Okay. And now we're on week two, and this week we're going to look at different types of arguments.
And in particular, we're going to look at deduction and induction.
These are two basic types of argument, and we'll be looking at different examples of each type.
Welcome back, everyone. So it didn't put you off entirely last weekend? Difficult though it was.
I'm sure it was difficult. Let's do a quick recap of last week so we can remember where we were.
If you remember, I said that arguments are sets of sentences such that one of them, the conclusion, if you remember,
is being said to be true and the others called the premises are being offered as reasons for believing the truth of the one.
Or reasons for believing the one. Okay, so that's what an argument is.
And I said it was important to distinguish arguments from two things.
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.
Can anyone remember what they are? No.
Intersession isn't an argument. An assertion is the second thing from which you should distinguish arguments.
So I said that there are two sets. I think you misunderstood my question slightly.
Whoever it was then. So there are two things from which you distinguish arguments.
But the first one is sets of sentences.
And I said that there are two things, two types of sets of sentence that you need to distinguish from an argument.
Can anyone remember what those two types of sets of sentences were?
Sorry, Peter. No. No. No.
Okay, maybe that's not a fair question. Okay. The first one is sets of sentences that aren't related at all.
Do you remember I talked about sea as salt in Melbourne. Melbourne's in Australia.
Well, until you are therefore in a bit of context, that's not an argument, is it?
It's just two unrelated sentences. And the second type of sets of sentence you should distinguish from arguments are those that are related,
but not as an argument is related, not as the sets of sentences that constitute an argument are related.
So in order for a set of sentences to be an argument,
it's got to be related in the sense that the conclusion is being said to follow from the premises.
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.
If it's if that relation isn't being said to be that, then it's not an argument.
The second thing from which you must distinguish an argument is it is a sentence.
And can anyone remember how you distinguish sentences from arguments or one way,
at least in which you would distinguish a sentence from an argument is.
What do you mean by premise that a premise has a very particular definition,
that the definition is that a premise is a sentence that's being offered as reason for believing the truth of the conclusion?
So what the questions is here is how do you distinguish a sentence or assertion from an argument?
A sentence. You could see as an incomplete argument, I suppose.
But that's not what I was thinking of. Certainly there's no conclusion.
Nothing being. Well, there is something being postulated. If the sentence is being asserted.
Isn't the. There's no relation, that's right.
But okay, look, let me look, hang on, there's one more that but the.
Say that again. That's right.
This is just a statement and a statement isn't an argument.
Is it? A statement isn't good or bad? Well, it could be, I suppose, couldn't it?
A statement is true or false. And an argument is good or bad.
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.
The only thing that can be true or false is the sentences that make up the arguments.
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.
But notice, it's the premises that are true and the conclusion that's true, not the argument itself.
The most the argument can be is truth preserving. OK, so that's distinguishing arguments from sets of sentences and from sentences themselves.
What we're going to do today is considered different types of argument.
And we're going to start using some of the concepts that you've already mentioned this morning.
So there are two basic types of argument. There are deductive arguments and they're inductive arguments.
This is a very basic type of argument because you'll see later there are lots of other types of arguments in these categories.
But these two categories are the most important. These are the ones you need to get a grip on.
Okay, let's look at deductive arguments first. Now, these are such that the truth is their premises guarantees the truth of the conclusion.
So if the premises are true, then the conclusion must be true, because if it's a good deductive argument, it's truth guarantying.
So here's a deductive argument. You'll be familiar with this one.
We used that last week. It's Friday. Marijan always wears jeans on a Friday.
Therefore, Marianne is wearing jeans. Notice that the conclusion of this argument is it's true.
But neither of the premises are. So that that should give you an idea that the argument is a good one.
The conclusion is true. But actually, neither of the premises are true.
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.
That's right. It's not Friday. Therefore, that premise is false. It's not true.
You'll have to take it from me on the authority that I don't always wear jeans on Friday.
I do happen to be wearing jeans today.
But of course, that's irrelevant because it's neither Friday nor is it the case that I always wear jeans on a Friday.
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.
Can you think of any situation? I really try and use your ingenuity here.
Let's see if we get in which that would be true. Okay.
It isn't true. We know that. But we're assuming for the sake of argument that it is true.
So imagine a situation where that's true and that's true for some reason.
I always wear jeans on a Friday. Could that be false?
Can anyone think right be? Well.
Well, that would that would not make that not true. Well, that sounds very Mary.
No, no, it doesn't. I may not. I may hate wearing jeans. That may be nothing to do with it.
I may wear jeans as a penance on a Friday because I once did something really ghastly and said to myself, right.
Okay, from now on, I'm always going to wear jeans on Fridays. So it doesn't say that I want to.
Can anyone think of a counterexample? OK, so it's true.
