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OK, well, welcome to the series of mini podcasts. Welcome to everyone here.

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Thank you for coming and welcome to everyone watching on podcast.

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So today we are going to do the third one in the logic series and this time we're going to do induction.

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So for an argument to be good, it's conclusion.

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We you'll remember from one of the other podcasts, there's follow from its premises.

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But we saw in an earlier podcast that there are two sorts of following from a deductive argument.

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The conclusion follows from the premises.

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If the argument is valid and you'll remember if it's valid, that's because if the premises are true, the conclusion must be true.

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But in an inductive argument, the conclusion follows the premises if the truth of the premises raises the probability of the truth of the conclusion.

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So whereas in a deductive argument, if the premises are true, the conclusion must be true in an inductive argument,

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the premises can be true without the conclusions having to be true to all the premises,

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to all the truth of the premises does raise the probability of the truth of the conclusion.

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So inductive arguments, whereas validity is an either or thing, inductive strength is a is a matter of degree.

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So here's a very weak inductive argument. Every time I've seen Marianne, she's been wearing earrings.

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I'm seeing Marianne tomorrow. Marianne will be wearing earrings tomorrow.

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Well, tomorrow, Saturday maybe I have a day off from wearing earrings on the Saturday.

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And here's a strong inductive argument. Every day in the history of the universe, the sun has risen.

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Tomorrow's another day. Tomorrow the sun will rise.

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Well, if it's really every day in the history of the universe, then that looks to be strong inductive argument.

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So in each of these arguments, the conclusion follows from the premises.

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But whereas these two premises raise the probability of that conclusion to a certain degree,

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these two premises raise the probability of that conclusion to a much greater degree.

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So inductive strength is a matter of degree, not either or.

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And even if the likelihood of the truth of the conclusion is significantly raised by the truth of the premises, it could still be false.

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Induction doesn't give a certainty as deduction does.

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So even if we look at this argument, which is inductively very strong indeed, we can see that that might be true and that might be true.

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Yet without that being true, possibly by tomorrow the sun will have blown up and it won't rise tomorrow.

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So the falsehood of the conclusion is consistent with the truth of the premises in an inductive argument,

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but not added up to a valid deductive argument.

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And that's because inductive reasoning depends on the principle of the uniformity of nature.

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The idea that the future will be like the past and this the idea that the future will be like the past, can't be justified without circularity.

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So if you say, well, well, you do always.

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And every time you put the kettle on in the morning, you're assuming that the future is going to be like the past.

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You're assuming that once again your kettle is going to boil.

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Well, maybe this is the time you'll get won't boil no matter how high you raise the temperature.

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Most unlikely, I think you'll agree. But why do you think the future is going to be like the past?

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Probable answer is because it's always been like the past in the past.

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But do you see that that that's a circular justification because you're using the past to justify claims about the future again.

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So any inductive argument is inductive because it rests on the principle of the uniformity of nature.

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Oops. Gone backwards and it's very important that it doesn't make induction inferior, that it doesn't give a certainty.

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Some people think that if deduction gives us certainty, an induction gives us only less than certainty.

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There's something inferior about induction. But that's not the case.

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It's just different. It's not inferior. And here's an inductive argument and a deductive argument just to see that.

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Do you see that this one's an inductive argument? So that's a white swan.

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You see a white swan, that's a white swan. You see another white swan.

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And then you think, well, actually, all the swans I've seen have been white, therefore all swans are white.

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So your inductively inferring a generalisation about all swans from all your observations of swans.

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And now here your deductively saying all swans are white.

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The creature in the next room is a swan. Therefore, the creature in the next room will be white.

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Do you see that's a deductive argument in that. If that's true and that's true, that must be true.

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But if that's true, that's true and that's true, that could still be false, couldn't it,

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because all swans you've observed doesn't actually necessarily cover all swans in the world or in the universe.

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So this one this argument rests on the principle of the uniformity of nature,

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the idea that if all the swans that you haven't seen are like the swans you have seen, then they'll all be white.

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But this one doesn't rest on the uniformity of nature, because here you're simply stating all swans are white.

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And if that's true and that's true, then that must be true.

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But of course, we've still got to say to yourself, well, how do you know that?

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And of course, well, how would we know that? What would be our justification for a claim like all swans are white, probably.

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It would be something like that, wouldn't it? So there's nothing inferior about induction,

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even though it doesn't give a certainty and we rely on induction almost everything we do, often successfully and without question.

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But in evaluating inductive arguments,

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we've got to use our judgement in a way that we don't have to use it with deduction because deduction is an either or matter.

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OK, well, there are different types of inductive arguments and have here of all types that are arguments from analogy,

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arguments from authority, inductive generalisations and causal generalisations.

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Let's have a look at all these here. This is an argument from analogy.

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So Jennifer liked my pen. This pen is similar to mine.

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Jennifer will like this pen. Can you see how that rests on the principle of the uniformity of nature?

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So Jennifer liked my pen. This similar pen is similar to my pen.

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Well, if Jennifer in the future likes the things she liked in the past, she should like this pen.

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So that's an argument from analogy and it's analogy because it rests on a similarity claim.

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Now, this one is the argument from authority. Einstein said that nothing goes faster than the speed of light.

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Einstein is an authority on physics. Therefore, nothing goes faster than the speed of light.

