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Okay. And now we're on week two, and this week we're going to look at different types of arguments.

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And in particular, we're going to look at deduction and induction.

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These are two basic types of argument, and we'll be looking at different examples of each type.

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Welcome back, everyone. So it didn't put you off entirely last weekend? Difficult though it was.

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I'm sure it was difficult. Let's do a quick recap of last week so we can remember where we were.

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If you remember, I said that arguments are sets of sentences such that one of them, the conclusion, if you remember,

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is being said to be true and the others called the premises are being offered as reasons for believing the truth of the one.

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Or reasons for believing the one. Okay, so that's what an argument is.

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And I said it was important to distinguish arguments from two things.

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Firstly, sets of sentences that aren't arguments. And if you remember, I gave the two sorts of sets of sentences that are not arguments.

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Can anyone remember what they are? No.

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Intersession isn't an argument. An assertion is the second thing from which you should distinguish arguments.

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So I said that there are two sets. I think you misunderstood my question slightly.

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Whoever it was then. So there are two things from which you distinguish arguments.

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But the first one is sets of sentences.

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And I said that there are two things, two types of sets of sentence that you need to distinguish from an argument.

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Can anyone remember what those two types of sets of sentences were?

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Sorry, Peter. No. No. No.

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Okay, maybe that's not a fair question. Okay. The first one is sets of sentences that aren't related at all.

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Do you remember I talked about sea as salt in Melbourne. Melbourne's in Australia.

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Well, until you are therefore in a bit of context, that's not an argument, is it?

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It's just two unrelated sentences. And the second type of sets of sentence you should distinguish from arguments are those that are related,

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but not as an argument is related, not as the sets of sentences that constitute an argument are related.

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So in order for a set of sentences to be an argument,

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it's got to be related in the sense that the conclusion is being said to follow from the premises.

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Okay, that's what an argument is, that one of the sets, one of the sentences of the set is being said to follow from the others.

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If it's if that relation isn't being said to be that, then it's not an argument.

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The second thing from which you must distinguish an argument is it is a sentence.

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And can anyone remember how you distinguish sentences from arguments or one way,

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at least in which you would distinguish a sentence from an argument is.

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What do you mean by premise that a premise has a very particular definition,

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that the definition is that a premise is a sentence that's being offered as reason for believing the truth of the conclusion?

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So what the questions is here is how do you distinguish a sentence or assertion from an argument?

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A sentence. You could see as an incomplete argument, I suppose.

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But that's not what I was thinking of. Certainly there's no conclusion.

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Nothing being. Well, there is something being postulated. If the sentence is being asserted.

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Isn't the. There's no relation, that's right.

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But okay, look, let me look, hang on, there's one more that but the.

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Say that again. That's right.

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This is just a statement and a statement isn't an argument.

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Is it? A statement isn't good or bad? Well, it could be, I suppose, couldn't it?

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A statement is true or false. And an argument is good or bad.

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Do you remember? And very important that, you know, you shouldn't call arguments true or false because arguments can't be true or false.

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The only thing that can be true or false is the sentences that make up the arguments.

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What an argument is, is truth preserving. So if you have truth in the premises, then and it's a good argument, then the conclusion will be true.

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But notice, it's the premises that are true and the conclusion that's true, not the argument itself.

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The most the argument can be is truth preserving. OK, so that's distinguishing arguments from sets of sentences and from sentences themselves.

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What we're going to do today is considered different types of argument.

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And we're going to start using some of the concepts that you've already mentioned this morning.

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So there are two basic types of argument. There are deductive arguments and they're inductive arguments.

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This is a very basic type of argument because you'll see later there are lots of other types of arguments in these categories.

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But these two categories are the most important. These are the ones you need to get a grip on.

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Okay, let's look at deductive arguments first. Now, these are such that the truth is their premises guarantees the truth of the conclusion.

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So if the premises are true, then the conclusion must be true, because if it's a good deductive argument, it's truth guarantying.

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So here's a deductive argument. You'll be familiar with this one.

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We used that last week. It's Friday. Marijan always wears jeans on a Friday.

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Therefore, Marianne is wearing jeans. Notice that the conclusion of this argument is it's true.

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But neither of the premises are. So that that should give you an idea that the argument is a good one.

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The conclusion is true. But actually, neither of the premises are true.

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So this will be something we'll look at again when we look at what a good argument is next week relating to the real world.

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That's right. It's not Friday. Therefore, that premise is false. It's not true.

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You'll have to take it from me on the authority that I don't always wear jeans on Friday.

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I do happen to be wearing jeans today.

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But of course, that's irrelevant because it's neither Friday nor is it the case that I always wear jeans on a Friday.

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But what's important about this argument is that it's deductive, it's truth guaranteeing, at least conditionally upon the truth of the premises.

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Can you think of any situation? I really try and use your ingenuity here.

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Let's see if we get in which that would be true. Okay.

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It isn't true. We know that. But we're assuming for the sake of argument that it is true.

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So imagine a situation where that's true and that's true for some reason.

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I always wear jeans on a Friday. Could that be false?

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Can anyone think right be? Well.

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Well, that would that would not make that not true. Well, that sounds very Mary.

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No, no, it doesn't. I may not. I may hate wearing jeans. That may be nothing to do with it.

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I may wear jeans as a penance on a Friday because I once did something really ghastly and said to myself, right.

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Okay, from now on, I'm always going to wear jeans on Fridays. So it doesn't say that I want to.

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Can anyone think of a counterexample? OK, so it's true.

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It would be Friday on that day, but would this be true? No, it wouldn't, would it?

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So we've given what we've given there is a falsification of that. Not a counterexample to the argument.

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OK. Do you see where I'm getting at? What we're doing is we're distinguishing the truth of the premises from the truth.

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Preserving this of the argument. Lots of us can think of situations where that's false or whether that's false.

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But that's not what I'm asking you to do. What I'm asking you to do is to think of a situation where that's true and that's true.

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And that's false. It is, isn't it?

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Well, on the couple of other examples. Let's try one. So I'm on the moon or something like that.

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Very ingenious. I think what we do what we're talking about is a situation where all these are.

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So these two are true together. Do you see what I mean and what you're giving me is one where it's not Friday.

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Aren't you really what you're trying to make it? Not Friday somehow by shifting me out of its time zone in which it is Friday?

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No, it won't do. But we do not need to guarantee it because all we're doing we're saying this is true.

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If this is true and if this is true, we're not saying this is true.

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I mean, this is another very important distinction when you're doing logic.

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You're you're not talking about the actual truth value of a sentence.

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OK. So the truth value of that could be either true or false.

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Do you see what I mean? So that's the value of its truth. It's either true or false.

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And we're not saying it is true, but we're saying if it's true and if this is true, this can't be false.

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And as you rightly said, actually, if these two are true, it's impossible for this to be false.

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It really is, isn't it? Well, if we're looking at an argument, we're saying we're asking ourselves two questions.

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The questions are, does the conclusion follow from the premises?

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And in asking, that's what we're asking is if the premises were true, would the conclusion be true?

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If the premises are true? Would the conclusion be true?

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And if we look at these two premises and we ask that question, we're not asking whether the premises are true.

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We're saying if they're true. Would the conclusion be true? And the answer is yes.

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Can everyone see that this is a deductively valid argument?

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It's truth preserving. And therefore, it's very, very useful because we know that if the premises are true, the conclusion must be true.

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Now, in this particular case, this is not very useful because it's all hypothetical.

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But can you imagine if if this was something that we didn't know but we were wanting to test, then we could say, okay.

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It's Friday. Mariane always wears jeans on a Friday. Therefore, Marianne is wearing jeans.

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Then if you see that, I'm not wearing jeans. What do you know?

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One or other of these isn't true. Exactly. So if you see that Marianne isn't wearing jeans,

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you know either that it's not Friday that that one's false or that Marianne always wears jeans on a Friday is itself false.

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So, you know, either your hypothesis is false or your observation is false or.

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Oh, sorry. Well, you're quite right. Or both. That's right.

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So if you have a valid argument to deductively valid argument, the conclusion to which is false, you know that one of the premises must be false.

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And that's why truth preserving this is useful.

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Whatever the situation is, even if it turns out that delusions false anyway, again, that's something we'll talk about more next week.

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The only thing that's important for now is that you understand what a deductively valid argument is.

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You understand that it's truth preserving that if the premises are true, the conclusion must be true.

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Okay, everyone happy with that? Let's move on. Okay.

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You should know instantly that deduction is an either or thing.

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Either an argument is deductive or deductively valid or it's not OK.

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There's no in between there. It's one or the other.

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A good deductive argument gives us conditional certainty, certainty conditional upon the truth of the premises.

