So I. Right, then I think we ought to sort.
Um, so welcome to everyone here. Welcome to everyone on the podcast.
Um. Um, anyone who didn't get the, um, thing I sent out last week about the, um, argument that we tried to do.
Can you email me on that address and I'll bounce it on to you?
Um, and I'll make sure that the thing that I sent out to everybody here is also available online for the people looking at the podcast later on.
Right? Um, well, this week we're going to do different types of arguments.
Um, so versus last week we learnt how to set out arguments, logic, book style.
Do you remember how set done. What is it for an argument to be set out?
Logic books. Style. Come on.
We've got to get you warmed up, haven't I? Previous time to conclusion.
That's right. You. So you identify the premise and the second premise if there is one, and the third premise if there is one.
And then the conclusion. That's right. And the way I did it was just to label then premise one, premise two.
Conclusion. But you could just put the premise one, premise two and then align and then the conclusion.
There are different ways of doing it. Um, okay.
We dealt with ambiguities. Hold on one second.
How much did you miss? Okay. Uh, right.
We we dealt with ambiguities. Remember, there were different sorts of ambiguity.
What is ambiguous? Can anyone tell me? Start off with what is an ambiguity?
Two or more. It's a word or phrase that has two or more meanings.
That's right. So it starts in the context where it is.
It could mean two different things, which is very confusing.
And there are different types of ambiguities. Can anyone remember a couple of these types?
No. I was so sorry. Linguistic.
Um. No. What do you mean by linguistic?
You might have different meanings for. For example, is. Right.
Okay. That's lexical. A lexical ambiguous is one word which could mean different things.
So rum could mean the drink or, um, this is strange or something like that.
Or we use the example of bank, um, which could be all sorts of things that it could be a verb was, was a noun, all sorts of different things.
And then it also structural ambiguities where you have every particular love to say that, um,
does it mean there is a sailor such that every girl loves him or every particular love some sailor?
Um, so there are different sailors who loved by themselves or just one.
Um, and then there's ambiguity. Cross-reference. Does anyone remember what that is?
Or anaphora? You might have been taught in school and, um, before it references, when, um, you have a pronoun that links back to a name.
So, um, just subject comes to party because she doesn't like, uh, do you remember that?
She becomes ambiguous and the hook becomes ambiguous.
Okay. And then there are ambiguities of of just of sounds.
So the picture of water that you remember could be a picture or a picture with a title of other difficulty,
something that's a picture of water or a picture drawing of water.
Um, we then uh, to identify conclusions and premises.
Um, we learnt there that although that sometimes there are a conclusion on premise indicators,
what's the only foolproof way of identifying the conclusion of an argument.
Okay. So role innocence.
The role is it plays within the arguments from within a sentence.
Because of course a conclusion will be a sentence. That's exactly right.
So, um, what role does play by the conclusion? It's the census that is.
That's being asserted. Exactly. So. And the premises, which you can also tell in a foolproof way, only by rule that they are wards.
Three the reasons being given. So the conclusion that you said okay.
And we then we went to eliminate relevant seats. And that's where we got into a bit of hot water, isn't it.
Because you were all accusing me of throwing things out, uh, just for fun.
Um, but I hope that those of you who got the thing that I sent around see that actually, what make something relevant or irrelevant is the conclusion.
Because once you've identified the conclusion that you have the arguments because the premises are the reasons for that conclusion,
and anything that isn't the reason for that conclusion is irrelevant, isn't it?
So even if it seems very important, like God, I mean, what could be more important than God, perhaps?
Um, I'm afraid he gets left out. If what ever said about God is not a reason for believing that conclusion.
Um, we identified suppressed premises, and we saw that sometimes you have to put a suppressed punch in, and sometimes you don't.
When do you have to put it in its context?
Well it's controversial. Good. That's right. Because you can't leave it out as an argument.
If it's controversial, it would weaken the argument to have it in because it's controversial.
Um, when can you leave the premises out? But it's understood from the general context,
and it's obvious when it's blindingly obvious when all you'll be doing is sort of eking out the argument.
So I'm going to take my umbrella, you know, do I have to say,
because it's raining and if I don't take an umbrella, I'll get wet and I don't want to get wet.
Um, no, of course I don't. You mean you understand immediately when I say I'm going to take my umbrella?
Um. And finally, we learned how to make terms consistent.
What did that involve? Going to rain.
Uh. That's right. We had something like two words that meant the same thing.
Or two phrases that meant the same thing. So it's raining and it's pouring.
We could just choose one of them and get rid of the other, because that's all it does is confuse us.
Um. And we did the same thing with the cat is innocent.
Um, and the cat hasn't since, um, I said, in the context of this argument, there's no difference between them.
Um, okay. So that's that's what we did last week. Um, bit of revision for us.
Um, so now we know what arguments are, and we can distinguish arguments from other sets of sentences to remember,
we can distinguish them from, um, conditional sentences.
For example, um, we can analyse arguments and set them out.
Logic book solve. Um, okay.
So, so if you're not too badly, I'm for lecture three.
Uh, but we haven't yet asked on how to evaluate arguments.
And that's important because some of you last week were having trouble with the analysis of an argument because as you were analysing it,
you were trying to evaluate it as well. So you were saying this premises isn't true.
Well, maybe it's not. Um, but all we're interested in at the moment is whether it's a premise or not.
We're not interested in whether it's true or not at the moment, but we will be.
Um, so we're not even going to be able to start on analysis this week.
What we're going to start on this week is looking at two different types of argument.
And it's very important to to be able to identify the two different types of arguments.
So we're going to the first the normativity of critical reasoning.
Uh um uh of course I'll explain what normativity means.
We're going to look at the relation of following from uh, we're going to look at the two main types of arguments.
Um, and we're going to learn how to distinguish these two types from each other.
Deductive arguments from inductive. Um, so in critical reasoning we're concerned with whether or not an argument is good.
So importantly, it isn't a purely descriptive discipline.
A purely descriptive discipline is one that tries to say what the world is like.
So zoology, for example, will attempt to describe a different species.
So it will tend to categorise living things into species, uh, and into geniuses and so on.
And then it will try and describe each species and so on. But it doesn't really get into shoulds.
Um, in, um, biology, I mean, you might get into a situation where all you mean by should is you'll talk about normal,
um, some things being normal, you'll say you're really talking statistics.
So cats, uh, cats should have four legs.
You might say, well, yes, indeed they should. Statistically, most cats do have four legs, but this isn't a moral should.
Um, and so whereas with critical reasoning, uh, we've got a what's called a rational should, it's normative.
It lays down standards for us to follow. A good argument is an argument we want, and we want it because it is good.
So critical reasoning is a normative discipline.
Um, we're interested in when a conclusion follows from a set of premises and when it follows recessive premises, it's good.
Okay. So we're interested in arguments that are good. Um, and that's what an argument follows from a set of premises.
And we're also interested in which arguments are bad. Um, I mean, you need to be able to identify bad arguments as important.
These are doing good ones. So following from is a very important relation between premises and conclusion.
And there are broadly two varieties of following from um that's what we're going to learn to distinguish from each other today.
Um both deduction and induction. Uh varieties of following from.
So conclusion may follow deductively from a set of premises.
Or it may follow inductively from a set of premises.
And really these two types of arguments exhaust the types of arguments.
There are there are arguments within each type. But but deduction an argument is either deductive or it's in.
Up to um, and there are three questions you can ask to determine whether an argument is deductive or inductive.
Um, here are the three arguments. I'll let you. Sorry. Three questions that you need to ask.
And of course I'm going to look at each and explain them. Okay.