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Again, that rests on authority rather than analogy. And here's how to evaluate arguments from analogy.

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So if we have first thing we want to ask, as with any argument at all, whenever you're evaluating an argument,

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one of the first things you look for is, is the premise true or are the premises true?

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So if you're looking at this one, if these two premises are not true, then you've got no reason to believe the conclusion at all.

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If the premises are true, they raise the probability of the conclusion, though, as we know, it isn't certain.

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So first question to ask is, is the premise true? Second question to ask when evaluating an argument from analogy is, is there a similarity?

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So this pattern is similar to mine. Well, is that true?

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In what way is the pen similar to mine, the one that Jennifer liked before?

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And the next question is, is the similarity relevant? OK, well, maybe this pen is similar to mine in that they were both bought by Steve, let's say.

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Well, in that case, perhaps the similarity isn't relevant.

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It's there, but perhaps it isn't relevant because after all,

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if Jennifer liked the look of the pen, then the fact that it was bought by Steve is irrelevant.

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But if she liked the fact that the pen was red and this pen is similar because it's also red, then the similarity is relevant.

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And how strong is the similarity? The more alike this pen is to the pen that Jennifer liked, the more likely it is that Jennifer is going to like it.

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So I have a look at the strength of the similarity. The more points of similarity, the stronger the analogy.

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And are there any relevant analogies? So is there anything significantly different about my pen and this pen?

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If so, that might mean that the probability of the conclusion isn't raised very much, even if the premises are true.

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Okay, let's have a look at evaluating arguments from authority.

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So going back to this one, this is authority, the one about Einstein.

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Let's see what questions we've got to ask here. Firstly, again, is the premise true again and always we've got to ask, is the premise true?

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Second question we've got to ask is, is the person cited an expert in this area?

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Well, we're all prepared to accept that Einstein is an authority on physics, but that doesn't mean he's an authority on politics.

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So the fact that Einstein was a pacifist doesn't necessarily mean that pacifism is right.

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Even if we accept his authority on physics, we won't necessarily accept his authority elsewhere.

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So he's got to be not only an expert, but an expert in the particular area of the argument.

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The other thing we've got to ask is, is the expert biased? We might have an expert on television in an example using razorblades or something.

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There was a chap who was put forward as an expert, wasn't there?

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And you might ask, well, how much are they paying him to do this advertisement when he gives his recommendation

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for this particular product and it's an area in his area of expertise?

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Could he be biased? Could it be that we shouldn't listen to him?

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And finally, we might ask whether he's representative because physicists differ on a lot of things.

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Perhaps this expert is is an expert who holds a minority view.

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So whenever the BBC gets to get people together to talk about climate change,

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for example, you'll often have a scientist who speaks against climate change.

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Yes, he's an expert. He may or may not be biased, let's say he's not biased, but is he representative?

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Again, you've got to ask yourself, perhaps he's he's a dissenter on this particular opinion.

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And here's an inductive generalisation and on the other side, a causal generalisation.

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This is an inductive generalisation whenever I've tried to ring, but it's taken me hours to get through.

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Therefore, when I ring Beattie today, it'll take me hours to get through.

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So I'm inductively inferring from this premise to this conclusion perfectly reasonable.

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I think you'll agree this is a causal generalisation. Statistics say that married men live longer than single men.

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In other words, there's a correlation between being married and living longer between men who

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are married and therefore being married if male causes you to live longer.

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So here we're inferring from a correlation to a causal relationship.

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Let's have a look at how to evaluate these. So, again, first question always, is the premise true?

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Second question is how large is the sample? And let's say that whenever I've tried to ring Beattie, it's taken me hours to get through,

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but I've actually only tried twice and I just get very annoyed very, very easily and so on each on each of these two occasions.

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But I think you'll agree that the fewer the number of occasions on which I've tried to ring Beattie,

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the less credence we should attach to the conclusion of that argument.

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And we might also ask, is the sample typical?

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I mean, what I tried to ring Beattie at two o'clock in the morning, rather, at two o'clock in the afternoon.

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If I was, then maybe again, I shouldn't infer from that premise to that conclusion.

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And evaluating causal generalisations finally start off, of course, with is the premise true?

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A second question we ask is how strong is the correlation? OK, this correlation between men being married and men living a long time.

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But how I mean, is the correlation only about 60 percent of men who are married live longer or is it stronger than that?

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And the stronger the correlation, the better the argument here.

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Could the correlation be accidental? And sometimes correlations are accidental.

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When I was an undergraduate, we always talked about striking a match and a pineapple falling from a tree.

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You think? Well, even if there was a perfect correlation throughout the whole history of the

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universe between somebody striking a match and a pineapple falling from a tree,

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on the whole, you still think that correlation is accidental.

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You can't see how there would be a mechanism to underpin a causal relationship between those two types of events.

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You might also ask, could the causal relationship work the other way around?

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Could it be that men who live longer or sorry, men who are going to live longer get married?

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Perhaps there's something genetic that genetically inclines people to get married and also inclines them to live longer.

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That's the third one. So could the correlation be caused by a third thing that's attached that causes both the other two,

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which explains why the other two are correlated rather than that?

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There's, of course, the relation between those two.

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So, OK, they are that's induction and that's quickly for different inductive arguments and how to evaluate each of them.

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And there's the slide telling us a bit more about how to find out more.