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Well done. I can feel you getting it now. Okay. A bad one tells us nothing.

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Because if the argument isn't a good one, if it isn't truth preserving, then the conclusion could be either true or false.

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And we really don't know. Okay, so that's deduction.

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Let's move to inductive induction, inductive arguments as such that the truth of their premises makes the conclusion either more or less probable.

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Okay. It doesn't give us certainty. Makes the conclusion more or less probable.

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Now this means that inductive arguments can be either weak or strong.

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Okay. So here's an example of a strong inductive argument.

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The sun has risen, risen every day in the history of the universe. Therefore, the sun will rise tomorrow.

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Okay, that's a strong inductive argument. Why isn't that a deductive argument?

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So what may not be true, because arguments can't be true, of course, can they?

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This may not be true. OK. But but we're saying if this is true, then this will be true.

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So why is that? Not deductively certain. OK.

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So this could be true. And yet this false. And yet this is a good argument.

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Yes. Good. Well done. And that's exactly right. That's the hallmark of a strong inductive argument is even though you've got a very strong argument.

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I mean, if the sun has risen every single day in the history of the universe so far, I have no idea how old the universe is.

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But some. It's a it's old, right?

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If the sun has risen every day in the history of the universe, then it's hugely likely that the sun is going to rise tomorrow, isn't it?

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And then you say, but we can't be 100 percent certain because who knows, the sun may explode tomorrow.

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Or maybe the law that ensures that the sun rises every morning and she has a bit of a dogleg in it.

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So it's saying, OK, what the law is, is every morning the sun will rise, except on the 7th of October 2009, it's suddenly going to miss a day.

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And from then on, it's only going to rise every other day. Okay.

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For the rest of the history of time, do we know that that isn't what the laws.

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Do we know that the son that the law that ensures that the sun has risen every morning in the history of the universe so far,

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won't tomorrow miss a day that we.

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Well, it makes it weaker, but it means that we haven't got certainty.

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This could be true and this false. But it's a different type of argument.

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You mustn't think that because deductive arguments are certain, an inductive arguments aren't that therefore,

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inductive arguments are somehow inferior because actually they're dealing with different things.

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This is the sort of argument that science deals with, isn't it?

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You observe that nature has been like this all the times before and then you

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extrapolate into the future to assume it's going to be like that in the future.

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So every daffodil you've ever seen in your life so far has been yellow.

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You're going to assume that the next daffodil you see will be yellow. There's another bad example, you see, but you see what I mean.

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I hope my genes just Friday are safe because there's a woops, sorry, I'm going the wrong way.

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This is the argument, right? An argument is a set of sentences. There are three sentences in this argument.

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The argument claim that's being made by this sentence is that if this is true and this is true, then this will be true.

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This will be true. Okay. And this one, the inductive argument is saying, if this is true, this will be true.

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OK, now, in this case, we can say, but there could be a counterexample to this.

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The counter example might be that the sun explodes tomorrow or that the law of nature has

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had written into it from the history of time that it'll change tomorrow of all days.

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And we know that this doesn't give a certainty, but it gives us a jolly good reason for thinking that this is true, doesn't it?

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I mean, I could give you an inductive argument that goes like this, in fact, let me give you one.

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Every time I've seen Marianne, she's been wearing earrings. Therefore, next time I see Marianne.

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She'll be wearing earrings. Okay, now.

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Is that a strong inductive argument? No.

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Well, it's not very strong, is it? I mean, the next time you see me,

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you might have come knocking on my door at seven o'clock in the morning and I've just got up and I don't wear earrings in bed.

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So the next thing you know, we know too much about the world, about people,

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about earrings and things like that to know that that's good inductive argument.

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Well, let's go back to this one and notice that here we're arguing from this not to it.

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Okay. This is a premiss in our argument, not a conclusion. OK, whereas if we're looking here.

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I'm not going to run with the other way. I no, actually, what I was just about to tell you, that isn't going to work.

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How do we get to this? We've seen the sunrise every single day.

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We've seen lots of observations. And therefore, we naturally extrapolate to a generalisation like this.

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This is a different form of reasoning. This is inductive reasoning.

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And it's the same reasoning that causes us to say something like this. But in this case, the same reasoning isn't as strong.

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Here's another one who takes a lucky rabbit's foot into an exam.

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If they ever go into exam, who used to take your lucky racquet rabbit's foot into exam?

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Who has a lucky red jumper or something like that?

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We've all had the experience of something's really nice happening to us and we were wearing something or carrying something.

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And we think, you know, maybe I'll wear that again.

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I'll be lucky again because we extrapolate from what's happened in the past to what's going to happen in the future.

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I've lost you, I can see. I can. I'm looking at your faces and you've gone right.

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The only thing you need to remember is that a deductive argument. You've got certainty.

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Because if the premises are true, the conclusion must be true.

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In an inductive argument, you haven't got certainty, you've only got probability.

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Okay, this ARG, this premiss gives you probable reason to believe this.

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If this premise is true, this conclusion is probably true.

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Okay. But it's not certainly true. And if this premise is true, then this conclusion is not even probably true, isn't is it?

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This is a very weak inductive Olguin. This this gives you some reason for believing this, but not very much.

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Have a look at these. Go through. I'm going to give you a couple of minutes to do them on your own.

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So you really try and work this out for yourself, decide which of those are deductive arguments and which of those are inductive arguments.

193
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And then we'll have a look at them together. So the sun is coming up.

194
00:21:20,110 --> 00:21:23,890
Well, actually, let's do them together. I think that's probably easier at this point.

195
00:21:23,890 --> 00:21:30,550
Let's have a look at the sun is coming out. So the rain should stop soon, which is the conclusion of that eye.

196
00:21:30,550 --> 00:21:40,330
Okay. Well, but well, let's let's do the canonical way, shall we, just so we've all got it, which is the conclusion of this argument.

197
00:21:40,330 --> 00:21:48,790
The rain should stop soon. That's what we're claiming. And the reason we're giving for that claim is the sun is coming out.

198
00:21:48,790 --> 00:21:55,060
So the the premises, the sun is coming out. Therefore, the rain should stop soon.

199
00:21:55,060 --> 00:22:00,550
Now, just the truth is that premiss make the truth as a conclusion certain.

200
00:22:00,550 --> 00:22:07,990
No, you can't have more or less certain. Sorry. It's more or less probable, but not more or less certain.

201
00:22:07,990 --> 00:22:13,440
Okay. So this is inductive or deductive. Put up your hands if you think it's inductive.

202
00:22:13,440 --> 00:22:16,750
Yay! You see. I knew. Got it. Really. Okay.

203
00:22:16,750 --> 00:22:20,560
Good. That's the end deal. What about this one. Let's do it the canonical way.

204
00:22:20,560 --> 00:22:31,990
What's the conclusion. All right, I'm going to make you do the things that I make undergraduate used to make undergraduates to notice this.

205
00:22:31,990 --> 00:22:37,990
Can you make that a proper sentence? John won't be at the party.

206
00:22:37,990 --> 00:22:51,730
That's right. It's obvious what the sentence should be, isn't it? So, OK, the conclusion is John won't be at the party and the premises are good.

207
00:22:51,730 --> 00:22:56,260
There are two parts to premises here. One is, Jane, is that the party?

208
00:22:56,260 --> 00:23:00,880
And the other is if Jane is at the party, John won't be at the party.

209
00:23:00,880 --> 00:23:07,900
Notice that that's a complex sentence that's constituted of two sub two sentences within the sentence.

210
00:23:07,900 --> 00:23:14,290
But you don't separate those two to make them two different premises because the sentence being asserted as if,

211
00:23:14,290 --> 00:23:18,040
Jane, is that the party, John, won't be. That's the premise. Good.

212
00:23:18,040 --> 00:23:22,420
Okay, so we've got an argument that goes if Jane is that the party, John, won't be at the party.

213
00:23:22,420 --> 00:23:27,820
Jane is at the party. Therefore, John won't be at the party. Is that deductive or inductive?

214
00:23:27,820 --> 00:23:33,870
Put up your hands if you think it's inductive. OK.

215
00:23:33,870 --> 00:23:37,740
Put up your hand using his deductive. Well done.

216
00:23:37,740 --> 00:23:42,360
OK, so you are getting this. Okay. It's the site. The house is a mess.

217
00:23:42,360 --> 00:23:48,750
Therefore, Lucy must be at home. What's the conclusion? Just Lucy must be at home.

218
00:23:48,750 --> 00:23:53,610
The ZET therefore just marks the conclusion rather than being the conclusion.

219
00:23:53,610 --> 00:23:57,930
Okay. Lucy must be home premiss. The house is a mess. Inductive or deductive.