Anyone have any questions so far? Nope.
Okay, let's, um, write. The first property that distinguishes deduction from induction is the fact that a good deductive argument is truth preserving.
Unbiased deductive arguments aren't truth preserving, and inductive arguments are not truth preserving at all.
So if an argument preserves the truth, it is a good deductive arguments.
If it doesn't, it may still be a detective argument, but it's a bad one, and no inductive argument ever preserves the truth.
So what do I mean by an argument? Speaking truth preserving?
Well, an argument is truth preserving if and only if, and that I double f is not me misspelling if.
By the way, whenever you see I double f, I suppose it could be an error, but it usually means if and only if.
Um. So uh um, you get the f going in both directions if p than q and if q, then p.
So an argument is truth preserving if and only if it's not logically possible for its premises to be true.
Well, its conclusion is false. Okay. So it's a very strong relation.
Uh, this is the relation of entailment. So premises entail the conclusions when it's not logically possible for a set of premises to be true.
And a conclusion is false.
Um, and just before we look more closely at that, you've got to be able to distinguish logical impossibility from physical impossibility.
This is actually crucial for a lot of philosophy, but it's particularly crucial for critical reasoning because it's slower and slower.
I'm not going too fast. Okay, okay.
Um, so okay, let me go back to this one.
An argument is truth preserving if and only if it's not logically possible.
So this is why you've got to know the difference between logical impossibility and, um,
physical impossibility if it's not logically possible for its premises to be true and its conclusion false.
Um, so we've got to be able to distinguish logical impossibility and physical impossibility.
Uh, by the same token, logical and physical possibility.
Something is physically impossible if it's inconsistent with the laws of nature,
and it's logically impossible if it's inconsistent with the laws of logic.
Um, um, something's inconsistent. Two things are inconsistent if they can't both be true together.
Okay, so, um, if the laws of nature are as they are, um,
something is physically impossible if it can't be the case consistently with the way the laws of nature are and with physical,
uh, logical impossibility. It's the laws of logic that matter.
So it's physically impossible for a human being to swim three miles underwater without breathing apparatus.
Do you see that? If somebody told you that done that, you would know that they were not speaking the truth because it simply can't be done?
Um, it's also physically impossible for A to talking intelligently about cats.
I mean, even even Oedipus. I talked to him about cancer.
Yes. He still doesn't talk back intelligently about it, or even I'll intelligently to that.
Um, but both these things are logically possible.
Logic has nothing to say about with my cat discusses Kant,
and it has nothing to say about whether you can swim under water for three miles without breathing apparatus.
Um, it's logically impossible, on the other hand, for a square to be a circle.
Um, so all those people, like my father talk about squaring the circle.
It's nonsense. You cannot square a circle because if something's a square, it cannot be a circle.
And you can tell that just from the very ideas involved.
Uh, an a man can't be a married bachelor, because if he's a bachelor, he's not married.
And if he's married, he's not a bachelor. Just like if something's a square, it's not a circle.
And if it's not a circle, it's not a square. We know that.
And we know that a person can't have exactly three and exactly four children.
These things are ruled out by logic. Um, in other words, it's in the very nature of the concepts square and circle,
marriage and bachelor and so on that we don't need to leave our own chair to know that there are no square circles.
This is why it's so comfortable to be a philosopher. Um, so here's an exercise.
Give me two examples of states of affairs that are logically possible but not physically possible.
Can you do that? Can you give me two examples? Of states of affairs that are logically possible but not physically possible.
So if you remember, one example was that my cats can't talk intelligently about cats.
Uh, and another one is this a human being can't swim for three miles underwater without breathing apparatus?
Another example like that. The sunset over froze to death.
The sun so hot you froze to death. I'm not sure that isn't a logical impossibility.
I mean, because you're working on the words freeze and hot, aren't you?
And actually, they logically exclude each other. Don't like, um.
Don't have a good pace. Comply. That's a very good one.
This Pink Floyd pace, as far as logic is concerned.
Fine. Pigs. All fine. But yes, there are no pigs that can fly.
Um, okay. Uh, yes.
You must be looking at the. Okay. And the other examples.
Yes. You mean like it? I believe I believe that you believe you did it, but I didn't like you sort of see it.
Yeah. Yeah, yeah. Hey, can anyone think of another example of something that's physically impossible but logically possible?
I can jump to the meat. Uh, good. It's logically possible for you to jump to the moon.
But it's physically impossible, isn't it? Yes. Good. Okay.
I think you're getting the idea. Anyone else want to have a go? I saw through the wall.
You saw through the wall? Good. Yeah, that. That's physically impossible, but logically it's fine.
Um, so there are lots of things like this that are physically impossible, ruled out by the laws of nature, but not ruled out by the laws of logic.
That's false. And of course, there may be worlds out there that have different laws of nature.
Um, and so when we want to know what's going on in those worlds,
it's to logic that we look not to the laws of nature, because they're not going to tell us what these worlds like.
Uh, can I only get two examples of state, some things that are logically impossible?
Okay, so you might see it being frozen by a hot sun might be a logical impossibility.
Anyone think of another logical impossibility? So it's, uh, it's raining cats and dogs.
Uh, funnily enough, that's that's a physical impossibility is not a logical impossibility.
Actually, it does rain frogs occasionally, I understand, but it actually does.
Burnt by ice. Um, being burnt by ice ash.
It's just. I know what you mean by burnt, doesn't it? But actually, if you put your tongue on the ice, the, um, in the Antarctic, you will.
You are in trouble. Um, and it's actually called a burn, isn't it?
Um, yeah. A female born, a female boy.
Yes. That's a good example of a logical impossibility.
Yeah. Okay. Any anything else?
It's quite difficult just thinking of examples. But I hope you're getting the idea of the difference between physical and logical impossibility.
Logical impossibility is inconsistent with the laws of logic.
It's actually ruled out by the very concepts involved and physically possibilities ruled out by the laws of nature.
So whereas, um, the logical impossibility can be determined a priori.
In other words, we don't need experience of the world to determine what a logical possibility is is all you need is two concepts.
Um, with physical impossibility, you need to know what the world is like.
Science tells us what's physically possible and impossible.
Um, so what about these? By means of genetic manipulation, we can produce pigs that are able to fly.
Is that physically impossible? Logically impossible? Or are we unable to tell physically?
Is it it's physically impossible? That's right. I mean, actually, maybe by genetic manipulation, we will produce pigs in five days.
Um, we think we want some. Um, Joe has exactly twice as many siblings as Janet.
He has Susan and the twins do that.
Do you see how that's logically impossible? If somebody told you that, you would.
You think for a minute, but then you think, no, that can't be right.
And the reason it can't be right is if he's got three siblings, then he cannot have exactly twice as many as Janet has.
However many Janet has. Um, muon neutrinos can travel faster.
The speed of light in a vacuum. Physically possible.
Logically impossible to physically just wait.
Yes, for a moment. That might be not, uh, logically possible and physically possible.
Um, but some of this, uh, microscope is shaking or something.
Um, okay. Physicists succeeded in building a time machine.
Is that physically impossible? Logically impossible or such that we can't tell physically?
Um, so we can't tell on that one because it looks as if time machine time travel is logically impossible.
Because if you could travel back and kill one of your parents before you were born, then the.
Do you see the logical inconsistency that we get there?
Um, well, if it's logically inconsistent, it shouldn't be physical, physically possible.
But there are physicists who argue that it's not only not logically impossible, it's physically possible.
Um, and I actually, I if you look on YouTube, if you put in time travel physically possible,
you'll get us a physicist who believes that it is physically possible.