It would be Friday on that day, but would this be true? No, it wouldn't, would it?
So we've given what we've given there is a falsification of that. Not a counterexample to the argument.
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.
Preserving this of the argument. Lots of us can think of situations where that's false or whether that's false.
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.
And that's false. It is, isn't it?
Well, on the couple of other examples. Let's try one. So I'm on the moon or something like that.
Very ingenious. I think what we do what we're talking about is a situation where all these are.
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.
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?
No, it won't do. But we do not need to guarantee it because all we're doing we're saying this is true.
If this is true and if this is true, we're not saying this is true.
I mean, this is another very important distinction when you're doing logic.
You're you're not talking about the actual truth value of a sentence.
OK. So the truth value of that could be either true or false.
Do you see what I mean? So that's the value of its truth. It's either true or false.
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.
And as you rightly said, actually, if these two are true, it's impossible for this to be false.
It really is, isn't it? Well, if we're looking at an argument, we're saying we're asking ourselves two questions.
The questions are, does the conclusion follow from the premises?
And in asking, that's what we're asking is if the premises were true, would the conclusion be true?
If the premises are true? Would the conclusion be true?
And if we look at these two premises and we ask that question, we're not asking whether the premises are true.
We're saying if they're true. Would the conclusion be true? And the answer is yes.
Can everyone see that this is a deductively valid argument?
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.
Now, in this particular case, this is not very useful because it's all hypothetical.
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.
It's Friday. Mariane always wears jeans on a Friday. Therefore, Marianne is wearing jeans.
Then if you see that, I'm not wearing jeans. What do you know?
One or other of these isn't true. Exactly. So if you see that Marianne isn't wearing jeans,
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.
So, you know, either your hypothesis is false or your observation is false or.
Oh, sorry. Well, you're quite right. Or both. That's right.
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.
And that's why truth preserving this is useful.
Whatever the situation is, even if it turns out that delusions false anyway, again, that's something we'll talk about more next week.
The only thing that's important for now is that you understand what a deductively valid argument is.
You understand that it's truth preserving that if the premises are true, the conclusion must be true.
Okay, everyone happy with that? Let's move on. Okay.
You should know instantly that deduction is an either or thing.
Either an argument is deductive or deductively valid or it's not OK.
There's no in between there. It's one or the other.
A good deductive argument gives us conditional certainty, certainty conditional upon the truth of the premises.
Well done. I can feel you getting it now. Okay. A bad one tells us nothing.
Because if the argument isn't a good one, if it isn't truth preserving, then the conclusion could be either true or false.
And we really don't know. Okay, so that's deduction.
Let's move to inductive induction, inductive arguments as such that the truth of their premises makes the conclusion either more or less probable.
Okay. It doesn't give us certainty. Makes the conclusion more or less probable.
Now this means that inductive arguments can be either weak or strong.
Okay. So here's an example of a strong inductive argument.
The sun has risen, risen every day in the history of the universe. Therefore, the sun will rise tomorrow.
Okay, that's a strong inductive argument. Why isn't that a deductive argument?
So what may not be true, because arguments can't be true, of course, can they?
This may not be true. OK. But but we're saying if this is true, then this will be true.
So why is that? Not deductively certain. OK.
So this could be true. And yet this false. And yet this is a good argument.
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.
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.
But some. It's a it's old, right?
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?
And then you say, but we can't be 100 percent certain because who knows, the sun may explode tomorrow.
Or maybe the law that ensures that the sun rises every morning and she has a bit of a dogleg in it.
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.
And from then on, it's only going to rise every other day. Okay.
For the rest of the history of time, do we know that that isn't what the laws.
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,
won't tomorrow miss a day that we.
Well, it makes it weaker, but it means that we haven't got certainty.
This could be true and this false. But it's a different type of argument.
You mustn't think that because deductive arguments are certain, an inductive arguments aren't that therefore,
inductive arguments are somehow inferior because actually they're dealing with different things.
This is the sort of argument that science deals with, isn't it?
You observe that nature has been like this all the times before and then you
extrapolate into the future to assume it's going to be like that in the future.
So every daffodil you've ever seen in your life so far has been yellow.
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.
I hope my genes just Friday are safe because there's a woops, sorry, I'm going the wrong way.
This is the argument, right? An argument is a set of sentences. There are three sentences in this argument.
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.
This will be true. Okay. And this one, the inductive argument is saying, if this is true, this will be true.
OK, now, in this case, we can say, but there could be a counterexample to this.
The counter example might be that the sun explodes tomorrow or that the law of nature has
had written into it from the history of time that it'll change tomorrow of all days.
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?
I mean, I could give you an inductive argument that goes like this, in fact, let me give you one.
Every time I've seen Marianne, she's been wearing earrings. Therefore, next time I see Marianne.
She'll be wearing earrings. Okay, now.