220
00:23:57,930 --> 00:24:02,060
Put out your hand. If you think inductive. Well done.

221
00:24:02,060 --> 00:24:09,750
Can you give me a counterexample to that argument? Yes, that's right.

222
00:24:09,750 --> 00:24:13,430
OK. So the house is a mess, but Lucy isn't at home.

223
00:24:13,430 --> 00:24:18,050
You've had burglars instead. Good. Okay. I think he's in the bathroom or the bedroom.

224
00:24:18,050 --> 00:24:24,400
He's not in the bathroom, so he must be in the bedroom. Conclusion's obvious.

225
00:24:24,400 --> 00:24:29,210
It must be in the bedroom. And the two premises, either he's in the bathroom, all the bedroom.

226
00:24:29,210 --> 00:24:34,010
He's not in the bathroom. Okay. Deductive or inductive?

227
00:24:34,010 --> 00:24:38,150
Deductive. Well done. Okay. Dog would have bought it if it saw a stranger.

228
00:24:38,150 --> 00:24:42,860
It didn't bark. So it didn't see a stranger. Deductive.

229
00:24:42,860 --> 00:24:48,770
Good. No one in Paris understands me. So my French must be rotten or the Parisians are stupid.

230
00:24:48,770 --> 00:24:53,780
Sir, I got this from a book inductive.

231
00:24:53,780 --> 00:24:57,080
Okay. It's difficult that one, but it is inductive. You're quite right.

232
00:24:57,080 --> 00:25:04,050
Because what's the conclusion? That's right.

233
00:25:04,050 --> 00:25:08,400
It's actually a complex conclusion, isn't it. My French must be rotten.

234
00:25:08,400 --> 00:25:13,370
All the Parisians are stupid and on the premises. No one in Paris understands me.

235
00:25:13,370 --> 00:25:23,480
So it may be the case that if that's true. These are true, but but there are other reasons for nobody understanding me on that as well.

236
00:25:23,480 --> 00:25:29,780
OK, good. So you have actually got it. Even if we got tied up in a few knots there.

237
00:25:29,780 --> 00:25:37,190
No. Not in safety. Right. Logicians study deduction by studying valid argument forms.

238
00:25:37,190 --> 00:25:42,910
And now it's very important to distinguish form from content.

239
00:25:42,910 --> 00:25:49,790
Okay. And arguments are deductively valid in virtue of their forms rather than their contents.

240
00:25:49,790 --> 00:25:53,960
Now, that's not true of all deduction, but it's true of most deduction.

241
00:25:53,960 --> 00:25:59,540
So let's have a look. What I mean here, all men are mortal, Socrates and man.

242
00:25:59,540 --> 00:26:06,430
Therefore, Socrates is mortal. OK. All actions that produce the greatest happiness to the greatest number.

243
00:26:06,430 --> 00:26:10,550
I got very bored writing it out. So the greatest happiness is greatest number.

244
00:26:10,550 --> 00:26:14,630
All actions that produce the greatest happiness, the greatest number are right. Morally right.

245
00:26:14,630 --> 00:26:18,860
That is, that action produced the greatest happiness of the greatest number.

246
00:26:18,860 --> 00:26:27,280
Therefore, that action was right. Okay. Can you see that the form of those two arguments is exactly the same?

247
00:26:27,280 --> 00:26:32,200
Can you see that? So the content of the two arguments is quite different.

248
00:26:32,200 --> 00:26:39,640
This is an argument about Socrates and mortality. And this is an argument about morality and the greatest happiness of the greatest number.

249
00:26:39,640 --> 00:26:45,340
Completely different topics, completely different content. But each of the arguments has the same form.

250
00:26:45,340 --> 00:26:51,670
Can anyone try and write down the form? Tell me the form of that argument.

251
00:26:51,670 --> 00:26:58,600
This the structure of it. Do you not know what I mean?

252
00:26:58,600 --> 00:27:05,430
No. Okay, let's do it together. All A's are B.

253
00:27:05,430 --> 00:27:10,740
S isn't a, therefore, s is a B. Did you get that?

254
00:27:10,740 --> 00:27:15,480
All A's are B, so. Aye, aye.

255
00:27:15,480 --> 00:27:19,410
Let's stir an interpretation here. Aye aye.

256
00:27:19,410 --> 00:27:23,210
Equals. Let's do it properly here.

257
00:27:23,210 --> 00:27:30,910
X is a man. X is mortal.

258
00:27:30,910 --> 00:27:39,700
S is Socrates, and the form this is all A's are V.

259
00:27:39,700 --> 00:27:45,730
S is an A, therefore S is a B with me.

260
00:27:45,730 --> 00:27:51,430
Let me do it again. Can you see unsighted? So if this is the interpretation, this is.

261
00:27:51,430 --> 00:27:57,040
I've just changed the words for symbols here. And the symbols are only letters.

262
00:27:57,040 --> 00:28:02,200
So a A of X says X is a man.

263
00:28:02,200 --> 00:28:08,760
X is mortal. Is B an s. Is Socrates. So all A's are B.

264
00:28:08,760 --> 00:28:13,490
S is an A. S is therefore. S is a B you with me.

265
00:28:13,490 --> 00:28:23,310
So it's safe to do that for the other argument. What would we have to say that A is there.

266
00:28:23,310 --> 00:28:30,590
Good X is A is an action, B, X is.

267
00:28:30,590 --> 00:28:36,970
Difficult. Gone. Produce.

268
00:28:36,970 --> 00:28:41,260
No. Okay. All men are mortal.

269
00:28:41,260 --> 00:28:46,890
All actions that produce the great suffering disgrace number are right.

270
00:28:46,890 --> 00:28:55,920
OK. So actually, a isn't actions is is its actions. That produced the no not right actions, actions that produced the greatest happiness, great.

271
00:28:55,920 --> 00:29:01,970
No. So all men are mortal and all actions that produces.

272
00:29:01,970 --> 00:29:06,710
Right. Happiness. The greatest number. Right. You with me.

273
00:29:06,710 --> 00:29:12,740
So all A's, all men are B's mortal.

274
00:29:12,740 --> 00:29:16,580
All A's actions produce a gross happiness. Gross number.

275
00:29:16,580 --> 00:29:22,970
All right. OK. And then the next one, that action produced the greatest happiness.

276
00:29:22,970 --> 00:29:31,610
The greatest number. You've got Socrates. Here is a particular thing, just as that action is a particular thing.

277
00:29:31,610 --> 00:29:40,990
OK. And you're saying that particular thing is a man, i.e., falls into this class here.

278
00:29:40,990 --> 00:29:45,310
And therefore, he falls into the other class, too. Okay.

279
00:29:45,310 --> 00:29:50,290
So both those arguments have the form. All A's are B.

280
00:29:50,290 --> 00:29:58,900
S isn't A, therefore S is a B. Now, the point of this is just to get you to distinguish form and content.

281
00:29:58,900 --> 00:30:04,480
Can you see that an argument can have different forms. And yet the same content.

282
00:30:04,480 --> 00:30:11,560
Sorry, different contents. And yet the same form. OK. So these are two arguments of exactly the same form, different contents.

283
00:30:11,560 --> 00:30:22,000
What's important about this is that logic is topic neutral. Once you've learnt how to do logic, it doesn't matter what you're doing it with or on.

284
00:30:22,000 --> 00:30:28,630
It's always the same. Logic is the same. Whether you're talking about the colour of chairs, whether you're talking about biochemistry,

285
00:30:28,630 --> 00:30:33,160
whether you're talking about the philosophy of time, doesn't matter what you're talking about.

286
00:30:33,160 --> 00:30:40,150
If an argument is valid, it'll be valid by virtue, its form, whatever the topic is you're talking about.

287
00:30:40,150 --> 00:30:48,610
So logic is the ultimate transferable skill. If you've learnt logic, you can do it with whatever you happen to be talking about,

288
00:30:48,610 --> 00:30:55,670
whatever it is you're interested in, whether it's art history or fashion.

289
00:30:55,670 --> 00:31:00,610
Right. Okay, let's have a look at a few argument forms.

290
00:31:00,610 --> 00:31:06,730
Here's a valid argument form. If P, then Q p.

291
00:31:06,730 --> 00:31:12,880
Therefore Q. What's pee standing in for here?

292
00:31:12,880 --> 00:31:19,510
What type of thing is it standing in for? Can anyone tell me a good or a sentence?

293
00:31:19,510 --> 00:31:25,180
I was going to say, but the premise is even better. Yes, well done. So this is one sentence.

294
00:31:25,180 --> 00:31:31,990
What's this? No.

295
00:31:31,990 --> 00:31:37,280
No, not even that it's. Oh, actually, I am. That's a premise.

