. That's right. And this is the world in which they're both false. Absolutely. That you do. You're really doing well here. And they talked and undergraduates can't do that. And it's because they haven't separated the possible worlds because each these possible worlds is quite separate from me, from the other. 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?

Okay. And in the world where P is true here, the premise is going to be true. Okay. And in the world by appears false. And false again. Exactly, so. OK. And that's going to be the same here because we've got exactly the same letter here. OK. Now, do we know whether this argument is valid? We'll look at a structure in turn. Is this a world in which the premise is true and the conclusions false? No. Okay, so that's OK. It's valid.

There is this world where the premise is true and the conclusion false. Hang on. This is number two, the second world. Is this a world where the premise is true and the conclusion false? No, it isn't. That's okay. Is this a world where the premise is true and the conclusion false? No. And is this world where the premise is true and the conclusion false? No, I don't. Who said yes? Look, is this a world where the premise is true? And the conclusion false? No.

So there's no possible world. Does each of these is a possible world and these are all possible worlds. And there isn't one where the premise is true and the conclusion false is the. This is a circular argument, so we know that this argument is valid. Now I'm going to add not pee in here, session's about it queue at all. I've just complicated things by adding you ignore it. That's not pee. OK, what's the truth? Value here is true. So in this world, not P is false.

Good. So that's not that is not OK in this world. P is true. So not P is false. Again in this world P is false. So not P is true. You really do well. Okay. And in this world P is false. So not P is true. Okay. So now we're looking at two premises and let's see if we can find a world in which the premises are true and the conclusion false. Okay, so this world, the world number one, we've got two premises. Is this a world where the premises are both true? And the conclusion false?

No, because the premise is not both true. This one's false, isn't it? So, okay, this is valid. That's all right. Here's one. OK. Is this a world where the premises are both true and the conclusion false? No, it isn't, is it OK? Is this a world where the premises are both true and the conclusion false? No. And is this a world in which the premises both true and conditional? So is the argument valid? Yes, good, really good. I think the thing is you can at any premiss to a circular argument.

And it remains valid. So it may be that a circular argument when I look at that, therefore, you think this isn't an argument. So obviously not valid. 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. But in the media, blind you with science, hide the premise. That is the conclusion in amongst lots of other premises. So you wouldn't see you.

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? You as a rational animal would recognise the validity. What you wouldn't recognise is that the argument is valid because it's circular. Are you with me? So circular arguments are jolly useful if you're trying to confuse someone. And the reason they're useful is because you, as rational animals, are validity detectors.

That's what you do. You know, if we're in the pub and I'm giving you an argument, you're sitting there thinking is such a good argument. Is she right? It's. You're asking yourself whether my argument is valid. You're setting yourself to validity detection node. Chris. If they if somebody. Mm hmm. Yeah. Yeah, yeah, yeah. You could use it. The thing about that is it's self-referential because the liar. If if I say I'm telling the truth and you don't know whether I'm lying or a liar or not.

You don't know whether that sentence is true. But, yes, you could use truth tables for that. Yeah, yeah. Yeah. Two different answers. Still give you. I'm just a bit confused, my first one was that one. So you could keep that you could you could use that. 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? First you say. Well, a mammals, therefore, whales are not mammals. Yeah. Okay.

Yeah. If you look at it, that that's truth table. I've just done exactly that argument. If we provide the interpretation that says P is whales are mammals. Do you see, because when you look at that, Piers, whales are mammals, not pee. Sorry. This is Piers, whales, mammals. This says it's not the case. The whales are mammals and this is whales are mammals. So that's the truth table for that argument. Yes. And I do that, and I then didn't do it because I realised it wasn't circular.

But if I do the truth table for that one, what's going to happen? Does anyone recognise this argument? If P, then Q, p, therefore Q. 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. 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.

What's this argument? You've seen it today already. Or rather, this is a formalisation of an argument you've seen today. So thank you. Exactly. So if it's snowing in, the mail will be late. It is snowing. Therefore, the mail will be late. And if I write out the truth table and you'll just have to take these four. Uh. Whoops. Yes, that's right. Uh. OK, let's leave there for. Is this a world in which the premises are all true and the conclusion false?