So I'm not going to say I think I'm inclined to think it's logically impossible.
Whereas, uh, sort of is our point about all of this in the sense of you have to almost as a caveat or that says,
given what we know today with physical impossibility, that's exactly what we have to say.
Yes. Because, um, the laws of nature, we may be able to work with them to produce a peak that can fly.
I mean, obviously we can't work against them, but that's things. Currently, sons flying pigs are, uh, against nature.
But logical impossibility, no.
Logical impossibility seems more fixed because the laws of logic seem more fixed.
But actually, um, quantum mechanics, for example, has called into question, um, a couple of the laws of classical logic.
So, um, where it says a distinction between the laws of nature,
i.e. the natural uniformity that govern our worlds and the laws of nature that we put together, i.e., uh, descriptions of the natural uniformity.
So you see the difference. So there's the laws, uh, laws, if you'd like, and the natural uniformity that we describe in the same way,
the laws of logic, there's all a description of these laws, and there are the laws themselves.
Um, we. They have the wrong description and they need to tighten it up at some point.
So we can't be sure we've got the right understanding of either type of law.
But it's certainly true with physical possibility that it's, um, malleable according to often physical knowledge.
So. Well, let me just ask other any other questions about physical and logical impossibility before I move on,
because that is it's quite an important distinction. Chris Quine produced an argument against logical certainty.
Um. So no challenge is that what he does?
Is he he's, um, he what he challenges is the existence of analytic truths.
Um, so he doesn't think that there are truths.
This is not realisable. Okay.
Um, okay. So an argument is truth preserving if and only if it's not logically possible for its premises to be true and its conclusion false.
That's the definition we had up there before.
Um, and it's important to notice that the actual truth value of the premises is irrelevant, uh, to determining whether an argument preserves truth.
So have a look at this argument. All heavenly bodies revolve around the earth.
The sun is a heavenly body. Therefore, the sun revolves around the earth.
Do you see that if those premises are true, the conclusion must be true.
Yeah, yeah. Do you see that? But the conclusion is false, as is at least one of the premises.
Okay. Do you see that? So we have an argument that preserves truth but doesn't generate truth.
Um, so that's the importance of the distinction. You've got to distinguish between an argument's preserving truth and generating truth.
And if it preserves truth, what you're saying is if there is truth in the premises, there will be truth in the conclusion.
And that suits this argument very well. So if if these premises were true, the conclusion would be true would have to be true, wouldn't it?
Couldn't possibly be false. It's logically impossible, in fact, for that purpose to be that conclusion to be false.
If those premises are true, and that's what it is for an argument to be truth preserving.
So if an argument has that property, then it's called valid.
As we'll discover next week. And the premises entail the conclusion.
Um, this is a good deductive argument.
And that's so even though the conclusion is false.
Um, can anyone tell me why? We'll look at this a bit next week, but can anyone tell me why the property of being truth preserving is useful,
even though you can end up with a false conclusion?
Why should we care that our argument should be truth preserving, even though you could end up with an argument with a false conclusion?
Because you can trace back to find the false premise.
Good. If an argument is truth preserving, you know either that it's argued that its conclusion is true if its premise is true,
or you know that if the conclusion is false, at least one of the premises must be false.
And of course, you can look back to find which premise is false.
And of course, this is all swans are white. The thing is, in Swan River in Australia, if it's a swan will be white.
Um, but it's black. Um, you know that one of your premises is false.
Um, so it can be empirically very useful to have the property of truth preserving.
This is an argument. So we can be certain of an argument that preserves the truth, that it's a good deductive argument.
So it's not just deductive. It's also good deductive argument.
If it preserves the truth. Um, we can be just as if the second argument doesn't preserve the truth.
Then it's either a bad deductive argument or it's an inductive argument.
Okay, so it could be one or the other, but it's it's certainly not a good deductive argument.
So let's do this exercise which is following arguments is truth preserving.
In other words is a good deductive argument.
Have a look at them yourself and put your hands up when you think you've got the answer to one.
Let's say. Hands up when you think you've got the answer to one.
Tom is a banker. All bankers are rich. Therefore Tom is rich.
Okay, ladies. Earn. It.
That's a good. That's a good to Touch Bar. Does everyone agree?
Yep. Okay. You are absolutely right. If Tom is a banker, and if all bankers are rich, then Tom must be rich.
Mustn't eat. There's no question about it. So that's a truth preserving arguments.
Um, and it's a good deductive argument.
Therefore, um, what about Sue? And Tom leads similar lives, but Sue smokes and Tom doesn't.
Therefore, Sue is more likely to die from heart disease than Tom puts up your hand when you think you know whether that's truth preserving or not.
I'll let a few more put their hands up first. Okay, so tell us, do you think it's true, Sonny?
No, because I think it's missing something. Yeah. Um, as it says.
No. Okay. Stop there. Well, that's. It is.
No. And that's because there is a possibility that the conclusion is false, even if the premise is true.
Um, why is that? Because it doesn't make any link between smoking and what is it that needs an extra premise, right?
And this is the premise, uh, I mean, it could be a premise that we just want to leave out, or it could be a controversial premise.
What is the, um. Well, actually, no, don't ask for it.
You're quite right. There is something left out. And that premise could be true.
And that. And that conclusion is false. So we know that that argument doesn't preserve the truth.
So there could be truth in the premises, but no truth in the conclusion.
So it's not truth preserving. So either that's a bad deductible argument or it's an inductive argument.
And we'll see later, which it is. What about all dogs are mortal?
Lucy is mortal. Therefore Lucy is a dog. Which happens when you think you know.
Okay, gentlemen. They're not. It's not truth preserving.
That's right. Okay. It's actually a it's a bad deductive argument.
This one, isn't it? Um, and we'll see why it is later on.
But. Yes. Uh, so all dogs are lawful. Lucy is mortal.
Therefore Lucy is a dog. Those two premises can be true.
And yet that conclusion false quite easily, couldn't they?
Lucy might be humans and mortal. Um, what about number four?
Have a look at that and put your hands up when you think you know whether it's.
Gentlemen that it's so good to have, um, everyone else agree.
So, you know, before you. So I know before, uh. I'm sorry.
I thought you were wrong, but actually, I think you're right. Can you guess wrong?
So pretty clearly involves conceptual computer code. Yeah, exactly.
So that's a good deductive argument. If that if it's true that killing is wrong and it's true that therapeutic cloning involves killing,
then it must be true that therapeutic cloning is wrong. Okay.
Uh, so if you want to deny that, you'd have to go back and deny one of the premises, wouldn't you have to say one of those premises is false?
Okay, what about number five? Hands up when you think you've got.
I'm giving this one away. Yes. All right, let's go.
What it's about. Um, no.
All you need at the moment is it's not a good deductive argument.
It's not truth preserving. Um, actually, it's not a deductive argument, as we'll see later on.
Um, every person with Huntington's disease who's been examined has had the HD gene on chromosome four.
Therefore, everyone with HD has the gene on chromosome full.
You see, that could be true. And that could be false.
I mean, it's true that it's unlikely to be false, but it could be false, couldn't it?
It could be that, um, we just haven't examined any of the HD people who have got the HD genome on prem.
So five perhaps, or or whatever. Is there any biologists in the room who can, um.
What about this one? If the liquid is acidic, it will turn this paper blue.
This liquid does not turn litmus paper blue. Therefore, this liquid is not acidic and up.
Um do that. Mhm. Yeah it is a good.
Okay. Everyone agree. Good. Okay. So we've got a feel for when an argument is truth preserving or not.
And we know that if it's true that it is a good deductive argument.