296
00:31:37,280 --> 00:31:44,850
Actually, that's a premise. That's only a sentence. Can you see why?

297
00:31:44,850 --> 00:31:53,550
That's right. OK, so if P, then Q is one premiss, P is the other premiss and Q is the conclusion.

298
00:31:53,550 --> 00:32:00,150
So all we done then sort of thinking about actual sentences we've just put in what are called sentence letters.

299
00:32:00,150 --> 00:32:04,170
Any letter will do. Doesn't matter, just so long as you get the form of the argument.

300
00:32:04,170 --> 00:32:09,240
Right. Can you think of an argument that fits that form.

301
00:32:09,240 --> 00:32:13,980
OK. Just think for yourself now of an argument that fits that form.

302
00:32:13,980 --> 00:32:20,370
You could use one that we've already used. You could use one to do with the colours of the chair in this room.

303
00:32:20,370 --> 00:32:26,800
Quite difficult. But see if you can think of one Gontran. I'm happy.

304
00:32:26,800 --> 00:32:32,980
I am. Therefore, I will see. Give her a clap.

305
00:32:32,980 --> 00:32:45,010
Well done. That's exactly right. Can anyone think of another one? No, there's no all there.

306
00:32:45,010 --> 00:32:58,070
No. Just the impossible. Cannot. If the impossible cannot happen, then.

307
00:32:58,070 --> 00:33:01,760
No, you're not quite getting the idea. Now, this will be happening to lots of you.

308
00:33:01,760 --> 00:33:05,990
This is not just just you. The form is if sentence.

309
00:33:05,990 --> 00:33:11,180
Then sentence. Sentence. Therefore, sentence.

310
00:33:11,180 --> 00:33:15,050
And these two have got to be the same sentence. These two have got to be the same sentence.

311
00:33:15,050 --> 00:33:20,960
So the form of this has got to be if P, then Q P, therefore.

312
00:33:20,960 --> 00:33:26,180
Q Think of another one thing. You think to yourselves first and then then when you feel confident that you've got it.

313
00:33:26,180 --> 00:33:32,000
Put your hands up and we'll try. This is really doing logic.

314
00:33:32,000 --> 00:33:35,330
So did he. If you find it odd. That's right.

315
00:33:35,330 --> 00:33:52,040
It's in the nature of the beast. Are you?

316
00:33:52,040 --> 00:33:57,800
Well, sit down and think for yourself and then try again. No, you've just said you didn't.

317
00:33:57,800 --> 00:34:07,440
No, sir. Okay. Go on, Nusaybin. And the chairs are blue, then these chairs and.

318
00:34:07,440 --> 00:34:11,580
No, that was an F, P and Q, wasn't it?

319
00:34:11,580 --> 00:34:21,960
And we're looking for an if P then. Q These words that are left are the logical words and it's getting the logical words right.

320
00:34:21,960 --> 00:34:26,760
If then and or not, that's hugely important.

321
00:34:26,760 --> 00:34:35,750
Have you got one. Sir.

322
00:34:35,750 --> 00:34:40,080
Okay. If he gets a bus then he's ecofriendly. He does get a bus.

323
00:34:40,080 --> 00:34:47,160
Therefore he's ecofriendly. Good. Well done, Paul. If it rains, I raise an umbrella.

324
00:34:47,160 --> 00:34:52,990
My umbrella is up. Therefore, it is rain. Oh. Something wrong with that?

325
00:34:52,990 --> 00:34:57,490
What was wrong with it? Now that the sentences were great?

326
00:34:57,490 --> 00:35:02,860
Say it again, though. OK.

327
00:35:02,860 --> 00:35:08,710
OK. So Piers, it is raining. OK. Q is I raise an umbrella.

328
00:35:08,710 --> 00:35:14,480
He now was paying my umbrella is up.

329
00:35:14,480 --> 00:35:20,840
What was P? It's raining. So what do you need there instead?

330
00:35:20,840 --> 00:35:25,100
It is raining then for your brother. Do you see what you were doing?

331
00:35:25,100 --> 00:35:32,480
Those you are committing the fallacy of affirming the consequent very common fallacy.

332
00:35:32,480 --> 00:35:39,470
Well, do phalluses next week. I think so. But you say it has to be you have to have the letters in the right order.

333
00:35:39,470 --> 00:35:48,650
Because what you gave me initially wasn't a valid argument, but a valid argument could easily be made from it just by transposing those.

334
00:35:48,650 --> 00:35:53,440
Do you have another if this.

335
00:35:53,440 --> 00:35:59,780
I'll take my son, so therefore I'll take my alterable.

336
00:35:59,780 --> 00:36:10,880
Exactly. So, Piers, it is Sunny. Q is I'm taking my dog for a walk and the argument is, if it's sunny then I'm taking my dog for a walk.

337
00:36:10,880 --> 00:36:15,020
It is sunny. Therefore, I'm taking my dog for a walk.

338
00:36:15,020 --> 00:36:20,330
Okay. Now, that has to be valid, doesn't it? Sorry, that has if those premises are true,

339
00:36:20,330 --> 00:36:28,550
that conclusion has to be true because any argument of this form must be a good argument is deductively valid.

340
00:36:28,550 --> 00:36:39,710
Everyone else wants to try another one. Good.

341
00:36:39,710 --> 00:36:43,820
OK. If the postman is striking, then we will have no letters.

342
00:36:43,820 --> 00:36:50,520
The postman, all striking, therefore will have no letters. So P is.

343
00:36:50,520 --> 00:36:56,260
The postmen strike. No, not if because the F. OK. The postman striking and Q is.

344
00:36:56,260 --> 00:37:01,120
We will have no letters. So if the postman is striking them, we'll have no letters.

345
00:37:01,120 --> 00:37:05,500
The postman are striking. Therefore we'll have no letters. Good.

346
00:37:05,500 --> 00:37:17,720
Okay. One more and then we'll move on. This is looking good.

347
00:37:17,720 --> 00:37:23,030
That's right. If he's breathing, then he's alive. He is breathing. Therefore, he's alive.

348
00:37:23,030 --> 00:37:26,660
OK. Yeah, good. OK. Dead easy, isn't it?

349
00:37:26,660 --> 00:37:30,940
Once you get the idea of it. And here's the story.

350
00:37:30,940 --> 00:37:35,020
So again, the light.

351
00:37:35,020 --> 00:37:39,410
The third part of the dead parrot.

352
00:37:39,410 --> 00:37:44,900
Yes. I'm sure we could meet on there. Here we are. If there are no chance factors in chess, then chess is a game of skill.

353
00:37:44,900 --> 00:37:48,740
There are no chance factors in chess. Therefore, chess is a game of skill.

354
00:37:48,740 --> 00:37:58,680
What s p here? Go to what's queue.

355
00:37:58,680 --> 00:38:02,280
Good. Well done. Here's another argument, OK?

356
00:38:02,280 --> 00:38:05,610
That was Motus opponents, by the way. So you know how to do.

357
00:38:05,610 --> 00:38:10,920
No, no, no. Just pens his most toplines, the mode of denial.

358
00:38:10,920 --> 00:38:16,590
If P then Q not Q, therefore not P.

359
00:38:16,590 --> 00:38:21,840
Okay, if P then Q not Q therefore not P.

360
00:38:21,840 --> 00:38:27,860
So this is saying in effect that P is sufficient for Q.

361
00:38:27,860 --> 00:38:40,810
Sorry. I've I got it the wrong way round.

362
00:38:40,810 --> 00:38:45,060
And it is absolutely like he must be. Now, I have got it right.

363
00:38:45,060 --> 00:38:57,370
We run. It's what we're saying here is that Q is necessary for P and so Q isn't the case then P isn't the case.

364
00:38:57,370 --> 00:39:03,450
Right? Well, let's have a look at the example and then you can come up with your room.

365
00:39:03,450 --> 00:39:07,320
Actually this example is wrong because that shouldn't be in there.

366
00:39:07,320 --> 00:39:12,190
But let's, let's do it. If the dog didn't know the visitor well the dog would have barked.

367
00:39:12,190 --> 00:39:17,370
Okay. The dog didn't bark. Therefore, the dog did know the visitor.

368
00:39:17,370 --> 00:39:21,870
That shouldn't be in there. That's the one that I was saying I'd got wrong before we started.

369
00:39:21,870 --> 00:39:31,710
So if you take that not out, I won't draw on the screen there. So on your handouts, make sure that you take that not out on slide 16.

370
00:39:31,710 --> 00:39:36,810
Write that down. I think it's 16. Yep. Because that's that's incorrect.

371
00:39:36,810 --> 00:39:44,670
But you do see how that argument is valid. If it's true that if the dog didn't know the visitor well, the dog would have barked.