No. OK. So that's right. Is this a will that the premises are all true and the conclusion false? No. Is this one where the premises are all true and the conclusion false? Is this one? No. OK. So that argument is valid. But if I change this to a Q. Sorry, I'll get another pen, because it's a. Uh. Okay. Is this a world where the premises are all true? And the conclusion false? Okay. Is this a well with the premises rolled through and the conclusion false? No.

Is this a world where the premises Royal Troon, the conclusion false? It is, isn't it? Okay. That is quite sufficient to show that this argument, any argument of that form is invalid, because here's a world just here's a possible world in which the premises are true and the conclusion falls and all the rest becomes irrelevant because you only need one counterexample. And we can even say what the counterexample is because that argument is invalid in the world where P is false.

And Q is true. So if we put in the interpretation we had before, what was P? It's snowing and Q is the male is late. So in the world where P is false. In other words, it's not snowing, but the male is late because of that puncture. That's the counterexample to this argument. Do you see. Do you see how useful logic is? It's fantastic. And you say you're doing it now. Okay. You've got a fair amount of help here, but it wouldn't take me long to show you how to do this yourself.

The really difficult bit is the interpretation from English into formal logic. That's that's the really difficult bit. But this bit dead simple once you know how to do it. And this is formal logic. Okay. Right. Actually, that takes me quite neatly onto the next slide, because I wanted to point out that there are two sorts of logic. So far we've been looking at formal logic. But I also want say something about philosophical logic, because that's a bit different.

But firstly, just to say something a bit more about formal logic. You've got to distinguish film from contents, the form of the argument from the content of the argument. So this is the form of the argument up here. The content is supplied by the interpretation. So you notice that you give this a completely different interpretation. But the form would still be the same. And that's actually very important because what that tells us is that logic is topic neutral.

Once you know how to do logic, it doesn't matter what subject you're talking about. The logic will work for any subject at all. So let's look at this one. Let's look at here are two arguments. Sorry, I'll move this over. All men are mortal. Socrates is a man. Therefore, Socrates is mortal. All actions that produce the greatest happiness, the greatest number are right. That action produces the greatest happiness of the greatest number.

Therefore, that action was right. Now, can you see that these two arguments, completely different subject matter only. This is about mortality. And Socrates. And that's about ethics. The greatest happiness is the greatest number, etc. But they've got the same form. And now I want you to practise your logic by telling me what the form of this argument is. Okay. Work it out for yourself and then put your hands up when you've got it without yelling it out.

Work out what the form of that argument is. Remember that there are logical words and there are English words and it's the logical words you want to leave in. And the English word. Well, they're all English words, but these are logical words in provide an interpretation for the non logical words. Don't worry if you find this difficult. This is difficult stuff. Put up your hands if you think you've got it.

Let me give you a tip that all is a word that you live in and is is a word that you'll leave in. Put up your hand if you think you've got knots of. Good. We're getting that. Symbolic logic because of the form is captured in symbols. Good. Okay. Good food, you want to have a go? Okay. Oh, no. Oh, surely somebody could invent something better than this. Do you think what a crayon. Yes. Yes. Would work, wouldn't it. All. All. A is B o, all A's, r, b.

Can I. Can I change it? Yeah. Okay. All A's are B and C is A therefore give the girl a gold star. Fantastic. You said all A's r b. S isn't a therefore s is a B. A lot of us out there. Well, let's provide the interpretation for each of these arguments. Okay. So the interpretation says, what does a mean. What does he mean. And what does s mean. And we've got two arguments. So we need to provide two interpretations. This is a here.

If you do decide if we do, the first argument first acts as a man is what it is, actually I'll put that in because these are projects is a man is a predicate. So you need to have a place holder. X is a man. B is. X is mortal. Yep. An s. Socrates. Well done. OK. The interpretation here A is X is a bit long winded, this one. A is an action, an action that produces the greater toughness. What's the gross number? And B is is right. X is right. Well done. And X is.