Is that a strong inductive argument? No.
Well, it's not very strong, is it? I mean, the next time you see me,
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.
So the next thing you know, we know too much about the world, about people,
about earrings and things like that to know that that's good inductive argument.
Well, let's go back to this one and notice that here we're arguing from this not to it.
Okay. This is a premiss in our argument, not a conclusion. OK, whereas if we're looking here.
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.
How do we get to this? We've seen the sunrise every single day.
We've seen lots of observations. And therefore, we naturally extrapolate to a generalisation like this.
This is a different form of reasoning. This is inductive reasoning.
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.
Here's another one who takes a lucky rabbit's foot into an exam.
If they ever go into exam, who used to take your lucky racquet rabbit's foot into exam?
Who has a lucky red jumper or something like that?
We've all had the experience of something's really nice happening to us and we were wearing something or carrying something.
And we think, you know, maybe I'll wear that again.
I'll be lucky again because we extrapolate from what's happened in the past to what's going to happen in the future.
I've lost you, I can see. I can. I'm looking at your faces and you've gone right.
The only thing you need to remember is that a deductive argument. You've got certainty.
Because if the premises are true, the conclusion must be true.
In an inductive argument, you haven't got certainty, you've only got probability.
Okay, this ARG, this premiss gives you probable reason to believe this.
If this premise is true, this conclusion is probably true.
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?
This is a very weak inductive Olguin. This this gives you some reason for believing this, but not very much.
Have a look at these. Go through. I'm going to give you a couple of minutes to do them on your own.
So you really try and work this out for yourself, decide which of those are deductive arguments and which of those are inductive arguments.
And then we'll have a look at them together. So the sun is coming up.
Well, actually, let's do them together. I think that's probably easier at this point.
Let's have a look at the sun is coming out. So the rain should stop soon, which is the conclusion of that eye.
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.
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.
So the the premises, the sun is coming out. Therefore, the rain should stop soon.
Now, just the truth is that premiss make the truth as a conclusion certain.
No, you can't have more or less certain. Sorry. It's more or less probable, but not more or less certain.
Okay. So this is inductive or deductive. Put up your hands if you think it's inductive.
Yay! You see. I knew. Got it. Really. Okay.
Good. That's the end deal. What about this one. Let's do it the canonical way.
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.
Can you make that a proper sentence? John won't be at the party.
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.
There are two parts to premises here. One is, Jane, is that the party?
And the other is if Jane is at the party, John won't be at the party.
Notice that that's a complex sentence that's constituted of two sub two sentences within the sentence.
But you don't separate those two to make them two different premises because the sentence being asserted as if,
Jane, is that the party, John, won't be. That's the premise. Good.
Okay, so we've got an argument that goes if Jane is that the party, John, won't be at the party.
Jane is at the party. Therefore, John won't be at the party. Is that deductive or inductive?
Put up your hands if you think it's inductive. OK.
Put up your hand using his deductive. Well done.
OK, so you are getting this. Okay. It's the site. The house is a mess.
Therefore, Lucy must be at home. What's the conclusion? Just Lucy must be at home.
The ZET therefore just marks the conclusion rather than being the conclusion.
Okay. Lucy must be home premiss. The house is a mess. Inductive or deductive.
Put out your hand. If you think inductive. Well done.
Can you give me a counterexample to that argument? Yes, that's right.
OK. So the house is a mess, but Lucy isn't at home.
You've had burglars instead. Good. Okay. I think he's in the bathroom or the bedroom.
He's not in the bathroom, so he must be in the bedroom. Conclusion's obvious.
It must be in the bedroom. And the two premises, either he's in the bathroom, all the bedroom.
He's not in the bathroom. Okay. Deductive or inductive?
Deductive. Well done. Okay. Dog would have bought it if it saw a stranger.
It didn't bark. So it didn't see a stranger. Deductive.
Good. No one in Paris understands me. So my French must be rotten or the Parisians are stupid.
Sir, I got this from a book inductive.
Okay. It's difficult that one, but it is inductive. You're quite right.
Because what's the conclusion? That's right.
It's actually a complex conclusion, isn't it. My French must be rotten.
All the Parisians are stupid and on the premises. No one in Paris understands me.
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.
OK, good. So you have actually got it. Even if we got tied up in a few knots there.
No. Not in safety. Right. Logicians study deduction by studying valid argument forms.
And now it's very important to distinguish form from content.
Okay. And arguments are deductively valid in virtue of their forms rather than their contents.
Now, that's not true of all deduction, but it's true of most deduction.
So let's have a look. What I mean here, all men are mortal, Socrates and man.
Therefore, Socrates is mortal. OK. All actions that produce the greatest happiness to the greatest number.
I got very bored writing it out. So the greatest happiness is greatest number.