And if it's not truth preserving it's either a bad deductive argument or it's an inductive argument.
So that's the first question that we ask to distinguish deductive arguments from inductive.
But it would be reasonable to ask at this point perhaps why is deduction useful?
Um, um,
and if we believe the premise is a good deductive arguments and it's logically impossible for the premises to be true and the conclusion false,
then to believe the premises is to believe the conclusion, isn't it.
Mhm. Do you see that in a, in a good deductive arguments the conclusion doesn't go any further than the premises.
What is contained in the premises is contained in the conclusion.
So you actually in a way you learn nothing from a deductive argument to good deductive arguments.
Um, it doesn't tell us anything we don't already know. It's just it's it gives us the logical consequences of what we've already known.
Well, if human beings were perfectly rational and believed all the logical consequences of all their beliefs, then deduction wouldn't be useful.
The reason it is useful is because we're not perfectly rational.
Um, we often need consequences of our belief spelled out to us.
Um, and that's what deduction does. And I just dissolved this sentence.
I put it in. I slightly changed it to make it even better, but it came from life savings, right?
Okay. So, um. Uh. Deductive arguments.
If the premises are true, then the conclusion must be true.
There is no logically possible situation in which the premises are true and the conclusion false.
That's a good deductive argument on purpose.
So just back a little bit, um, on the on the need for the conclusion and not just the conclusion,
not linked the two premises in a way that wouldn't have happened without the conclusion.
Uh, yes. I mean, the conclusion is the logical consequence of the two premises table together links them.
Well, it links and because it you've got to put them together in order to get the conclusion.
I mean, so if you have, um, all heavenly bodies revolve around the earth, that would have, um, separable something.
It wasn't possible. Uh, no, it's it's logical that this is truth, but, uh,
but if you only have that premise without that one, then that one wouldn't logically follow, would it?
No, but you would say didn't advance knowledge anymore, but it linked premises on premise.
It links them and he can tell the lies. That's certainly true.
I mean, the fact is that that that belief is a consequence of that, a logical consequence of that belief and that belief.
So it links them because you need both of those beliefs to get that.
Does that satisfy you? Yes. Good.
Okay. Um, so, Beverly. Samberg.
Okay. The second question we ask to distinguish deductive arguments from inductive arguments, um,
is it's a matter of whether the conclusion follows from the premises an either or matter, or is it a matter of degree.
So does this conclusion follow from the premises?
Either definitely or definitely not. Or could you say, well, you know, maybe it does, maybe it doesn't.
So let's have a look. It's an either or matter. The argument is deductive okay.
So if it's either good or bad then it's a deductive argument.
If it's a matter of degree. If it's not it's not bad.
It's you know, it's better than the last one or something like that.
Then it's an inductive argument.
Let's so we know that the conclusion of a deductive argument follows from its premises if, if and only if the argument is truth preserving.
So if a deductive argument is not truth preserving, its conclusion doesn't follow from its premises.
It's either it does or it doesn't. It's either truth preserving or it's not.
It's it can't be anything in between. Um, so the evaluation of a deductive argument is an either or matter.
Either the conclusion follows from the premises or it doesn't.
There's no maybe no degrees of following from at all when we're talking about deduction.
Um, so okay, here's a good argument all by this a rich Deepak is a banker.
Therefore Deepak is rich. Do you see that if those premises are true, the conclusion must be true.
And here's the bad one. All by who's a rich? Deepak is rich.
Therefore Deepak is a banker. Do you see that those two premises could be true without the conclusion is being true.
And we can see that immediately. Can't wait to snoop on this.
No. Maybe here. One is good, one is bad, and there's nothing in between.
And that's always the case with deductive arguments. Question over here on the having one thing is can you see okay.
Well therapeutic cloning. Yes, yes. It didn't say oh, uh, let me go back and see what it did.
I think it inspired all, but let me see. Wait a few Rocky whistle a little.
Not when you say so. Killing is wrong. Therapeutic cloning involves killing.
Therefore therapeutic cloning is wrong. You mean this doesn't say all killing is wrong?
No, but it does imply it, doesn't it? I says, quite generally, killing is wrong, right?
There's no degree that the. So we would I mean, the only way you could make that conclusion false is by making that not true.
In other words, you'd have to say some killing is wrong. Most killing is wrong, but it's not the case that all killing is wrong.
Okay, can I just say, I just thought that was a good objection.
For what if you then. So there's a question of degree around the therapeutic cloning.
Sometimes it involves killing. Well, then you would be falsifying that premise.
Yeah. So with this argument's.
It's a truth preserving argument in that if that premise is true and that premise is true, then that conclusion must be true.
And if you don't think that conclusion is true, you've got to question either that premise or that premise,
and you could question them in the way that you've just discussed.
Yeah. Any questions about that?
No. Let's go on to, um, I've got my maybe one, I assume.
Okay. Um, so which one is good? One is bad, and that's always the way it's going to be.
Um, so what did you tell us about. Which is good. Um, one is truth preserving, i.e. when its conclusion follows deductively from its premises,
its premise is all conclusive reason for believing its conclusion.
Okay, it's either good or it's bad. So if it's good, then it's premises are conclusive reason for believing the conclusion.
And that's because deductive arguments. Uh, monotonic.
Okay, so here's a new word for you. This time it's a new word.
And if it's not, um, deduction is monotonic.
And what that means is that we can add anything we like to a good deductive argument without making it bad.
Good. Um. We cannot if if a good argument is good, if a good deductive argument is good, it's conclusively good.
And if it's bad, it's conclusively bad. Um, so there's nothing we could learn that would change a good deductive argument to being a bad one.
So let's have a look. Here's just good deductive argument.
Do you would you like to have a go at giving me a premise that might change that from a good argument to a bad argument?
Have a think about it. Some some bad guys.
Oh, good. Sorry. Uh, sorry.
Good. Thank you. So rich. Um.
Well, that's also, I think, a premise that's changing one of the premises there, which is not playing the game.
Sorry. Sorry.
Um, okay. I did not say that. Um, I'll tell you what.
Let me show you what I've got. What I thought you might come up with.
Because I think that might be easier. Um, you can try putting in.
What am I trying to put in there? I can't remember now. I know, it's not.
So I tried to I. It's not the case that Deepak is a banker here.
So there's the argument. First premise, second premise, some conclusion.
And I'm adding that in, in the hope that that might make it a bad argument.
Okay. Do you think it does make it a bad argument though?
Okay. It doesn't, does it? It certainly doesn't change it from, um, if all these premises are true, this conclusion is true, does it?
Which actually, if all these premises are true, anything follows from a contradiction.
And we've got a contradiction in here, haven't we. Here. Do you see.
So, so anything follows from it. And what about this one.
What have I added here? No banker is rich, so I've actually contradicted that one.
Um, but we've got exactly the same thing. We haven't we? It hasn't gone from being the case that all the premises are true without, uh,
so it's being the case that if all the premises is true, the conclusion must be true again.
So with deduction, you've got absolute comp.
It's conclusive. Uh, it's either good or it's bad and there's nothing you can do.
I'm not sure I understand that. Okay. Um.
Let's see. Let me do the bad one and see if that helps.
And if not, we'll go back. Okay, so by the same token, we can add anything we like to a bad deductive argument without making it good.
Once again, there's nothing we can learn that would change it from a bad argument to a good argument.
So, um, I think I've done that. Okay, here's a bad deductive argument.
All bankers are rich. Deepak is rich, therefore deeper. Deepak is a banker.
And I've asked again the same question. Is there any premise we could add to that that would change it from a bad argument to a good argument?