Well done, well done, that action, because that action is a designator, isn't it? That action, it picks out one particular thing, in this case, an action in the same way that Socrates is a designator. It picks out one particular thing, Socrates. So we're saying the first one. Anything that's a man is mortal. So anything that has this property also has that property. Socrates has this property, the first one. Therefore, Socrates has the other one.

OK. And we're saying exactly the same thing in that one, except we're talking about something completely different. We're talking about actions and whether they produce the great stuff in disgrace number or not. So do you see why logic is topic neutral? Once you've learnt logic, it doesn't matter what you're thinking about. You can think clearly about it. And this is one of the joys of being a philosopher as far as I'm concerned, because it means you can put your nose in anywhere.

It really doesn't matter what you're talking about. There's a philosophy, a mind, a philosophy, a biology, a philosophy of chairs. Probably somebody was trying to persuade me to run a weekend school on the philosophy of accountancy yesterday. If anyone would like to do that, they can share it.

No, actually, I'm sure that there is a philosophy of accountancy and actually, if there are, I'm sure, philosophical issues in there. There is a philosophy of everything because of this logic is the methodology of philosophy, and it can be applied to any subject at all. And that's because logic is topic neutral. Okay, let's move on. So what we do in formal logic, as you've seen, is we strip an argument of its content.

We're not interested in the content. We reveal its form and then we can test mechanically for validity. And you've seen me test mechanically for validity here. That's one way of testing mechanically for validity. Okay. Now, the trouble with that is what happens if I add another premise here. So I have an AR as well. It hurts to see it's going to get unwieldy, isn't it?

And just for fun, I always get undergraduates to do one with four or five premises in so that their truth table goes on and on and on. And it's very, very boring to work it out. And then I show them that they can do this instead. I could find a. OK. Now, you'll just have to believe me that that arrow means if then. OK, so that that formula there means if P then Q And that little sign there means it is not the case.

So that means not. Q And what I've done here, you remember the argument we had if P then cupie therefore. Q I've got the premise there, the first premise there. The second premise there. And I've negated the conclusion. Okay. Because the argument was if P 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, a situation in which the premises are both true and the conclusions false.

Let's see if I can find an argument like that or a situation like that. And I then apply completely mechanical rules that I could again teach you in a in an hour or so to get this. OK. That's the conditions under which that arch. That is true of that all true. That is true. Are there two situations? It's true. Just in case. Not P or Q and you can't. There is no possible worlds with both Q and not Q in it. So that's not a possible world. There is no possible world with not pee and pee in it.

So that's not a possible world. There is no possible world in which the set consisting of the premises and the negation of the conclusion are true together. Okay. Now you won't have understood that, but I hope you can see that I know what I'm talking about and that it would be very easy to teach you how to do this so that all you have to do is any argument at all if you can translate it into symbols. And that's the biggest if if you can introduce it translated into symbols.

There is a set of rules such that you can apply these rules and test it, just as I have done and say quite categorically, this is a situation in which, sorry, this is an argument is valid. And let's do the invalid one. Just see again how it works. The invalid one is if P then Q Q therefore P. So I'm negating P because that's the conclusion. And I want to see if there's a possible world in which these are all true together that sets consisting of the premises plus the negation of the conclusion.

Well that's true. Just in case not P or Q again. But we don't have any contradictions here do we. See we've got not p, not P, q there's one possible world in which that set are all true. The sentences in that set are all true and we've got Q not P. Q So that's another world in which the sets consisting of the premises plus the negation of the conclusion are all true. So either of these, any situation in which Q are not P is true is a counterexample to that argument.

And you go to your interpretation now, you find out what cures you find out what not P is. And you know what your counterexample is magic, isn't it? Well, yeah, p it is snowing. Q The male is linked. 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. You have no idea why I've represented the truth. Conditions of that like that. And I would have to tell you that.

And I'd also given that that's actually quite difficult to understand, I have to convince you that that is the case. But I would be able to do it. I promise you. And once I'd done it, you would then be able to take any argument and show whether or not it's valid or invalid. And one, if if you showed it was invalid, you'd also be able to give me the counterexample because you would know which world is such that the premises are both true and the conclusion false is nice.