All actions that produce the greatest happiness, the greatest number are right. Morally right.
That is, that action produced the greatest happiness of the greatest number.
Therefore, that action was right. Okay. Can you see that the form of those two arguments is exactly the same?
Can you see that? So the content of the two arguments is quite different.
This is an argument about Socrates and mortality. And this is an argument about morality and the greatest happiness of the greatest number.
Completely different topics, completely different content. But each of the arguments has the same form.
Can anyone try and write down the form? Tell me the form of that argument.
This the structure of it. Do you not know what I mean?
No. Okay, let's do it together. All A's are B.
S isn't a, therefore, s is a B. Did you get that?
All A's are B, so. Aye, aye.
Let's stir an interpretation here. Aye aye.
Equals. Let's do it properly here.
X is a man. X is mortal.
S is Socrates, and the form this is all A's are V.
S is an A, therefore S is a B with me.
Let me do it again. Can you see unsighted? So if this is the interpretation, this is.
I've just changed the words for symbols here. And the symbols are only letters.
So a A of X says X is a man.
X is mortal. Is B an s. Is Socrates. So all A's are B.
S is an A. S is therefore. S is a B you with me.
So it's safe to do that for the other argument. What would we have to say that A is there.
Good X is A is an action, B, X is.
Difficult. Gone. Produce.
No. Okay. All men are mortal.
All actions that produce the great suffering disgrace number are right.
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.
No. So all men are mortal and all actions that produces.
Right. Happiness. The greatest number. Right. You with me.
So all A's, all men are B's mortal.
All A's actions produce a gross happiness. Gross number.
All right. OK. And then the next one, that action produced the greatest happiness.
The greatest number. You've got Socrates. Here is a particular thing, just as that action is a particular thing.
OK. And you're saying that particular thing is a man, i.e., falls into this class here.
And therefore, he falls into the other class, too. Okay.
So both those arguments have the form. All A's are B.
S isn't A, therefore S is a B. Now, the point of this is just to get you to distinguish form and content.
Can you see that an argument can have different forms. And yet the same content.
Sorry, different contents. And yet the same form. OK. So these are two arguments of exactly the same form, different contents.
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.
It's always the same. Logic is the same. Whether you're talking about the colour of chairs, whether you're talking about biochemistry,
whether you're talking about the philosophy of time, doesn't matter what you're talking about.
If an argument is valid, it'll be valid by virtue, its form, whatever the topic is you're talking about.
So logic is the ultimate transferable skill. If you've learnt logic, you can do it with whatever you happen to be talking about,
whatever it is you're interested in, whether it's art history or fashion.
Right. Okay, let's have a look at a few argument forms.
Here's a valid argument form. If P, then Q p.
Therefore Q. What's pee standing in for here?
What type of thing is it standing in for? Can anyone tell me a good or a sentence?
I was going to say, but the premise is even better. Yes, well done. So this is one sentence.
What's this? No.
No, not even that it's. Oh, actually, I am. That's a premise.
Actually, that's a premise. That's only a sentence. Can you see why?
That's right. OK, so if P, then Q is one premiss, P is the other premiss and Q is the conclusion.
So all we done then sort of thinking about actual sentences we've just put in what are called sentence letters.
Any letter will do. Doesn't matter, just so long as you get the form of the argument.
Right. Can you think of an argument that fits that form.
OK. Just think for yourself now of an argument that fits that form.
You could use one that we've already used. You could use one to do with the colours of the chair in this room.
Quite difficult. But see if you can think of one Gontran. I'm happy.
I am. Therefore, I will see. Give her a clap.
Well done. That's exactly right. Can anyone think of another one? No, there's no all there.
No. Just the impossible. Cannot. If the impossible cannot happen, then.
No, you're not quite getting the idea. Now, this will be happening to lots of you.
This is not just just you. The form is if sentence.
Then sentence. Sentence. Therefore, sentence.
And these two have got to be the same sentence. These two have got to be the same sentence.
So the form of this has got to be if P, then Q P, therefore.
Q Think of another one thing. You think to yourselves first and then then when you feel confident that you've got it.
Put your hands up and we'll try. This is really doing logic.
So did he. If you find it odd. That's right.
It's in the nature of the beast. Are you?
Well, sit down and think for yourself and then try again. No, you've just said you didn't.
No, sir. Okay. Go on, Nusaybin. And the chairs are blue, then these chairs and.
No, that was an F, P and Q, wasn't it?
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.
If then and or not, that's hugely important.
Have you got one. Sir.
Okay. If he gets a bus then he's ecofriendly. He does get a bus.
Therefore he's ecofriendly. Good. Well done, Paul. If it rains, I raise an umbrella.
My umbrella is up. Therefore, it is rain. Oh. Something wrong with that?
What was wrong with it? Now that the sentences were great?
Say it again, though. OK.