I got a couple of that I'm going to try, but let me just say, if I put something in here that's false.
Okay. Do you see that? I'm not changing it from a good argument to a bad argument.
If something in there is false and it, um, it's not the case that all the premises are true.
Therefore, the conclusion doesn't have to be true either. And if I put something in there that's true then.
Or if all the premises are true, the conclusion will still have to be true.
Let's let's try that. So I'm not convincing myself that.
Um, okay. So I put in here.
It's not the case that Deepak is a banker. So all bankers are rich.
Deepak is rich. It's not the case that Deepak just banker. So I've contradicted the conclusion there.
Yeah, yeah. Okay. Does that change it from a from a bad argument into a good argument?
And has it become truth preserving? No it hasn't.
Has this become truth preserving? No no, no.
And you'll find that nothing you can add will change it from being.
Not truth preserving to being truth preserving.
And in exactly the same way with a good argument.
Nothing you could add would change it from being, uh, truth preserving to being, not truth preserving.
Let me, um, do one more thing. So I'm okay.
You're okay. That's where I was confused as I thought that, um, you're actually making.
You still think it's a good argument? And I wasn't saying that.
I think it was a battle. What you're not doing is changing it from a good argument to evolve, or indeed, from a bad argument.
But let's have a look at, um, induction. So okay, this is what I'm claiming.
Um, either if a good if a deductive argument is good, it's premises,
a conclusive reason to believe a conclusion, there's nothing we're going to learn is going to change that.
And what is deductive argument is bad that its premises are new whatsoever to believe the conclusion.
And again, nothing is going to change that. It's either good or it's bad.
And that's the end of us. Um, and that doesn't mean that the conclusion of a bad deductive argument might not be true.
Do you see that? It means only that it's premises and no reason to believe the conclusion?
So I think I'm going to give you a, um.
So it's a fine deductive argument. If it's Monday, Mario will be wearing jeans.
Marianne is wearing jeans. Therefore it's Monday.
Um, it is about to start developing today.
Yes. Good. Thank you. I've got to the point where, um.
Okay, but is that conclusion false? No, it isn't, is it?
No, it is Monday. But it's not. Our reason for believing it's Monday.
Doesn't depend on that argument, does it? At least I hope so.
Because if it depended on that argument, too. But. So you can have a bad descriptive argument with a true conclusion in exactly
the same way you can have a good deductive argument with a false conclusion.
So if you have a good deductive argument with a false conclusion, you know what?
What do you know? If the conclusion of a good deductive argument is false.
One of the premises is false. Good. Well done. That's the question.
You still have extra pence after the first if if you claim one, your double if it's not, change history, please.
Good argument. No it would. Then you say if and only if it's Monday.
Marianne will be wearing jeans. Marianne is wearing jeans.
Therefore it's Monday. Um, you would change it from a, um.
I think that would make it a good argument. Um.
And you're changing. Yes. You know, but you'd be changing the premises.
Just curious to know that if you just change quite a tiny bit. Bit?
Well, yes, but you'd be actually making an if into an if and only if it's not making a tiny change.
It's making a huge change logically. Yeah, yeah.
Okay. So either department is good premises,
a conclusive reason to believe the conclusion it's truth preserving or deductive
argument is bad because it's premises and no reason at all to believe its conclusion.
So with deduction is always an either or matter.
Um, but no inductive argument preserves the truth.
Um, so we can't evaluate inductive arguments by appeal to whether or not they preserve the truth.
Um, the very strongest inductive argument still doesn't preserve the truth.
So we evaluate them according to how strong they are.
And of course, strength is a matter of degree, isn't it?
So here an inductive argument is strong if and only if the truth of its premises make its conclusions significantly more likely to be true.
And an inductive argument is weak if and only if the truth of its premises makes its conclusion only slightly more likely to be true.
And here are some examples. Well, actually, I've asked you a question, but I think you who who think so on the right hand side is the strong one.
I know right hand side. No, that's that's this one. Uh, but that one.
Yes. Uh. Yes, ma'am. No you're right.
Mhm. Yes. Okay. Who thinks the one on the left hand side is strongest. Is that some of the stuff?
Yes. I think that's a very strong inductive argument, isn't it?
Someone who's written every day in the history of the universe suggests it is highly likely it's going to rise again tomorrow, isn't it?
Um, whereas every time I've seen Marianne, she's been wearing earrings.
Next time I see Marianne, she'll be wearing earrings. Okay, it's probably true, isn't it, that every time you've seen me, I've been wearing earrings.
Um, but you've only seen me three times. Some of you, um.
It's not really enough. Maybe next time you come around to my house at 4:00 in the morning.
Get out of bed. I promise you, I don't wear earrings in bed.
Uh, so that's a that's a fairly weak inductive algorithm, but do you see, they both have the same form, if you like.
Um, so in each case, you'll say all the things that I've seen like this have been this.
Therefore, the next one, one I haven't seen will be like this. Um,
inductive straight is a matter of degree because one of the premises of an
argument make the conclusion more or less likely is itself a matter of degree.
Um, and inductive strength is not monotonic.
Okay, so I taught you that new word deduction is monotonic.
What that means is you can add anything you'd like to a good argument.
You can't change it from being good. You can't stop it being good. You can add anything you like to a bad deductive argument.
Can't stop it being bad. But evidence of strength is not monotonic.
The addition of a new premise to an inductively strong argument might make it inductively weak.
And I've got some examples coming up. Um, and also, the addition of a new premise to an inductively weak argument might make it inductively strong.
So let's have a look at how this works. Um, so take the relatively strong inductive argument.
Jones confess therefore Jones is guilty.
Oh you agree? Probably. That's a pretty strong inductive argument,
but then adds ten independent witnesses testify to Jones being 100 miles away from the scene of the crime at the time it was committed.
Suddenly it looks very weak, doesn't it? Um. Um.
Um, do you see that?
So what we've done is we've taken a strong inductive argument, we've added another piece of information, and we've weakened the argument completely.
Um, wait, um, Jones is a twin.
Well, uh uh, well, would you remember when I said about ambiguity,
we've got to assume that the Jones is referring to the same person, um, in the in the same context.
Okay. Or take the relatively weak inductive argument.
Jones, whose presence at the site cream site sign proves.
Therefore. Jones, just go to the cream. Okay. Um, and ask the which which I think you'll agree is weak inductive argument.
Yes. Okay. And the extra premise, uh, Smith, the policeman who tried to stop Jones killed the man, saw Jones plunge the dagger.
I was hopeful with that one. Um, suddenly a weak argument looks very much stronger, doesn't it?
Um, so induction is not monotonic.
You could you can strengthen and weaken inductive arguments by discovering new information.
You can't do that with deduction. Deduction. If it's good, it's good, it's bad, it's bad.
And that's the end of it all. You in danger?
They're turning the doctor argument into a deductive argument by the addition of the additional statement.
Um, it's very easy to turn inductive arguments into deductive arguments by adding the right premises.
Uh, have I done that here? I would have thought you're in danger of doing that in the second statement.
Well, no, not if Jones died of electrocution. Okay.
And he might have done mine pretty consistently with that has been kind of a good I mean, I haven't actually said what the crime is here.
Okay. Um. Yes.
I may not be. You could come back to me on that one if you want to later on.
Okay. So let's have a look at this. This is, uh, exercise three, which is very similar to exercise two.
Um, what we want to know now is whether it's being good or bad as a matter of degree or a matter of, um, either or.
Um, whereas last time you identify the good deductive arguments, um,
now you could also identify the bad deductive arguments and distinguish them from arguments.