It wasn't the case. He therefore paid. I understanding that as the therefore. You said P, therefore, Q Yeah. That's not a therefore it's it's an implication, not an entailment. That's saying if P, then Q not P, therefore. Q. I mean, don't worry too much about that. That would be. OK. So what I was asking was just would you be using. I'm just trying to get an idea. Yeah. Might use that kind of diagram. Is it because you're actually trying to challenge somebody and say, well, in fact.

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. They'd be saying if P, then Q and P, then Q. So if these are true, then Q is true. So if it's if it's true that if it's snowing, the mayor will be late. And it's true that it's snowing. Then it must be the case of the male is late. And I would do this sort of diagram and I'd say, you know, you're right.

That's absolutely right. But then if somebody tried the other argument. So as I'm reading Descartes, for example, and I think, okay, he what he's saying is that it's possible that all our beliefs about the external world are false. Okay. And one of his premises is this one of his premises is that one of his premises? Is this. Is it true that that conclusion really follows from those premises? So I would do the truth table. And I would say, no, it isn't true or yes, it is true.

And that would enable or you could look at the reader and the leader in tonight's paper and say, okay, here's the argument, premise one premise to premise three. 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.

Calculus would probably be needed. This is the propositional calculus, but you'd need a slightly more sophisticated one predicate calculus and you'd be able to determine whether the argument is a good one or not. Because what you're determining is that the argument is a good one or not. That still doesn't tell you whether the conclusion is true, does it? Why not? Exactly. It might be the fact that an argument is valid isn't telling you that the premises are true.

So as a philosopher, what you're interested in is the validity of the argument. You're also interested in the truth of the premises. If it's a 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. You know, we don't go around getting our hands dirty ideas. They do say, no, it doesn't work like that because firstly, you've got to be able to formalise an argument.

And there there are huge problems. If this is the class of oral arguments in the world. OK, all arguments here. You can formalise. I mean, I'm making this up. But let's say you can formalise that many in the predicate calculus. You can formalise that many in the in day Ontake logic. You can formalise that many in modal logic. This lot. You can't formalise at all. And therefore, you can't apply the rules. Now, what we hope as formal logicians is that we will learn how to formalise those.

And for example, the predicate calculus was developed only a couple of hundred years ago. Aristotle developed syllogistic logic. But it took Frager to develop predicate logic. And that was a huge leap forward. Modal logic has only been developed. Well, it's still being developed. The logic of probability. Ditto dialectic logic. We're still working on it. So, you know, you're right at the cutting edge here.

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. But you know that. I mean. So, no, it's not the case. And of course, also the real skill is in translating the argument.

And you'd know that if I if I made you do some, because it's really, really difficult to translate from English into a symbolic language. And there are lots of things left out. And it's very frustratingly inaccurate. And so there are there are real problems. But but we all do it all the time. Believe me, I sit in my study doing tables like that. It's much more interesting than you might think. I there are cases there may be more than one promise.

Yeah. Well, I mean, there are more there's more than one premise in the arguments I've been doing, of course. That's one premise. That's another premise. And of course, there could be I mean, there could be 10 premises here. I could still apply these rules. No, no. You 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. Yes. So the number of premises that's true is not very relevant.

It's than if there's at least one that's false. He has a valid argument with a false conclusion. I think I wrote it down. I know I've written it here. If it's Tuesday, then Marianne isn't lecturing. It is Tuesday, therefore, Marianne isn't lecturing. Okay. Well, that's a valid argument, isn't it? You want to hear it again? If it's Tuesday, then Marianne isn't lecturing. It is Tuesday.

Therefore, Marianne isn't lecturing. Now, if those premises were true, the conclusion would be true, wouldn't it? Okay. But the premises aren't true, are they? Neither is the conclusion. So you can have a valid argument with a false conclusion. If you know that the conclusion is false, of course you can go back and say one of the premises must be false. But there are often situations where we actually don't know whether the conclusion is true or false.

And therefore, we don't know whether the premises are true or false. We know this is logic is in some ways the servant of science in other ways. Of course, science is the servant of logic. I mean, they they work together. Oh, yes. It tells you a lot. It tells you whether an argument is valid and you know that if. OK. Think of the difference between something's generating truth and something's preserving truth.