OK. So Piers, it is raining. OK. Q is I raise an umbrella.
He now was paying my umbrella is up.
What was P? It's raining. So what do you need there instead?
It is raining then for your brother. Do you see what you were doing?
Those you are committing the fallacy of affirming the consequent very common fallacy.
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.
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.
Do you have another if this.
I'll take my son, so therefore I'll take my alterable.
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.
It is sunny. Therefore, I'm taking my dog for a walk.
Okay. Now, that has to be valid, doesn't it? Sorry, that has if those premises are true,
that conclusion has to be true because any argument of this form must be a good argument is deductively valid.
Everyone else wants to try another one. Good.
OK. If the postman is striking, then we will have no letters.
The postman, all striking, therefore will have no letters. So P is.
The postmen strike. No, not if because the F. OK. The postman striking and Q is.
We will have no letters. So if the postman is striking them, we'll have no letters.
The postman are striking. Therefore we'll have no letters. Good.
Okay. One more and then we'll move on. This is looking good.
That's right. If he's breathing, then he's alive. He is breathing. Therefore, he's alive.
OK. Yeah, good. OK. Dead easy, isn't it?
Once you get the idea of it. And here's the story.
So again, the light.
The third part of the dead parrot.
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.
There are no chance factors in chess. Therefore, chess is a game of skill.
What s p here? Go to what's queue.
Good. Well done. Here's another argument, OK?
That was Motus opponents, by the way. So you know how to do.
No, no, no. Just pens his most toplines, the mode of denial.
If P then Q not Q, therefore not P.
Okay, if P then Q not Q therefore not P.
So this is saying in effect that P is sufficient for Q.
Sorry. I've I got it the wrong way round.
And it is absolutely like he must be. Now, I have got it right.
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.
Right? Well, let's have a look at the example and then you can come up with your room.
Actually this example is wrong because that shouldn't be in there.
But let's, let's do it. If the dog didn't know the visitor well the dog would have barked.
Okay. The dog didn't bark. Therefore, the dog did know the visitor.
That shouldn't be in there. That's the one that I was saying I'd got wrong before we started.
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.
Write that down. I think it's 16. Yep. Because that's that's incorrect.
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.
It's a good guide. Dog got guard, dog, guide, dog, dog.
It didn't bark. Therefore, it must have known the visitor well, mustn't it?
OK, so see if you can come up with something of that form now.
I'll take the example out, so it's not confusing. Have you come up with an already.
Well done. Fantastic. Absolutely right.
So, Piers, I have money. Q Is I would be in the pub sat right.
I'm not in the pub, therefore I have no money. If I had if I had money.
So having money would be sufficient for you to be in the pub, ok.
But you're not in the pub, therefore you haven't got any money. Okay, anyone else want to have a go?
Gentlemen. Good.
You've got it, I think. Does anyone else want to have a go? Or does everyone feel that they've got.
That was it. Sorry.
Say it again. If the sun is out, I will take my dog for a walk.
OK, so here's the sun is out and Q is I'll take my dog for a walk.
Oh, I'm sorry. Those of you who saw the error.
That's quite right. Okay. What should be here? I'm not taking my dog out for a walk.
Therefore, the sun is not out.
Yep, that's right. Good. Okay. Try one more than us. We've got that as I got it wrong.
Yes. OK. No, we are not in the wrong place there, didn't we?
How did it go again? If I'm hungry, then I won't concentrate.
I right. It will be I will write this one down because there are knots in there that we need to get.
Right. Because as you say. OK, so pee is. I am hungry.
Q is. I can't concentrate. OK.
Notice that we've changed. Q The Q is actually a negative here.
That's where we're. It's very easy to get tied up. So be very careful of this.
Negatives immediately make things quite difficult. So but Nipon, we can do it.
Okay. So. Q is I can't concentrate now not. Q Therefore is I can concentrate therefore I'm not hungry.
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.
I've forgotten who and who said this. So I'm looking at all the wrong people. But okay.
One more on this one, because it is quite difficult, Paul. Oh, actually, we had you, Paul.
So do we have you for. Okay.
Good. OK. If I've if I catch my train, though, so I start again.
If I missed my train, I'll be late. I'm not late.
Therefore, I haven't missed my train. You don't have to use the same words as always, you.
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.
Or do you see what I mean?
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.
Do you see that?
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?
This is quite hard enough without adding layers of complication in.
Okay, good. You did that well. So what have I got? Well, we've already tried that.
Good. Let's try another one. This is a disjunctive syllogism.
P or Q, not P therefore.
Q Okay. I have got that one. P or Q, not P, therefore Q.
OK. Oh, good. Look at you. Hands going up immediately, no.
No. Brilliant. OK.
It's either raining or it's sunny. It's not raining.
Therefore, it's sunny. Good. Well done. On Battement.