So Tom is a banker. All bankers are rich, therefore Tom is rich.
What's that? Let's go to deductive us as it was before.
Yeah, it doesn't change. Um, Sue and Tom lead similar lives, but Sue smoke.
And Tom doesn't. Therefore, Sue is more likely to die from heart disease than Tom.
Stick your hand up when you've got the. When you think you've got the answer to that.
And. So what we want to know.
We know that it's not a good deductive argument from the last time.
But is it a data? It is a bad deductive argument.
Or is it an inductive argument? So it's inductive.
Exactly. So we could what could we add to that to make the conclusion much less likely?
Why would you want to make people suffer? Well, just because if we can.
We know it's inductive. Oh, yeah. If we.
If we can't, we know it's. So what? What could we add to that?
You could have the Thomas go to that hall. Um, all the Thomas all all Thomas family died of heart disease.
Died young of heart disease. Yes. That that would immediately change the strength of that argument, wouldn't it?
So as it is, it looks pretty strong. Um, but we can weaken it immediately by giving it a bit of Thomas family history.
So it's a question when it, um, when it suggests that. So, um, Tom Latimer lives.
Um, probably if you leave the first statement out.
Uh, it might be stronger because Sue smokes and then Tom doesn't.
So obviously, Sue is more likely to die when it suggests that Sue and Tom lead similar lives.
Uh, is not true because she smokes and he doesn't.
It isn't it? Well, they could lead some lives apart from that.
I mean, they could both exercise, both eat lots of fruit and vegetables, but not eat much animal fat.
Um, okay. What about all dogs are mortal.
Lucy is mortal. Therefore Lucy is a dog. Put your hand up. If you say you know whether that's a bad deductive argument or an inductive argument.
Uh, deductive. It's bad inductive bias. How do you know that?
Because the premises. Uh, tell me more. Well, you have, uh.
It's not true. It's not true. Uh, true. So is it.
It's not truth preserving. And in fact, the premises are no reason whatsoever for believing the conclusion all day.
So whereas with the first one, the premise is a conclusive reason for believing the conclusion,
with the third one, the premises are no reason whatsoever for believing the conclusion.
Okay, that's a bad deductive argument. What about number four?
Can we we know that's a good deductive argument, don't we?
Okay. What about number five? Is that a bad deductive argument or an inductive argument to indicate that it's inductive?
That's right. Okay. So every person with Huntington's disease who's been examined has had the genome chromosome full.
Therefore everyone with HD has the HD gene on chromosome four.
Um, what would we want to. I mean, could you add anything to that to make it a bad inductive argument?
I mean, as it stands, it looks pretty strong. What might we do to change it into a weak one?
We've been examined. Yeah. Yeah, exactly. If we've only examined five people, then it suddenly looks a lot less strong.
Good. Okay. And the last one was a good inductive.
Deductive good. Okay, so we now know that if an argument preserves the truth, it's a good deductive argument.
If an argument doesn't preserve the truth, it's either a bad deductive argument or it's an inductive argument.
And we know that if an argument is either good or bad, with no matter of degrees or no maybes, um, then it's a deductive argument.
And if it's being good or bad, it's a matter of degree that it's an inductive argument.
Okay. So that's we've looked at our first question and our second question.
Now let's look at the third. So the third question was can we evaluate the argument a priori.
Now to be able to evaluate something a priori is able to say whether it's good or bad or true or false or whatever, something normative.
Um, without experience, without needing to go and look at the world.
If you'd like, you can do it simply from, um, logic on its own.
Um, um, the opposite is a posterior. All right.
Which is when you have to actually go and look at the world.
So let's have a look at this. To be able to evaluate, uh, an argument a priori is to be able to tell whether the argument is good or bad by
appeal only to the structure of the argument and to the logical words used in it,
um, without need of any information about the world.
Now, you might as well say you need information about language, and that indeed is true.
So you need some information about the world. Um, but you don't need more than information about language and meanings.
Um, so these are the logical words.
And if then not or and if and only if, um, there are other logical words, but we wouldn't worry about those at the moment.
Um, and this gives you an indication of what's meant by the structure of an argument.
So here's an argument we use last week. Um, if it's snow, the mail will be late.
It is snowing. Therefore, the. Will be late. Can you see that?
If you, um, want to take. It is snowing.
He. Then you've got f p under the chair again and the male will be late.
Becomes cu. So if P then cu p 30.
Do you see the structure of the occupants? Um, can be brought out just by taking away the sentences in the argument.
Leaving the logical words. Um, okay.
Is this is good argument. Put your hands up when you've decided, rather than yelling out.
Put your hand up when you've decided up. So I can see it. Because.
Because I'll ask when there's a sort of critical mass of people who know, they'll think they know.
Okay. What do you think? Is it a good argument? Yes. Yes it is.
Isn't it good? Does anyone know what it means?
Which it is or what it is for something to be possible?
No. Okay, good. I'm not surprised because I made them up.
Um, but you see that actually, the content is completely irrelevant to your ability to evaluate the arguments.
Um, you really don't need to know anything about the subject matter in order to be able to say that that argument is good.
And the reason for that is that what makes that argument good is the way the logical words itself combines.
It's the structure of the arguments. It's nothing to do with the contents of the arguments.
And that's true of all deductive arguments.
All deductive arguments can be evaluated a priori.
Um, so oh, here's another one. Okay.
Is this a good argument? No no no it isn't.
And you can tell that because this is actually a Bob's deductive argument.
Whereas the last one was a good deductive argument. Um, and it's interesting to note that the facts deduction is a priori.
Actually means that it's topic neutral. Um, this is what makes logic or deductive logic anyway such a useful transferable skill.
Because it doesn't matter what you're talking about, what you're thinking about.
Um, if you can recognise a deductive argument, you will be able to evaluate it.
Even if you know nothing whatsoever about the subject matter.
The subject matter is completely irrelevant to evaluating a deductive argument,
because what matters is the logical words and the way that combined, excuse me in the first premise.
Who's speaking? Um, okay. In the first press, um, of the last one of the nonsense words that, um, if which is a positive and I'm having a negative.
Then the first premise in those terms stands up.
But it's nonsense. Well, um.
What you're doing is you're trying to put content in that's going to make it's nonsense.
But it's already nonsense, isn't it? I mean, you don't need to do anything to make it not cold.
It's nonsense already, but it's still a good argument for bad arguments or whatever is is.
What was causing you always cold? Which is a positive then?
Which is a negative. And that is a premise that cannot stand up in logic.
Well. It's true. No, it's the contents.
It's. The logic is what you're saying is it's false.
Yes. Yeah, but. Well, actually, it's not even false because it is meaningless, isn't it?
But if you if widgets are positive, then widgets are negative.
Mm hmm. I mean that that's nonsensical. It doesn't have meaning.
Yes, but you only know that from the content that you're putting in there.
And my aim in using this is to show that you can decide whether something is a good argument or not.
Without knowing what the content is like a is about.
So wanting to put in some content that doesn't make sense is not changing my arguments at all.
So you could use positive and negative if you said they were positive. And negative meant well, is what I mean.
Why yes. I mean why would you? Okay.
If my aim is to show you is that you can tell whether an argument is good or bad
and deductive argument is good or bad without knowing what the content means.
I take it that I because you were able to see that the first argument was good, and that the first second argument was bad.
I take it that I've proved my point. Yes. Okay.
Now I could go back and discuss, but I'm inclined not to,
because I don't see why changing one nonsensical argument into another nonsensical argument is going to gain a something.
Okay. May I move on? Yes. I'm not sure if I've dealt with your better.