Logic doesn't generate truth. If you haven't got truth in the premises, you won't have it in the conclusion. But if you have got truth in the premises, you preserve it in the conclusion by using a valid argument. And that's what you hope you, because there are things that we know about the world. And there are things that we want to know about the world. So we want to extend our knowledge from what we already have to what we don't already have.

And one of the ways of doing that is, is by using logic. If this is true and this is true, then this must be true. If this is true, yeah. Yeah. Well, let's say I'm a scientist and I say, well. If the Higgs bows on exists, then my building, this whacking Great Hadron Collider at a cost of millions and millions and millions of pounds might enable me to find it. Of course, if if the Higgs boson doesn't exist.

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. So if statements are actually we use them all the time. I mean, if you think of any of your practical reasoning that says, okay, I want to do liver for supper tonight.

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 actions or conclusions about knowledge or you can't you can't reason without if statements. This is. Yeah. I mean, it was when this was developed that computing became possible. Yeah. Yeah. Absolutely the same. Exactly. So. Yeah. Yeah. No. I mean what you're doing when you're doing, applying those truth tables and the Tablo rules is acting like a computer.

You're making like a computer. There is a tendency towards a new ice age in the proceedings. Exactly. I mean, you might have two conflicting theories. Are you saying if this is true, then this will be the results? Let's see if this is the result. But if this is true, this will be the result. And if we can find out whether it's this or that, then I know which there is the correct one.

Do you see all reasoning? You cannot do without. If statements. And I can tell you under exactly what conditions, if statements would be true. I might not. I might need to go into the laboratory to see if and if statement is true. I wouldn't because there's no way laboratory could be. I think it will be because of our activities. But some people didn't say that. And they say it is a natural thing that's happened to.

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. But without that bit of reasoning, first, you wouldn't even know what you were looking for. And the thing is, if logic can rule out something, then there's no point in going to the laboratory at all.

I mean, if I can show an argument is invalid, then any scientist who's trying to get funding on the back of that argument is is in serious trouble. Because why? Why should I fund him? Okay, moving on, because we've only got five minutes left. But that's all right because. OK. I was going to talk very briefly about philosophical logic. I've talked about formal logic, but philosophical logic is the philosophy of logic.

I said there are philosophies of everything, including biology, accountancy, whatever. But the philosophy of logic is, as you can imagine, pretty damn important to philosophers because the philosophy of Lord of Logic looks at the notions without which logic can't work. So we've talked about truth a lot today, haven't we? I've drawn truth tables. I've drawn truth trees. I've said if this is true, that's true. So the notion of truth is absolutely central. Well, what is truth?

Gone. Tell me you've all sat there looking intelligence as we've talked about truth. So I assume you understand the word. Tell me, what is truth? Something is correct, what's correct, then? I mean, you're just giving me a synonym there, aren't you? Whoever it was. Okay, so what? Okay, what is false then? No. No. Okay. But that doesn't tell me what either are. It's true. You can't have truth without falsehood. You can't have falsehood without truth. But what is truth? A fact. Okay.

What's a fact? Let's let's. What is a fact? Certain knowledge is it is knowledge of fact. I mean, there's the knowledge that I'm wearing a dress. And there's the fact I'm wearing a dress. Are they the same thing? No, because there are facts of which we know nothing out there. So so facts are nothing to do with knowledge, but reality sounds like a synonym for truth here. A fact is actually something that makes a true sentence true.

Isn't it? Think about it. What and what is a fact? You know, there are facts you can't prove. I mean, are there three consecutive sevens in the decimal expansion of PI? If there aren't, then you can't prove it. I'm told there are. By the way. So that's out of date. But just imagine the decimal expansion of PI is an infinite expansion. If there aren't three consecutive sevens, there's no way we're to be able to prove it.

But it would still be a fact, wouldn't it? So knowledge of a fact and a fact are two quite different things. And what is a fact? A fact is something that makes a true sentence true. So talking about facts doesn't tell me anything about truth. So come on. Come on. You you've all been dealing with truth. What is it? You. So then how do we know we do not need to know it at all? No, you're all confusing. Not all of you may be epistemology and metaphysics here.