372
00:39:44,670 --> 00:39:49,770
It's a good guide. Dog got guard, dog, guide, dog, dog.

373
00:39:49,770 --> 00:39:56,060
It didn't bark. Therefore, it must have known the visitor well, mustn't it?

374
00:39:56,060 --> 00:40:03,730
OK, so see if you can come up with something of that form now.

375
00:40:03,730 --> 00:40:11,910
I'll take the example out, so it's not confusing. Have you come up with an already.

376
00:40:11,910 --> 00:40:15,190
Well done. Fantastic. Absolutely right.

377
00:40:15,190 --> 00:40:24,100
So, Piers, I have money. Q Is I would be in the pub sat right.

378
00:40:24,100 --> 00:40:29,560
I'm not in the pub, therefore I have no money. If I had if I had money.

379
00:40:29,560 --> 00:40:34,870
So having money would be sufficient for you to be in the pub, ok.

380
00:40:34,870 --> 00:40:41,090
But you're not in the pub, therefore you haven't got any money. Okay, anyone else want to have a go?

381
00:40:41,090 --> 00:40:50,150
Gentlemen. Good.

382
00:40:50,150 --> 00:40:54,530
You've got it, I think. Does anyone else want to have a go? Or does everyone feel that they've got.

383
00:40:54,530 --> 00:40:58,220
That was it. Sorry.

384
00:40:58,220 --> 00:41:04,850
Say it again. If the sun is out, I will take my dog for a walk.

385
00:41:04,850 --> 00:41:10,340
OK, so here's the sun is out and Q is I'll take my dog for a walk.

386
00:41:10,340 --> 00:41:14,210
Oh, I'm sorry. Those of you who saw the error.

387
00:41:14,210 --> 00:41:21,500
That's quite right. Okay. What should be here? I'm not taking my dog out for a walk.

388
00:41:21,500 --> 00:41:25,420
Therefore, the sun is not out.

389
00:41:25,420 --> 00:41:41,030
Yep, that's right. Good. Okay. Try one more than us. We've got that as I got it wrong.

390
00:41:41,030 --> 00:41:45,730
Yes. OK. No, we are not in the wrong place there, didn't we?

391
00:41:45,730 --> 00:41:55,190
How did it go again? If I'm hungry, then I won't concentrate.

392
00:41:55,190 --> 00:42:08,390
I right. It will be I will write this one down because there are knots in there that we need to get.

393
00:42:08,390 --> 00:42:17,700
Right. Because as you say. OK, so pee is. I am hungry.

394
00:42:17,700 --> 00:42:23,300
Q is. I can't concentrate. OK.

395
00:42:23,300 --> 00:42:29,660
Notice that we've changed. Q The Q is actually a negative here.

396
00:42:29,660 --> 00:42:33,800
That's where we're. It's very easy to get tied up. So be very careful of this.

397
00:42:33,800 --> 00:42:39,830
Negatives immediately make things quite difficult. So but Nipon, we can do it.

398
00:42:39,830 --> 00:42:51,940
Okay. So. Q is I can't concentrate now not. Q Therefore is I can concentrate therefore I'm not hungry.

399
00:42:51,940 --> 00:42:58,550
Are you, are you with me. Do you see how that works. So you had the right sentences, you were just not using the negatives the right way.

400
00:42:58,550 --> 00:43:02,450
I've forgotten who and who said this. So I'm looking at all the wrong people. But okay.

401
00:43:02,450 --> 00:43:06,660
One more on this one, because it is quite difficult, Paul. Oh, actually, we had you, Paul.

402
00:43:06,660 --> 00:43:17,020
So do we have you for. Okay.

403
00:43:17,020 --> 00:43:26,230
Good. OK. If I've if I catch my train, though, so I start again.

404
00:43:26,230 --> 00:43:31,000
If I missed my train, I'll be late. I'm not late.

405
00:43:31,000 --> 00:43:38,610
Therefore, I haven't missed my train. You don't have to use the same words as always, you.

406
00:43:38,610 --> 00:43:45,810
Now, this is this is actually the important point. You don't have to use the same words as almost the words have the same meaning.

407
00:43:45,810 --> 00:43:48,600
Or do you see what I mean?

408
00:43:48,600 --> 00:43:57,970
But it's a very when you're learning logic, it's a very good idea to use the same words because it cuts out one area of complication.

409
00:43:57,970 --> 00:43:58,620
Do you see that?

410
00:43:58,620 --> 00:44:05,280
It just, you know, why would you why change your language when what it's going to do is confuse you, keep things as simple as possible?

411
00:44:05,280 --> 00:44:09,450
This is quite hard enough without adding layers of complication in.

412
00:44:09,450 --> 00:44:14,370
Okay, good. You did that well. So what have I got? Well, we've already tried that.

413
00:44:14,370 --> 00:44:19,950
Good. Let's try another one. This is a disjunctive syllogism.

414
00:44:19,950 --> 00:44:23,940
P or Q, not P therefore.

415
00:44:23,940 --> 00:44:48,700
Q Okay. I have got that one. P or Q, not P, therefore Q.

416
00:44:48,700 --> 00:44:54,050
OK. Oh, good. Look at you. Hands going up immediately, no.

417
00:44:54,050 --> 00:44:57,860
No. Brilliant. OK.

418
00:44:57,860 --> 00:45:01,970
It's either raining or it's sunny. It's not raining.

419
00:45:01,970 --> 00:45:06,840
Therefore, it's sunny. Good. Well done. On Battement.

420
00:45:06,840 --> 00:45:11,730
I know some suicides. I have a hunch. It's not up to them.

421
00:45:11,730 --> 00:45:20,140
Good. Well done. Anyone else? Good.

422
00:45:20,140 --> 00:45:24,420
OK. I think you've got it one. Good.

423
00:45:24,420 --> 00:45:27,620
Well done. OK, I've noticed that that works.

424
00:45:27,620 --> 00:45:41,430
If if you've got an exclusive or because all is actually an ambiguous word in English, it can mean either or it can be not both.

425
00:45:41,430 --> 00:45:47,610
And if this was either, this has got to be either or hasn't it?

426
00:45:47,610 --> 00:45:52,290
If it were not both, you couldn't get the conclusion, could you?

427
00:45:52,290 --> 00:46:00,600
So that that's where English can me lead us to stray a little bit because English is itself ambiguous.

428
00:46:00,600 --> 00:46:04,440
Okay, here's my example either. This is actually Bertrand Russell example.

429
00:46:04,440 --> 00:46:11,190
Either we hope for progress through improving morals or we hope for proof, progress from improving intellect, intelligence.

430
00:46:11,190 --> 00:46:17,220
We can't hope for progress through improving morals. Therefore, we must hope for progress through improving intelligence.

431
00:46:17,220 --> 00:46:24,900
What this should tell you instantly, we've been looking at very simple ones. But actually, these forms can be very complicated.

432
00:46:24,900 --> 00:46:30,030
One of the things I'm going to ask you to do this week while you're at home is when you read your newspaper,

433
00:46:30,030 --> 00:46:35,000
you listen to your television or argue with your friends in the pub or whatever you happen to do.

434
00:46:35,000 --> 00:46:44,040
And I want you to to try and identify arguments that come up whenever you hear the words, if then and or not.

435
00:46:44,040 --> 00:46:50,880
If and only if all these logical words. All is lovely, logical words.

436
00:46:50,880 --> 00:46:55,180
Just you got to be sensitised to them this week because I want you to.

437
00:46:55,180 --> 00:47:01,260
You have to every time you hear this, then I want you identifying the form of the argument in which you find it,

438
00:47:01,260 --> 00:47:06,340
cause it might not be in an argument might it might be just a free-standing assertion.

439
00:47:06,340 --> 00:47:17,250
But have a look, see if there is an argument there. This is second second sentence.

440
00:47:17,250 --> 00:47:24,930
Yes. Each of the premises is an asserted sentence, a sentence that's being asserted as it is.

441
00:47:24,930 --> 00:47:32,910
So Russell is saying, you know, it's true that either we hope for progress this way or we hope for it this way.

442
00:47:32,910 --> 00:47:37,590
Okay. There's no other option. We can't hope for it this way.

443
00:47:37,590 --> 00:47:42,460
He's asserting, therefore, we must hope for it that way.

444
00:47:42,460 --> 00:47:54,840
Okay. Well, what's incorrect?

445
00:47:54,840 --> 00:48:03,770
Hang on. What's false here? So is it the first premise, let's start to use the language now?

446
00:48:03,770 --> 00:48:13,960
Is it the first premise that false or the second? Well, I'm pretty intelligence isn't a sentence on appears here and here.