I know some suicides. I have a hunch. It's not up to them.
Good. Well done. Anyone else? Good.
OK. I think you've got it one. Good.
Well done. OK, I've noticed that that works.
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.
And if this was either, this has got to be either or hasn't it?
If it were not both, you couldn't get the conclusion, could you?
So that that's where English can me lead us to stray a little bit because English is itself ambiguous.
Okay, here's my example either. This is actually Bertrand Russell example.
Either we hope for progress through improving morals or we hope for proof, progress from improving intellect, intelligence.
We can't hope for progress through improving morals. Therefore, we must hope for progress through improving intelligence.
What this should tell you instantly, we've been looking at very simple ones. But actually, these forms can be very complicated.
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,
you listen to your television or argue with your friends in the pub or whatever you happen to do.
And I want you to to try and identify arguments that come up whenever you hear the words, if then and or not.
If and only if all these logical words. All is lovely, logical words.
Just you got to be sensitised to them this week because I want you to.
You have to every time you hear this, then I want you identifying the form of the argument in which you find it,
cause it might not be in an argument might it might be just a free-standing assertion.
But have a look, see if there is an argument there. This is second second sentence.
Yes. Each of the premises is an asserted sentence, a sentence that's being asserted as it is.
So Russell is saying, you know, it's true that either we hope for progress this way or we hope for it this way.
Okay. There's no other option. We can't hope for it this way.
He's asserting, therefore, we must hope for it that way.
Okay. Well, what's incorrect?
Hang on. What's false here? So is it the first premise, let's start to use the language now?
Is it the first premise that false or the second? Well, I'm pretty intelligence isn't a sentence on appears here and here.
So what? So is that the false premise sold that one?
Right. I think I'm going to put this on one side because, A,
we're not really looking at the truth of the premises and B, you've got to take the premises as they are here.
This is what's being asserted. So we're not saying this is true or that this is true.
What we're saying is, if this is true and this is true, then this must be true.
Okay. These conditionals are very important decision by presupposition.
What will get onto that later on?
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.
OK. Let's move on. Here's another one like Nitz law.
A is F, A equals B, therefore B is F.
I'll give you my example of that. It's quite difficult. One, Jane is tall.
Jane is the bank manager. Therefore, the bank manager is tall.
If these are true. Is that true. Has to be.
Doesn't it. Can't be anything else. Don't think of a couple of examples of that one.
Go for it. Don't spark. No, I don't think it's going to work.
Why is that not going to work? Let's see. Why is this not going to work?
Well, dogs bark doesn't have the form. A is A is.
F is. The chair is blue. Marianne is tall. The board duster is lost, etc.
Not a dog. You could say the dog.
The dog is barking, but dogs bark is saying of one class of things that they fit another class of things.
And that's not the form of that sentence is it. This chair was comfortable from this chair.
Gone. Not quite. No. What we've got here.
This is a very interesting ambiguity here.
Is is a very slippery word. In English is you can have the is of predication and the is of identity.
And your attempted argument there. And don't worry about this at all.
This is a perfectly reasonable mistake to make you equivocated between these two is.
So you said this chair is blue. Is that right?
Right. Then you said this chair is comfortable. OK.
Now this. Well, actually, those those are both houses of predication, aren't they?
Whereas what we're looking for here is an is of identity, isn't it?
A is B is the very same thing as B. So here we've got a predication, haven't we?
A is F. A has a certain property. And here we have this thing.
A is the same thing as this thing. B, therefore B is F K you see how that has to be true.
This is a it's a law of logic. This one isn't it. This is life and it's law.
It is a law of logic. If A is F. If Marijan is tall.
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.
Here's an is of Prescod predications. So we're predicating tallness of Jane Artley with me.
And here we've got the issues of identity, haven't we? Jane is the bank manager.
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?
Yes, that's exactly that's what we're doing.
We're looking at two examples of deductively valid arguments, arguments that are valid by virtue of their form.
OK, good. One last one, I think. Here's a syllogism. Now, this should be easy.
All FSG A is an F, therefore A is G. All Fords are cars.
Okay. A is a Ford. Therefore, A is a car.
Yes. Well done. That stuff too. And you'll also want to give one more example and we'll move on.
Good. I see where you're getting to. Yeah. The grandma got a bit mixed up.
But yes. Okay. So all my clothes are wet. That's pair of jeans is one of my clothes.
Sort of. Therefore it is wet. I see where you're coming from.
Okay. You've got them. Okay.
All miracles are impossible. Resurrection is a miracle.
Therefore they're OK. It works doesn't it. Well done. We knew we'd get there somewhere.
It's deadly this. Let me just give you a logical problem with that just because I think you might enjoy it.
You said the resurrection is a miracle, therefore the resurrection is impossible.