Perhaps we can talk afterwards. If you. If you replaced it with P's and Q's.
And it's clear what is clear with all of these positives.
But you say all soon. Well, yeah. Let me carry on.
Now I'm going to, um, replace things with P's and Q's.
Uh, all of these I could show you. How do you see these two arguments have exactly the same structure.
Yeah, know. Not because anyone wants to deny that.
Can you help me work out? Well, the structure is using P's and Q's.
Let's use that one. Um, he is p and q, then q p p.
Therefore. Therefore q q q.
And so here means it is snowing and q means the mail is late.
What's P in the second document. Yeah.
Yeah. And I mean the the actual produces the greatest happiness is greatest.
Um, but what's Q if he's right it's or the act is to remove the cross-reference the actors.
Right. Yes. Exactly. So so we've got exactly the same structure.
Does the basis arguments stuff into it? Why don't you use p q uh, instead of r an X or something?
Uh, yes. It's just convention that. Yeah. Yeah, it's a convention to do with pigs and queens.
No no no no no no I, I think so.
And actually some people would use um s ends here just because saying begins with s and then the mail begins to say um,
but it would be then less relevant to that one.
Um, so it's convention that we use P and Q. Okay.
So hang on here because not all widgets I've ever seen have been having, um, therefore all widgets are having to.
Okay. Can we tell whether that's a good argument or not to the fact that we can't, can we.
Why not? Doesn't she don't say in the world you don't know how many widgets you see.
You don't know what widgets are and you don't know what it is.
Do we have another? And you I mean, no, just you do need to know what the content is,
and you need to know something about the contents in order to be able to evaluate that argument.
So with a deductive argument it can be evaluated a priori, i.e. on the basis only of its structure in the logical words um,
if it can only be evaluated by appeal to some background information, some, um, information that you have, then it's an inductive argument.
Okay. Um, so, um, inductive arguments can be evaluated only a posteriori.
And in the light of an understanding of the content of the arguments, uh, and by bringing to bear background information about the world,
so long as you can strip the content out of the deductive arguments and still determine whether it's a good or bad argument,
there's no way you can stretch the content out with good inductive arguments and still hope to evaluate it.
So can we evaluate these arguments a priori or not?
Um, Jennifer is tall. Jennifer is the bank manager.
Therefore the bank manager is tall. Put your hand up when you've decided whether it can be evaluated a priori.
Okay. What do you think? Yes it can. Yes it can.
Okay. So the it's the structure of that argument that tells us whether it's, um, a good argument or not.
So is it good? Yes. Yes, it's a good argument, isn't it?
What about crocodiles is dangerous. James's dog is dangerous.
Therefore James's pet is crocodile. I think I was getting tired of this.
Uh, can we evaluate that argument? Can't we?
Yes. It's, uh. Uh, it's a bad job.
Too long, doesn't it? We can see this is bad. We don't need to do anything.
Um, it's wrong to tell a lie. Just tell your mum her hair looks good.
Was a lie. Therefore, Jane's telling her mum her hair looked good, was wrong.
Um, can we can we evaluate that argument a priori or not?
Yes, I think we can. It's such a good one.
Yeah, it's it's another good deductive argument.
Tomato plants are to be fed well, kept warm and watered frequently, usually thrive.
This tomato plants must be fed well and watered frequently. But it's dead that all this tomato plant hasn't been fed properly.
That's interrupted. Yes. Um that's inductive.
Um, might not be careful because you want to know why it's bad.
Yeah. Why is it bad? I mean, is it just that I can just out of its pot?
Um, okay. Yes. We need to know a little more about that situation.
Wouldn't we would need to have some background information. Um, what about this one?
This looks familiar. If this liquid is acidic, it will turn.
It was paper blue. This liquid turns litmus paper blue.
Therefore, this liquid is acidic. It's good for just about the last two springs.
Well, hot and sunny. But the summers were awful. This spring was hot and sunny.
Therefore, this summer will be awful. Yeah.
Why? Do we need to bring to bear background information?
What sort of background information will we need to bring to bear with the school counsellors?
With the data? What we didn't know.
We need more information. We need more to use with that information. Yes.
We would want a lot more than two years, wouldn't we? In order to generate that scenario?
Yes. Go back to five. Yes.
If the liquid is something other than acidic, it like to paper through two.
Um, what are you bringing to bear? To be honest, one analysis.
Let me have a look at that. Um, so I think to the point where it's actually quite difficult to, to know.
So if P then Q oh, that's a bad deductive argument.
Yeah. Do you why did we say it was a good one? Yeah, yeah.
That's because the last one that talked about newspaper in the city.
No, that's a bad argument. Can you see that. It's um, it's P then q q therefore P, which is not if p that q p therefore q.
Yes. Do you see. Yes. Got to be careful about that.
So that's, that's um, a policy of affirming the consequence.
Um, um, what would happen later on? I'm not sure that's me is good to talk to, but it's wrong to tell a lie.
Jane's telling her mum her hair looked good was a lie. Therefore, Jane.
Uh. It is. Well, it's just not why you say that is wrong.
I think it so let me let me just, um, see if it is.
Uh, so p is it's wrong to tell a lie.
Um. Oh, actually, no. Uh, I'll have to do it.
Um. I'm going to have to go into the predicate calculus.
Excuse me a second. Um, sorry. Okay, here's my interpretation.
F of x x is a lie. Okay of x x is wrong.
An x, which is a, um, a thing.
An action. In this case, Jane's telling her mom her hair looks good.
So we've got, um. Uh, all x.
If, uh, X is alive, then X is wrong.
Okay, that's the first time. Is, um. L x x is a sorry, l s x is a lie.
Do you see? We've got that. And therefore w x s rather.
Both of those offices. So. Everything is such that if it's a lie, it's wrong.
See, that's the first premise. Um, s is a lie.
Jane's telling her mom her hair looks good, is lying. Therefore S is wrong.
James telling her mom her hair looks good is wrong to be straight.
Good deductive argument. Sorry to see the logic.
Oh, good. But in reality, the premises are opening.
Oh, well, but we're not evaluation purposes. Yeah, we're we're not evaluating the arguments at the moment.
Uh, I'm not saying anything about whether the premises are true or false.
I mean, if widget samplers. Yeah. Nonsense.
Uh, what is positive? Can you go? Oh, sorry. So I wonder wonder, uh, would it make any difference to five if you put if and only if at the beginning,
it would always make a difference to change it to a different.
Only if always. I mean, I found that students, when they first start formalising something, um,
will immediately reach for a double arrow, which you see if and only if, um,
when actually all there is is an if or all the rest is an only if and actually
if and only if it's very different to if and it's different also to only.
Um so yes it would make a huge difference. Doesn't make it deductively valid or a good argument.
Um, it's exactly the same as one we had earlier when somebody was talking about, if, you know.
So if you have, if, if this liquid is acidic, it will turn litmus paper blue.
This. Yes it would be. Yes. Yes. Good. Yeah.
Uh, okay. So right. That's sort of the question asking for a right.
That's good. Two for the price one. Yeah okay.
Ooh exercise to do at home already. Right.
Well we got in that case we can we can wait a bit for that because I'm sure there must be more questions.
Okay. I usually summarise if I not done that this week.
Yes. Here we go. Um, so there's your exercises to do at home.
Um, and I will give you the answer sizes on your answer sheet next week.
Um, so you can have a look at those at home. And so this week we've looked at critical reasoning is normative not descriptive.
Do you remember that something's normative if it involves standards either moral standards or rational standards.
So right and wrong in some sense it involves norms.