447
00:48:13,960 --> 00:48:28,730
So what? So is that the false premise sold that one?

448
00:48:28,730 --> 00:48:31,820
Right. I think I'm going to put this on one side because, A,

449
00:48:31,820 --> 00:48:37,580
we're not really looking at the truth of the premises and B, you've got to take the premises as they are here.

450
00:48:37,580 --> 00:48:44,150
This is what's being asserted. So we're not saying this is true or that this is true.

451
00:48:44,150 --> 00:48:49,770
What we're saying is, if this is true and this is true, then this must be true.

452
00:48:49,770 --> 00:48:57,500
Okay. These conditionals are very important decision by presupposition.

453
00:48:57,500 --> 00:49:01,700
What will get onto that later on?

454
00:49:01,700 --> 00:49:11,450
So what I want to get us not just sensitising is now to deduction and induction into the form of an argument that that's what we need to get today.

455
00:49:11,450 --> 00:49:15,710
OK. Let's move on. Here's another one like Nitz law.

456
00:49:15,710 --> 00:49:20,630
A is F, A equals B, therefore B is F.

457
00:49:20,630 --> 00:49:24,890
I'll give you my example of that. It's quite difficult. One, Jane is tall.

458
00:49:24,890 --> 00:49:31,040
Jane is the bank manager. Therefore, the bank manager is tall.

459
00:49:31,040 --> 00:49:34,880
If these are true. Is that true. Has to be.

460
00:49:34,880 --> 00:49:41,540
Doesn't it. Can't be anything else. Don't think of a couple of examples of that one.

461
00:49:41,540 --> 00:49:47,430
Go for it. Don't spark. No, I don't think it's going to work.

462
00:49:47,430 --> 00:49:52,560
Why is that not going to work? Let's see. Why is this not going to work?

463
00:49:52,560 --> 00:49:57,360
Well, dogs bark doesn't have the form. A is A is.

464
00:49:57,360 --> 00:50:05,000
F is. The chair is blue. Marianne is tall. The board duster is lost, etc.

465
00:50:05,000 --> 00:50:08,730
Not a dog. You could say the dog.

466
00:50:08,730 --> 00:50:17,550
The dog is barking, but dogs bark is saying of one class of things that they fit another class of things.

467
00:50:17,550 --> 00:50:29,510
And that's not the form of that sentence is it. This chair was comfortable from this chair.

468
00:50:29,510 --> 00:50:33,920
Gone. Not quite. No. What we've got here.

469
00:50:33,920 --> 00:50:38,150
This is a very interesting ambiguity here.

470
00:50:38,150 --> 00:50:53,210
Is is a very slippery word. In English is you can have the is of predication and the is of identity.

471
00:50:53,210 --> 00:50:57,560
And your attempted argument there. And don't worry about this at all.

472
00:50:57,560 --> 00:51:03,980
This is a perfectly reasonable mistake to make you equivocated between these two is.

473
00:51:03,980 --> 00:51:07,520
So you said this chair is blue. Is that right?

474
00:51:07,520 --> 00:51:12,590
Right. Then you said this chair is comfortable. OK.

475
00:51:12,590 --> 00:51:21,780
Now this. Well, actually, those those are both houses of predication, aren't they?

476
00:51:21,780 --> 00:51:27,870
Whereas what we're looking for here is an is of identity, isn't it?

477
00:51:27,870 --> 00:51:34,410
A is B is the very same thing as B. So here we've got a predication, haven't we?

478
00:51:34,410 --> 00:51:40,110
A is F. A has a certain property. And here we have this thing.

479
00:51:40,110 --> 00:51:50,010
A is the same thing as this thing. B, therefore B is F K you see how that has to be true.

480
00:51:50,010 --> 00:51:53,710
This is a it's a law of logic. This one isn't it. This is life and it's law.

481
00:51:53,710 --> 00:51:58,630
It is a law of logic. If A is F. If Marijan is tall.

482
00:51:58,630 --> 00:52:06,850
Oh. I'll just give you the same example. So let me give it to you. If Jane is tall and Jane is the bank manager.

483
00:52:06,850 --> 00:52:14,880
Here's an is of Prescod predications. So we're predicating tallness of Jane Artley with me.

484
00:52:14,880 --> 00:52:21,370
And here we've got the issues of identity, haven't we? Jane is the bank manager.

485
00:52:21,370 --> 00:52:31,140
OK, if that's true and that's true, that has to be true, doesn't it, because the bank manager is Jane, isn't she?

486
00:52:31,140 --> 00:52:33,390
Yes, that's exactly that's what we're doing.

487
00:52:33,390 --> 00:52:41,190
We're looking at two examples of deductively valid arguments, arguments that are valid by virtue of their form.

488
00:52:41,190 --> 00:52:45,960
OK, good. One last one, I think. Here's a syllogism. Now, this should be easy.

489
00:52:45,960 --> 00:52:53,570
All FSG A is an F, therefore A is G. All Fords are cars.

490
00:52:53,570 --> 00:52:58,320
Okay. A is a Ford. Therefore, A is a car.

491
00:52:58,320 --> 00:53:03,630
Yes. Well done. That stuff too. And you'll also want to give one more example and we'll move on.

492
00:53:03,630 --> 00:53:07,000
Good. I see where you're getting to. Yeah. The grandma got a bit mixed up.

493
00:53:07,000 --> 00:53:14,310
But yes. Okay. So all my clothes are wet. That's pair of jeans is one of my clothes.

494
00:53:14,310 --> 00:53:18,180
Sort of. Therefore it is wet. I see where you're coming from.

495
00:53:18,180 --> 00:53:25,320
Okay. You've got them. Okay.

496
00:53:25,320 --> 00:53:31,480
All miracles are impossible. Resurrection is a miracle.

497
00:53:31,480 --> 00:53:36,990
Therefore they're OK. It works doesn't it. Well done. We knew we'd get there somewhere.

498
00:53:36,990 --> 00:53:42,930
It's deadly this. Let me just give you a logical problem with that just because I think you might enjoy it.

499
00:53:42,930 --> 00:53:49,160
You said the resurrection is a miracle, therefore the resurrection is impossible.

500
00:53:49,160 --> 00:53:57,140
And there's something very logically fishy about negative X and true negative existential sentences.

501
00:53:57,140 --> 00:54:10,330
Isn't that if we say Pegasus doesn't exist? Aren't we picking out something by the word Pegasus in order to say of it that it doesn't exist?

502
00:54:10,330 --> 00:54:16,360
In which case, how can a negative system should be true? See what I mean?

503
00:54:16,360 --> 00:54:20,470
Hamlet doesn't exist. You're picking out something. Hamlet.

504
00:54:20,470 --> 00:54:24,910
In order to say off him that he doesn't exist. Well, how can you do that?

505
00:54:24,910 --> 00:54:31,180
You shouldn't be able to do that. I'll just leave you with a little conundrum, because that's philosophical logic.

506
00:54:31,180 --> 00:54:37,540
And we're not doing that here. We're doing symbolic logic here. So now you know of two different types of logic.

507
00:54:37,540 --> 00:54:41,470
Okay, we've. This is the canonical example for that one.

508
00:54:41,470 --> 00:54:49,650
All men are mortal. Ta da da da. Now, I said that some arguments and deductive, valid, deductively valid, but not in virtue of their form.

509
00:54:49,650 --> 00:54:54,760
Here's just a couple that are valid in virtue of their content, apparently.

510
00:54:54,760 --> 00:55:01,570
Dale Tech logic. Now, this is cutting edge stuff we know very little about.

511
00:55:01,570 --> 00:55:06,700
Day on tech, logic logic. Day on tech. Logic is the logic of morality.

512
00:55:06,700 --> 00:55:15,310
Okay? What we're trying to look at is the area of discourse in which we talk about morality and say, how does it work logically?

513
00:55:15,310 --> 00:55:21,700
How can we get a valid argument form from more talk of morality?

514
00:55:21,700 --> 00:55:26,740
Now, look at this argument. Lying is wrong. Therefore, we shouldn't lie.

515
00:55:26,740 --> 00:55:32,370
Now, that looks like a deductively valid argument, doesn't it?

516
00:55:32,370 --> 00:55:38,500
In other words, if that's true. Surely this must be true as well.

517
00:55:38,500 --> 00:55:43,300
But if so, it's not true in virtue of its form. It's true in virtue of its what could you say?

518
00:55:43,300 --> 00:55:48,850
Lying is wrong. But I'm going to lie. Well, we all know that you could lie.

519
00:55:48,850 --> 00:55:56,080
But if you say if you truly believe that lying is wrong, you're also going to believe you shouldn't lie.