And there's something very logically fishy about negative X and true negative existential sentences.
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?
In which case, how can a negative system should be true? See what I mean?
Hamlet doesn't exist. You're picking out something. Hamlet.
In order to say off him that he doesn't exist. Well, how can you do that?
You shouldn't be able to do that. I'll just leave you with a little conundrum, because that's philosophical logic.
And we're not doing that here. We're doing symbolic logic here. So now you know of two different types of logic.
Okay, we've. This is the canonical example for that one.
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.
Here's just a couple that are valid in virtue of their content, apparently.
Dale Tech logic. Now, this is cutting edge stuff we know very little about.
Day on tech, logic logic. Day on tech. Logic is the logic of morality.
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?
How can we get a valid argument form from more talk of morality?
Now, look at this argument. Lying is wrong. Therefore, we shouldn't lie.
Now, that looks like a deductively valid argument, doesn't it?
In other words, if that's true. Surely this must be true as well.
But if so, it's not true in virtue of its form. It's true in virtue of its what could you say?
Lying is wrong. But I'm going to lie. Well, we all know that you could lie.
But if you say if you truly believe that lying is wrong, you're also going to believe you shouldn't lie.
Now, that doesn't mean you won't lie. But you'll feel guilty for doing that.
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?
Do you think you could possibly believe that lie? Really believe that lying is wrong and yet not believed that you shouldn't lie.
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.
You do think lines wrong or you don't want to feel any shame at all.
Which manifests manifests the fact that you don't believe that lying is always and everywhere wrong being wrong.
Oh, don't get me on that. I'm not going to follow that one up at all.
Oh, it's very important. Yes, but we're not. But but actually, we can safely leave it on one side here.
You if you're a Kantian, you think that this entails that instant.
You might want to put another premise in here. You might want to say we shouldn't do things that are wrong.
Did someone want to do that? Okay. Kant would say if you did that, you would.
You're manifesting the facts that you think that you could believe that something's wrong without believing you shouldn't do it.
And that just shows you don't understand what wrongness is.
To cance to have the proper moral concept, which is that, you know, lying is wrong or something like that,
you cannot believe that something is wrong without also believing you shouldn't do it.
So it doesn't mean you won't do it, because we all know that we do things we believe to be wrong.
But but your belief that it's wrong will manifest itself as guilt.
And if it doesn't, it manifests the fact you do not believe the first thing that lying is wrong.
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.
And it looks at that sort of inference and noticed that that's can't.
We can't give you a form for that. That's the very meaning of the word wrong.
There's something very special about the meaning of the word wrong logically.
Here's another one. Modal logic. Modal logic is the logic of necessity and possibility.
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.
If it's square. It's not circular and so on. Therefore, it's not possible that there are square circles.
So if P is necessarily true, then not P is not possible.
Can you hear that you or your capacity for reason would follow that quite quickly,
if A is necessary, then not A is not possible not to be the case, hasn't it?
So again, we have a deductively valid argument, but it is not deductively valid at least.
Actually, we're a lot further on with modal logic than we are in day on logic.
We can do quite a lot with modal logic these days. And here's a bit of temporal logic for you.
It's raining today. Therefore, tomorrow it will have been raining yesterday.
Is that true? Okay. If that's true, then that must be true, mustn't it?
Couldn't not. And that's because of a temporal logic. The way the logic of time works.
Okay. Let's move on to a bit short of time here.
Let's we'll move on to inductive arguments now, inductive arguments.
You remember, what's the hallmark of an inductive argument is if the premises are true, the conclusion might be true.
It probably is true. That's right. Okay, so the premises give us reason for believing the conclusion, but not in this case, certainty.
They don't give us conclusive reason for the really cute conclusion.
And that's because inductive arguments rely on the assumption of the uniformity of nature.
That's what Hume called it. David Hume. The idea that the future will be like the past.
So if we've seen the sun rise every day in the history of the universe, we expect it to rise tomorrow.
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,
we'll carry on doing that. And if we come on the seventh week, we'll be disappointed, sadly.
Okay. It was quite a good reason for believing that Marianne would be lecturing on Monday
at 2:00 that she has been lecturing at 2:00 every Monday for the last six weeks.
But it's not conclusive. And so on.
So we're we are one of the biggest problems of philosophy, in fact,
is how do we justify can we justify this assumption, the assumption that the future is going to be like the past?
Why should we think that the future has been like the past? Can anyone give me a reason exactly?
Because it it has always been the case that the future has been like the past in the past.
So that's a circular. Yes, exactly.
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.
The only reason we think that that works is because it always has worked in the past.
Therefore, we assume it will work that way in the future. But human beings just cannot not argue like that.
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.
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.
If you stop it, it stops. You don't catch it just slightly.
It was interesting. Anyway, that's what inductive arguments rely on.