Um, we've looked at the fact that there are two types just following from um, so deductive follow following from an inductive following from um,
we've seen that deductive arguments are truth preserving, or at least they are when they're good.
So I hadn't made that clear that. But that should be clear. The truth preserving if good.
Um, there are also such that there being good is an either or matter.
Uh, do you remember that they're monotonic?
Um, once you once. It's good. It can't be changed to anything else.
Um, um, deductive arguments are such that we can determine a priori whether they're good or not.
An inductive arguments are necessary, serving no matter how good they are.
They do preserve the truth in that very definite definition of truth preserving that I gave at the beginning.
Um, there also is such that there being good is a matter of degree.
Um, there's such that we can only determine whether they're good by bringing to bear,
uh, experience of understanding of the contents and or background information.
So that's it, folks, for today.
Uh, but we've got time for questions, which is so, um, um, um, let's see if I can turn this.
Does that make it easier? It makes it easier. Sorry.
Some of the other questions. I got a feeling that you mentioned earlier.
They also say white business as being.
Not the time to that. Um, black swans, but, uh, but then later you said that the premise don't have to be true, and the GOP said all sponsor wives.
This is a sport and therefore it is wives.
Even if swarms only showed you that student multitasking, creativity of swarms, animals or birds, let's pretend they're animals.
They're birds or they both shoot.
Yeah. Okay, here's an argument.
And here's another argument. Okay.
All sounds white. The animal in the next room is a swan.
Therefore, the animal in the next room is white. Is that an inductive argument or deductive argument?
It's deductive. Okay, so, um, um, what about every swan I've ever seen has been white.
Therefore, all swans of white is inductive.
So you see that? Um, I mean, I could say all swans I've seen have been white.
Um, it would still be inductive, wouldn't it? Um, it's the first one.
The top one. Deductive one is correct, even though it's not true.
Um, in real life, it is truth preserving. That's all argument, even though one of its premises is false.
It's that we'll be doing this more next week. And it's it's something that people are find very difficult.
Um, I think there's a sort of argument that goes in some people's heads that validity is good.
Truth is good. Therefore validity and truth are the same thing, but they're not.
You can have a valid argument with a false conclusion, and you can have an invalid argument with a true conclusion.
So the notion of truth preserving this, um, is very different from from truth, simplicity or truth generating.
Because. Can I take you back to the argument to back stabbing through the heart, the plunging the dagger?
Yes. Because I think I would argue you're turning that deductive argument with a hidden, uh, with the hidden premise.
Do you remember what it was? Uh, it was what I was talking about.
This and it. You were not honest since he wasn't right. But, uh.
Okay. Um, I would say that's a hidden premise which turns into one.
No, every inductive argument. You could find a hidden premise that turns it into a deductive argument.
I mean, uh, taking that one, every soul that I've seen has been white.
I have seen every swan.
Immediately becomes a detective. I mean, there's no problem.
We take your deductive argument, add to your premise to turn it into deductive.
Um, we can always do that. I don't think I've done that here.
Um, well, I would suggest the premises plunging daggers into heart are inevitably fatal.
Uh, not if you've already killed a chap from. I mean.
So you die with electric shock, and then I plunge a dagger into your heart.
I'm not guilty of murder. I may have the intention to murder you, Christopher, but I didn't do it.
It's already dead anyway. What's that was, anyway?
Because you don't know who his referred to. Um.
Um. John? Yes. You would have to assume that there's somebody.
I mean, we always see somebody dead here. Uh, that's what Hilton was, exactly.
But he's not dead because you're you're policing is trying to see. If I just like to listen to his own heart.
Of course. Yeah, yeah, that's true.
But we do sometimes have to take just take it for granted that there is a person here that was introduced to, I think, in talking about the cats.
We talked about her, didn't we, without make it absolute clear who we meant.
But you got three people. They got Smith. Smith.
You've got John. Um. Hit him. Yes.
That's what he is. Yes. You've got three people. It doesn't say whose heart it holds.
No. It's true. So when you've got the man.
Yes. Who is him? Clearly.
But it's the one. It's the. His.
Yes. Physical. Three members who tried to stop him.
Jones killed a man. So Jones plunge the jacket into his pocket so he could be Jones.
Smith. Uh, I think for any English person to be an US for a restroom reference.
Back to the science. Yes, I really do. Yes, yes.
And I know you're old English, but I think you're just saying it for fun.
Okay. Uh, well, look, supposing that. You a bit electrocution.
You said he could have been electrocuted, but he can because he's dealing with someone who's still alive.
He's going to kill. I don't try to prove he's been tried to stop Jones killing the man and failed.
His wife stated, sometimes you get daggers plunged into your hearts without killing you.
Coming. What are we talking about?
This is. It doesn't seem to be the slightest bit interesting.
Are you sure you have. When we look as students, logic deductive inductive reasoning basically takes subject to the tragedy of the equation,
not with deductive inductive argument, because you've got to bring to bear your background knowledge on the argument with deduction.
Yes. Um, your background knowledge is can be just taking this completely out of the equation.
Yep. That's just like deducting this computers use deduction.
They do. And don't cut it subjective to know how well we talk about something.
First you just have to be different is that we can make it problematic.
Yes. There's a big difference between deduction and induction in that with deduction
we have a very simple mechanical system that can be given to computers.
I mean, computers embody the, uh mechanistic testing evaluation system for deductive arguments.
Um, we can't do all deductive arguments that way. And we for example, if I say, um, uh, lying is wrong, therefore, you shouldn't lie.
Now that looks like a deductive argument. It couldn't be the case that that's true without that's being true.
Um, but we can't mechanistically test that because, um, it seems to depend on the meaning of the word role.
Um, so deduction, we could we could do the propositional calculus as a predicate calculus.
All very powerful systems, uh, that we can use to test deduction, but they don't test all deduction.
They still we we don't like logic, which is the logic of morality.
It's still very much in its infancy. And there are other um, there's also modal logic, which is less in its infancy by if it is possible.
Um, that just means possible. Then it is not.
Um. Yeah.
I've seen you've tried to think of something more interesting, but, um.
Yeah, I mean, you can see that's a deductive argument, but actually, again, that seems to dependable the meaning of the word possible there.
Um, so we might think that wrong and possible are both themselves logically,
but it's like and or if but if so, they act very differently and we don't know how they act.
But what is we a very good system for the vast majority of deductive arguments.
Um. If we can mechanise probability at all, it's only a very small part of it.
Um, so, yes, there is a problem for mechanistic systems because you need to bring to bear all sorts of background knowledge.
Yeah. Okay. One final question.
Is it correct? The speaker mentioned that, um, it could be subjective.
The inductive arguments could be subjective. Is that correct?
I don't like do you, uh, I banned graduates from using the word subjective to learn the third year.
Um, um, it's all you need to bring to bear some background information to that extent.
You're bringing your beliefs to bear on it.
Um, I'm still, you know, subjective is is a subjective state, is a state of a subject to, say, accessible to conscious awareness.
Um, so, but some subjective is not quite the right word, but it's certainly true that the different people could be more or less inductively bold.
So some of you here might say, every time I've seen my aunt, she's been wearing earrings.
Therefore, next time I see you should be wearing earrings, even though you met me three times.
But some of you might wait to meet me ten times before you prepared to say that.
Or whatever. Do you see? Um, so some people are very inductively bold, so they'll draw a generalised conclusion from very little evidence.
And other people wants quite a lot of evidence before they'll draw an inductive conclusion.
So there's certainly an element of subjectivity in how inductively followed you.
All right. We'd better stop there.
Um, and the, uh, presentation for today.
So here are some of the arguments. But at the end of last weekend and today.