520
00:55:56,080 --> 00:56:03,860
Now, that doesn't mean you won't lie. But you'll feel guilty for doing that.

521
00:56:03,860 --> 00:56:11,080
And that's just what I said. I said, if you believe lying is wrong, then you're going to believe you shouldn't lie, aren't you?

522
00:56:11,080 --> 00:56:23,150
Do you think you could possibly believe that lie? Really believe that lying is wrong and yet not believed that you shouldn't lie.

523
00:56:23,150 --> 00:56:30,050
Well, I think that if you find it okay, if you lie, either you're going to feel shame, which manifests your belief that lying.

524
00:56:30,050 --> 00:56:33,380
You do think lines wrong or you don't want to feel any shame at all.

525
00:56:33,380 --> 00:56:40,890
Which manifests manifests the fact that you don't believe that lying is always and everywhere wrong being wrong.

526
00:56:40,890 --> 00:56:45,880
Oh, don't get me on that. I'm not going to follow that one up at all.

527
00:56:45,880 --> 00:56:51,920
Oh, it's very important. Yes, but we're not. But but actually, we can safely leave it on one side here.

528
00:56:51,920 --> 00:56:57,350
You if you're a Kantian, you think that this entails that instant.

529
00:56:57,350 --> 00:57:03,720
You might want to put another premise in here. You might want to say we shouldn't do things that are wrong.

530
00:57:03,720 --> 00:57:10,580
Did someone want to do that? Okay. Kant would say if you did that, you would.

531
00:57:10,580 --> 00:57:18,470
You're manifesting the facts that you think that you could believe that something's wrong without believing you shouldn't do it.

532
00:57:18,470 --> 00:57:22,740
And that just shows you don't understand what wrongness is.

533
00:57:22,740 --> 00:57:29,900
To cance to have the proper moral concept, which is that, you know, lying is wrong or something like that,

534
00:57:29,900 --> 00:57:36,860
you cannot believe that something is wrong without also believing you shouldn't do it.

535
00:57:36,860 --> 00:57:41,490
So it doesn't mean you won't do it, because we all know that we do things we believe to be wrong.

536
00:57:41,490 --> 00:57:45,830
But but your belief that it's wrong will manifest itself as guilt.

537
00:57:45,830 --> 00:57:50,780
And if it doesn't, it manifests the fact you do not believe the first thing that lying is wrong.

538
00:57:50,780 --> 00:57:58,340
So anyway, we're not going to get into morality. I just wanted to say there is a logic type of logic called day on tech logic.

539
00:57:58,340 --> 00:58:03,050
And it looks at that sort of inference and noticed that that's can't.

540
00:58:03,050 --> 00:58:09,740
We can't give you a form for that. That's the very meaning of the word wrong.

541
00:58:09,740 --> 00:58:14,570
There's something very special about the meaning of the word wrong logically.

542
00:58:14,570 --> 00:58:22,550
Here's another one. Modal logic. Modal logic is the logic of necessity and possibility.

543
00:58:22,550 --> 00:58:29,270
It's necessarily the case that there are no square circles. In other words, there's no possible world in which there's a square circle.

544
00:58:29,270 --> 00:58:37,010
If it's square. It's not circular and so on. Therefore, it's not possible that there are square circles.

545
00:58:37,010 --> 00:58:44,640
So if P is necessarily true, then not P is not possible.

546
00:58:44,640 --> 00:58:50,010
Can you hear that you or your capacity for reason would follow that quite quickly,

547
00:58:50,010 --> 00:58:58,200
if A is necessary, then not A is not possible not to be the case, hasn't it?

548
00:58:58,200 --> 00:59:04,710
So again, we have a deductively valid argument, but it is not deductively valid at least.

549
00:59:04,710 --> 00:59:09,600
Actually, we're a lot further on with modal logic than we are in day on logic.

550
00:59:09,600 --> 00:59:16,050
We can do quite a lot with modal logic these days. And here's a bit of temporal logic for you.

551
00:59:16,050 --> 00:59:22,230
It's raining today. Therefore, tomorrow it will have been raining yesterday.

552
00:59:22,230 --> 00:59:27,780
Is that true? Okay. If that's true, then that must be true, mustn't it?

553
00:59:27,780 --> 00:59:34,130
Couldn't not. And that's because of a temporal logic. The way the logic of time works.

554
00:59:34,130 --> 00:59:39,240
Okay. Let's move on to a bit short of time here.

555
00:59:39,240 --> 00:59:43,710
Let's we'll move on to inductive arguments now, inductive arguments.

556
00:59:43,710 --> 00:59:52,960
You remember, what's the hallmark of an inductive argument is if the premises are true, the conclusion might be true.

557
00:59:52,960 --> 01:00:02,070
It probably is true. That's right. Okay, so the premises give us reason for believing the conclusion, but not in this case, certainty.

558
01:00:02,070 --> 01:00:06,270
They don't give us conclusive reason for the really cute conclusion.

559
01:00:06,270 --> 01:00:12,600
And that's because inductive arguments rely on the assumption of the uniformity of nature.

560
01:00:12,600 --> 01:00:18,480
That's what Hume called it. David Hume. The idea that the future will be like the past.

561
01:00:18,480 --> 01:00:24,900
So if we've seen the sun rise every day in the history of the universe, we expect it to rise tomorrow.

562
01:00:24,900 --> 01:00:32,160
If every time we've come here for Marianne's lecture on Monday at two o'clock and Marianne's been lecturing at two o'clock will come on,

563
01:00:32,160 --> 01:00:38,870
we'll carry on doing that. And if we come on the seventh week, we'll be disappointed, sadly.

564
01:00:38,870 --> 01:00:42,810
Okay. It was quite a good reason for believing that Marianne would be lecturing on Monday

565
01:00:42,810 --> 01:00:46,740
at 2:00 that she has been lecturing at 2:00 every Monday for the last six weeks.

566
01:00:46,740 --> 01:00:50,040
But it's not conclusive. And so on.

567
01:00:50,040 --> 01:00:55,260
So we're we are one of the biggest problems of philosophy, in fact,

568
01:00:55,260 --> 01:01:03,000
is how do we justify can we justify this assumption, the assumption that the future is going to be like the past?

569
01:01:03,000 --> 01:01:13,230
Why should we think that the future has been like the past? Can anyone give me a reason exactly?

570
01:01:13,230 --> 01:01:19,380
Because it it has always been the case that the future has been like the past in the past.

571
01:01:19,380 --> 01:01:23,310
So that's a circular. Yes, exactly.

572
01:01:23,310 --> 01:01:30,270
Every time you try and justify the belief that the future is going to be like the past, you'll find yourself arguing in a circle.

573
01:01:30,270 --> 01:01:35,070
The only reason we think that that works is because it always has worked in the past.

574
01:01:35,070 --> 01:01:42,750
Therefore, we assume it will work that way in the future. But human beings just cannot not argue like that.

575
01:01:42,750 --> 01:01:50,580
It's very interesting. I was playing with my cat the other day and I noticed that it doesn't go in for inductive reasoning.

576
01:01:50,580 --> 01:01:58,280
If you do that with a cat. If you do it with a human being, the human being will keep going and expect you to keep game with the cat doesn't.

577
01:01:58,280 --> 01:02:04,010
If you stop it, it stops. You don't catch it just slightly.

578
01:02:04,010 --> 01:02:09,950
It was interesting. Anyway, that's what inductive arguments rely on.

579
01:02:09,950 --> 01:02:14,610
OK. Tell me why this one. Tell me what it is.

580
01:02:14,610 --> 01:02:19,140
We're assuming that you this is a silly question. In fact, I don't like this question.

581
01:02:19,140 --> 01:02:21,060
I'm going to skip it.

582
01:02:21,060 --> 01:02:28,770
You can see why the assumption here is that because the sun has always done this, it will always continue doing that in the future.

583
01:02:28,770 --> 01:02:36,210
And the assumption here is that because in your experience, Marianne's always done this in the future, Marianne will always do this.

584
01:02:36,210 --> 01:02:41,820
But our background's knowledge comes in to say whether you think it's a strong argument or a weak argument.

585
01:02:41,820 --> 01:02:47,340
And I think you'll see that given what we know about physics, about astronomy, about the laws of nature,

586
01:02:47,340 --> 01:02:52,230
cetera, that is a strong argument given what we know about people and what they wear.

587
01:02:52,230 --> 01:02:59,190
That's a weak argument. But both of them rely on the assumption of the principle of the uniformity of nature.

588
01:02:59,190 --> 01:03:05,540
And there are sub categories within the category of inductive arguments.

589
01:03:05,540 --> 01:03:16,310
Here's one an argument from another analogy. A is like B, A is F, therefore, B is F.