Epistemology is what we know and metaphysics is what is the case. And there are two quite separate things. What are you going to know? Because a belief is usually to do with knowledge rather than because there might be facts about which we have no beliefs. I mean, you have no beliefs about my middle name. I shouldn't think you don't even have the belief that I have one. How do you know whether I have one? Okay, but there's still a fact about my middle name.

Irrefutable is to do with proof again, isn't it? Yeah, no, that's again to do with the pistol ology. The fact is, truth is a very, very difficult. You mentioned correspondence. There are two key theories about truth. Actually, here's another one. There's some belief that true truth is nothing, that the truth is completely redundant. Because if I say P is true, I'm not saying anything more than PMI. If I say peer's true onto my saying anything more than pee.

Would you say not? I'm not not I'm saying not not pee on sight. Because if if pee is true, then then not pee is false. So if if, if I'm saying pee I'm saying not not pee, not pee. You two can do this eventually. Is truth demonstrable? Not always. No, no. Definitely not moral regard such as factual. Well, I think there are facts about values. So. So I don't think there's any opposition between fact and value.

So I think there are moral truths and that what make a moral truth is that there are moral facts. You know, you can sing, you preach proof again. The proof is to do with knowledge anyway. One one people some people think there's no more to truth than coherence. What makes one believe true is that it coheres with your other beliefs. Other people think, well, hang on, I can have a set of beliefs here, all of which are coherence. And then if I negate the more that will be another set.

All of which are coherence, won't it? But which is true. So coherence can't be the right theory. Well, no, because truth. Truth seems to be a property of sentences and beliefs, doesn't it? Well, reality isn't a property of your beliefs, is it, or of your sentences. Exactly. But truth seems to be a prop. If there weren't any beliefs in this world, there wouldn't be any sentences with the sentences, express beliefs. OK, if I believe that that your what's your name? Deirdre is wearing red.

I just expressed that belief in saying Dajarra is wearing red. If there were no beliefs, there'd be no sentences. If there were neither beliefs nor sentences, there would be no truth, but they'd still be reality. Semantics means truth or means truth conditions. Yeah. That's because you're thinking of what makes things true. But, of course, truth is still the property of the sentence that you've uttered. I mean, what's true is the sentence. The reality is what makes it true.

This is this is really difficult stuff here. Just talk about semantics and syntax at the moment. If we look at one of the truth trees, again, I have stripped the semantics out of the arguments there. I've left the syntax. All I've left is the shape. If I want to put the meaning back in. I've got to put semantics back in and inputting semantics back in. What I'm putting in is conditions of truth and falsehood. That's what semantics is, and that's that's what meaning is.

Anyway, we've done it now. That's logic. That's your lot on logic. Oh, okay. Correspondence. Correspondence. So you've actually we've already looked at that. Truth is, correspondence between a sentence and a fact. But what's wrong with that is, is what is a fact of often something that makes a true sentence true.

And therefore, that's just a secular definition. It gets you absolutely nowhere. Oh, goodness. It's lots of people. Yeah, A.J., I would certainly be one of them, I think. So what is truth answer? I don't know. I know more than you do, obviously. But I don't know because this is still an ongoing question. What is truth? That's what philosophical logic looks at. We also I mean, validity. I gave you one of the paradoxes of entailment two minutes ago, and you weren't very happy with it.

Here's another two. Well, it would be if I can find them. We're running over our time. If anyone wants to go, they're most welcome. Um. No, I'm not going to be able to find it if I say the grass is green. Therefore, two plus two equals four. That's a valid argument because there's no possible situation which that conclusion is false. So how could there be a possible situation in which the premise is true? And the conclusion false? There couldn't be. That's one of the paradoxes of entailment.

And one of the things that philosophical traditions would like to know is why is our definition of entailment faulty in that way? Because that surely that argument isn't valid. And yet our definition of valid makes it valid. So there's something wrong with our definition of validity. And yet somehow we can run computers that run Large Hadron Collider. And find the Higgs suppose on on our logic. So our logic isn't totally wrong. How do we do with it? Okay, we're going to stop right there.

You know nothing about identity, but that's what I am sure we can talk about that some other time.