OK. Tell me why this one. Tell me what it is.
We're assuming that you this is a silly question. In fact, I don't like this question.
I'm going to skip it.
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.
And the assumption here is that because in your experience, Marianne's always done this in the future, Marianne will always do this.
But our background's knowledge comes in to say whether you think it's a strong argument or a weak argument.
And I think you'll see that given what we know about physics, about astronomy, about the laws of nature,
cetera, that is a strong argument given what we know about people and what they wear.
That's a weak argument. But both of them rely on the assumption of the principle of the uniformity of nature.
And there are sub categories within the category of inductive arguments.
Here's one an argument from another analogy. A is like B, A is F, therefore, B is F.
OK. A is like B, a notice.
These smaller lowercase letters stand in for particular things, whereas letters like this stand in for either properties or sometimes sentences.
But I tend to use P, Q, R for sentences and A for.
Oh, actually, that should be a smaller case now.
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.
And here's an example. The universe is like a pocket watch.
A pocket watch has a designer. Therefore, the universe has a designer. You will you'll be familiar with that Pascals.
No, it's not pastel. What is it? Palely.
Thank you. Uh. So the universe is like it was a pocket watch.
A is the universe, B is a pocket watch.
A is F. I've got this the wrong way round, haven't I?
Here's your homework, take that argument and put it into into proper canonical, logical form.
Come back and tell me where I've got that wrong visa. I've got several quite interesting little errors in there.
Some of them are just in the logic that I'm using. And some of them I've just transposed various things.
It should be easy for you to see where I've gone wrong. Do it.
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.
OK, George. Come up with your own argument from analogy. Got time for one or two, perhaps.
I only someone over here has not Strunsky so far. Yes.
OK. That would do. One of your premises isn't true. Well, actually, no.
Yes. One of your. Well, I suppose a universe is like a cabbage, isn't it, in a room, roughly.
So shape wise. Okay, well, that would work. Yep. One more.
Sorry, elegant. So Tricia's like Sylvia.
She's so good. Yep. Absolutely.
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?
Why is that? Why does that depend on the principle of the uniform uniformity of nature?
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.
So we're we're assuming the uniformity of nature, aren't we?
So if it's like that in one way, it'll be like that in another way as well.
Here's another argument, an argument from authority. Einstein is a brilliant physicist.
Einstein says relativism is true. Therefore, relativism is true.
Of course, we could put in a different thing here. Einstein says pacifism is the right creed.
Therefore, pacifism is the right creed. What have we done there?
We've changed a good argument to a bad argument. Why is one good and one bad?
Because he is an authority on physics. That's right. And he isn't an authority on politics.
So but we'll be looking at good and bad arguments from now on after next week.
OK. Causal arguments. We look to cause ligaments briefly. Last week, every time an A occurs, a B occurs.
Therefore, A's cause B. Now we have a huge tendency.
And in fact, that tendency was manifested here last week in this very room, wasn't it,
where we assume that where there's a correlation, there's also a causal relation?
Well, we know that that's not true, is it? We know that there can be correlations without causal relations.
But even so, we tend to our evidence for causation tends to rest on the correlation.
So if every time it occurs a B occurs, we'll tend to think that A's cause B's.
So we argue from observation of a correlation to an assertion about her, a causal relation.
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.
So A's cause B there was an A.
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?
Left or right, my left. That's left deductive inductive.
Yeah. That's right. Can you. That's. We're taking calls here what we're saying.
We're arguing to a causal claim, aren't we? From observations of correlation.
And here we're arguing from a causal claim. Indeed.
The conclusion of that one to a particular claim.
Okay, so that's deductive.
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.
Okay. This is this might be true and yet this be false.
But even so, that is reason to believe that, isn't it?
Okay. It's just not conclusive reason. Whereas these are conclusive reason to believe that.
Right. Your task for the week ahead.
See if you can find in your newspaper, magazine or Baucau or wherever.
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.
And you might also notice in your own behaviour, as you're talking to people, you'll find yourself.
And I'm hoping to sensitise you to these logical words so that they can't go will go past without you.
Thank you. So when you find yourself saying if, then that's a particularly good one,
if then or therefore or since or things like that, catch yourself and try and work out what your argument was.
Now, some of your argument is going to be far too complicated to work out like that at the moment.
Stick to simple ones safe and find yourself offering a simple argument, if you dare.
I said if you don't clean your room, then this would happen. You did not clean your room.
Therefore, you know,
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.
Okay. And next week we're going to look at actually identifying arguments and setting them out.
Logic bookstall. We've been doing that today, but we're going to do that with some rather more complicated arguments.
Next week we're going to look at arguments that you might make in the pub or in a newspaper or something like that.
We'll look at a few magazine leaders and things like that. Sorry.
Newspaper leaders. That's it.