590
01:03:16,310 --> 01:03:21,540
OK. A is like B, a notice.

591
01:03:21,540 --> 01:03:32,070
These smaller lowercase letters stand in for particular things, whereas letters like this stand in for either properties or sometimes sentences.

592
01:03:32,070 --> 01:03:40,720
But I tend to use P, Q, R for sentences and A for.

593
01:03:40,720 --> 01:03:42,650
Oh, actually, that should be a smaller case now.

594
01:03:42,650 --> 01:03:50,650
Now started explaining it, that should be smaller case of scrub that okay is like BASF, therefore B is F, you see how that works.

595
01:03:50,650 --> 01:03:54,880
And here's an example. The universe is like a pocket watch.

596
01:03:54,880 --> 01:04:01,990
A pocket watch has a designer. Therefore, the universe has a designer. You will you'll be familiar with that Pascals.

597
01:04:01,990 --> 01:04:06,890
No, it's not pastel. What is it? Palely.

598
01:04:06,890 --> 01:04:13,940
Thank you. Uh. So the universe is like it was a pocket watch.

599
01:04:13,940 --> 01:04:20,360
A is the universe, B is a pocket watch.

600
01:04:20,360 --> 01:04:27,290
A is F. I've got this the wrong way round, haven't I?

601
01:04:27,290 --> 01:04:36,080
Here's your homework, take that argument and put it into into proper canonical, logical form.

602
01:04:36,080 --> 01:04:41,900
Come back and tell me where I've got that wrong visa. I've got several quite interesting little errors in there.

603
01:04:41,900 --> 01:04:47,270
Some of them are just in the logic that I'm using. And some of them I've just transposed various things.

604
01:04:47,270 --> 01:04:52,780
It should be easy for you to see where I've gone wrong. Do it.

605
01:04:52,780 --> 01:04:58,300
And come on, if you want to come to cheque that with me next week. I'm very happy to have a look at it.

606
01:04:58,300 --> 01:05:14,270
OK, George. Come up with your own argument from analogy. Got time for one or two, perhaps.

607
01:05:14,270 --> 01:05:23,570
I only someone over here has not Strunsky so far. Yes.

608
01:05:23,570 --> 01:05:27,830
OK. That would do. One of your premises isn't true. Well, actually, no.

609
01:05:27,830 --> 01:05:32,630
Yes. One of your. Well, I suppose a universe is like a cabbage, isn't it, in a room, roughly.

610
01:05:32,630 --> 01:05:38,960
So shape wise. Okay, well, that would work. Yep. One more.

611
01:05:38,960 --> 01:05:43,280
Sorry, elegant. So Tricia's like Sylvia.

612
01:05:43,280 --> 01:05:47,330
She's so good. Yep. Absolutely.

613
01:05:47,330 --> 01:05:53,330
That'll do good. We've got that. Let's have a look at another inductive. Can you see how that's inductive, by the way?

614
01:05:53,330 --> 01:06:03,720
Why is that? Why does that depend on the principle of the uniform uniformity of nature?

615
01:06:03,720 --> 01:06:10,900
Well, it's again, we're assuming if one thing is like another in some ways, then it'll be like another in other ways.

616
01:06:10,900 --> 01:06:15,280
So we're we're assuming the uniformity of nature, aren't we?

617
01:06:15,280 --> 01:06:20,620
So if it's like that in one way, it'll be like that in another way as well.

618
01:06:20,620 --> 01:06:26,680
Here's another argument, an argument from authority. Einstein is a brilliant physicist.

619
01:06:26,680 --> 01:06:31,090
Einstein says relativism is true. Therefore, relativism is true.

620
01:06:31,090 --> 01:06:36,310
Of course, we could put in a different thing here. Einstein says pacifism is the right creed.

621
01:06:36,310 --> 01:06:39,850
Therefore, pacifism is the right creed. What have we done there?

622
01:06:39,850 --> 01:06:46,570
We've changed a good argument to a bad argument. Why is one good and one bad?

623
01:06:46,570 --> 01:06:54,250
Because he is an authority on physics. That's right. And he isn't an authority on politics.

624
01:06:54,250 --> 01:07:00,460
So but we'll be looking at good and bad arguments from now on after next week.

625
01:07:00,460 --> 01:07:06,610
OK. Causal arguments. We look to cause ligaments briefly. Last week, every time an A occurs, a B occurs.

626
01:07:06,610 --> 01:07:11,320
Therefore, A's cause B. Now we have a huge tendency.

627
01:07:11,320 --> 01:07:16,690
And in fact, that tendency was manifested here last week in this very room, wasn't it,

628
01:07:16,690 --> 01:07:22,120
where we assume that where there's a correlation, there's also a causal relation?

629
01:07:22,120 --> 01:07:28,690
Well, we know that that's not true, is it? We know that there can be correlations without causal relations.

630
01:07:28,690 --> 01:07:34,810
But even so, we tend to our evidence for causation tends to rest on the correlation.

631
01:07:34,810 --> 01:07:41,770
So if every time it occurs a B occurs, we'll tend to think that A's cause B's.

632
01:07:41,770 --> 01:07:51,490
So we argue from observation of a correlation to an assertion about her, a causal relation.

633
01:07:51,490 --> 01:08:02,020
And just to say quickly that causal arguments can be deductive or inductive, depending on whether we're arguing from a causal claim or to one.

634
01:08:02,020 --> 01:08:05,860
So A's cause B there was an A.

635
01:08:05,860 --> 01:08:18,350
Therefore, there will be a there will be a B every time every observed A has been followed by B, therefore A's caused B, which of these is deductive?

636
01:08:18,350 --> 01:08:25,510
Left or right, my left. That's left deductive inductive.

637
01:08:25,510 --> 01:08:31,280
Yeah. That's right. Can you. That's. We're taking calls here what we're saying.

638
01:08:31,280 --> 01:08:37,040
We're arguing to a causal claim, aren't we? From observations of correlation.

639
01:08:37,040 --> 01:08:42,230
And here we're arguing from a causal claim. Indeed.

640
01:08:42,230 --> 01:08:47,840
The conclusion of that one to a particular claim.

641
01:08:47,840 --> 01:08:52,910
Okay, so that's deductive.

642
01:08:52,910 --> 01:09:01,370
Well, you should be able to do this. Okay. That's deductive. Because if that's true, if that's true and that's true, then that must be true.

643
01:09:01,370 --> 01:09:06,710
Okay. This is this might be true and yet this be false.

644
01:09:06,710 --> 01:09:10,870
But even so, that is reason to believe that, isn't it?

645
01:09:10,870 --> 01:09:19,140
Okay. It's just not conclusive reason. Whereas these are conclusive reason to believe that.

646
01:09:19,140 --> 01:09:23,940
Right. Your task for the week ahead.

647
01:09:23,940 --> 01:09:29,640
See if you can find in your newspaper, magazine or Baucau or wherever.

648
01:09:29,640 --> 01:09:38,130
I've said for. But that's entirely arbitrary. Just see if you can find some arguments that fit the patterns that we'd be looking at today.

649
01:09:38,130 --> 01:09:44,670
And you might also notice in your own behaviour, as you're talking to people, you'll find yourself.

650
01:09:44,670 --> 01:09:51,630
And I'm hoping to sensitise you to these logical words so that they can't go will go past without you.

651
01:09:51,630 --> 01:09:58,710
Thank you. So when you find yourself saying if, then that's a particularly good one,

652
01:09:58,710 --> 01:10:07,440
if then or therefore or since or things like that, catch yourself and try and work out what your argument was.

653
01:10:07,440 --> 01:10:12,210
Now, some of your argument is going to be far too complicated to work out like that at the moment.

654
01:10:12,210 --> 01:10:18,870
Stick to simple ones safe and find yourself offering a simple argument, if you dare.

655
01:10:18,870 --> 01:10:23,100
I said if you don't clean your room, then this would happen. You did not clean your room.

656
01:10:23,100 --> 01:10:25,170
Therefore, you know,

657
01:10:25,170 --> 01:10:33,280
this this sort of thing is what you're trying to find out for and have a look and see if you can fit them into the forms that we've given here.

658
01:10:33,280 --> 01:10:37,890
Okay. And next week we're going to look at actually identifying arguments and setting them out.

659
01:10:37,890 --> 01:10:43,230
Logic bookstall. We've been doing that today, but we're going to do that with some rather more complicated arguments.

660
01:10:43,230 --> 01:10:48,480
Next week we're going to look at arguments that you might make in the pub or in a newspaper or something like that.

661
01:10:48,480 --> 01:10:52,080
We'll look at a few magazine leaders and things like that. Sorry.

662
01:10:52,080 --> 01:10:56,862
Newspaper leaders. That's it.