OK, well, welcome to the series of mini podcasts. Welcome to everyone here.
Thank you for coming and welcome to everyone watching on podcast.
So today we are going to do the third one in the logic series and this time we're going to do induction.
So for an argument to be good, it's conclusion.
We you'll remember from one of the other podcasts, there's follow from its premises.
But we saw in an earlier podcast that there are two sorts of following from a deductive argument.
The conclusion follows from the premises.
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.
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.
So whereas in a deductive argument, if the premises are true, the conclusion must be true in an inductive argument,
the premises can be true without the conclusions having to be true to all the premises,
to all the truth of the premises does raise the probability of the truth of the conclusion.
So inductive arguments, whereas validity is an either or thing, inductive strength is a is a matter of degree.
So here's a very weak inductive argument. Every time I've seen Marianne, she's been wearing earrings.
I'm seeing Marianne tomorrow. Marianne will be wearing earrings tomorrow.
Well, tomorrow, Saturday maybe I have a day off from wearing earrings on the Saturday.
And here's a strong inductive argument. Every day in the history of the universe, the sun has risen.
Tomorrow's another day. Tomorrow the sun will rise.
Well, if it's really every day in the history of the universe, then that looks to be strong inductive argument.
So in each of these arguments, the conclusion follows from the premises.
But whereas these two premises raise the probability of that conclusion to a certain degree,
these two premises raise the probability of that conclusion to a much greater degree.
So inductive strength is a matter of degree, not either or.
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.
Induction doesn't give a certainty as deduction does.
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.
Yet without that being true, possibly by tomorrow the sun will have blown up and it won't rise tomorrow.
So the falsehood of the conclusion is consistent with the truth of the premises in an inductive argument,
but not added up to a valid deductive argument.
And that's because inductive reasoning depends on the principle of the uniformity of nature.
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.
So if you say, well, well, you do always.
And every time you put the kettle on in the morning, you're assuming that the future is going to be like the past.
You're assuming that once again your kettle is going to boil.
Well, maybe this is the time you'll get won't boil no matter how high you raise the temperature.
Most unlikely, I think you'll agree. But why do you think the future is going to be like the past?
Probable answer is because it's always been like the past in the past.
But do you see that that that's a circular justification because you're using the past to justify claims about the future again.
So any inductive argument is inductive because it rests on the principle of the uniformity of nature.
Oops. Gone backwards and it's very important that it doesn't make induction inferior, that it doesn't give a certainty.
Some people think that if deduction gives us certainty, an induction gives us only less than certainty.
There's something inferior about induction. But that's not the case.
It's just different. It's not inferior. And here's an inductive argument and a deductive argument just to see that.
Do you see that this one's an inductive argument? So that's a white swan.
You see a white swan, that's a white swan. You see another white swan.
And then you think, well, actually, all the swans I've seen have been white, therefore all swans are white.
So your inductively inferring a generalisation about all swans from all your observations of swans.
And now here your deductively saying all swans are white.
The creature in the next room is a swan. Therefore, the creature in the next room will be white.
Do you see that's a deductive argument in that. If that's true and that's true, that must be true.
But if that's true, that's true and that's true, that could still be false, couldn't it,
because all swans you've observed doesn't actually necessarily cover all swans in the world or in the universe.
So this one this argument rests on the principle of the uniformity of nature,
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.
But this one doesn't rest on the uniformity of nature, because here you're simply stating all swans are white.
And if that's true and that's true, then that must be true.
But of course, we've still got to say to yourself, well, how do you know that?
And of course, well, how would we know that? What would be our justification for a claim like all swans are white, probably.
It would be something like that, wouldn't it? So there's nothing inferior about induction,
even though it doesn't give a certainty and we rely on induction almost everything we do, often successfully and without question.
But in evaluating inductive arguments,
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.
OK, well, there are different types of inductive arguments and have here of all types that are arguments from analogy,
arguments from authority, inductive generalisations and causal generalisations.
Let's have a look at all these here. This is an argument from analogy.
So Jennifer liked my pen. This pen is similar to mine.
Jennifer will like this pen. Can you see how that rests on the principle of the uniformity of nature?
So Jennifer liked my pen. This similar pen is similar to my pen.
Well, if Jennifer in the future likes the things she liked in the past, she should like this pen.
So that's an argument from analogy and it's analogy because it rests on a similarity claim.
Now, this one is the argument from authority. Einstein said that nothing goes faster than the speed of light.
Einstein is an authority on physics. Therefore, nothing goes faster than the speed of light.
Again, that rests on authority rather than analogy. And here's how to evaluate arguments from analogy.
So if we have first thing we want to ask, as with any argument at all, whenever you're evaluating an argument,
one of the first things you look for is, is the premise true or are the premises true?
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.
If the premises are true, they raise the probability of the conclusion, though, as we know, it isn't certain.
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?
So this pattern is similar to mine. Well, is that true?
In what way is the pen similar to mine, the one that Jennifer liked before?
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.
Well, in that case, perhaps the similarity isn't relevant.
It's there, but perhaps it isn't relevant because after all,
if Jennifer liked the look of the pen, then the fact that it was bought by Steve is irrelevant.
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.
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.
So I have a look at the strength of the similarity. The more points of similarity, the stronger the analogy.
And are there any relevant analogies? So is there anything significantly different about my pen and this pen?
If so, that might mean that the probability of the conclusion isn't raised very much, even if the premises are true.
Okay, let's have a look at evaluating arguments from authority.
So going back to this one, this is authority, the one about Einstein.
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?
Second question we've got to ask is, is the person cited an expert in this area?
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.
So the fact that Einstein was a pacifist doesn't necessarily mean that pacifism is right.
Even if we accept his authority on physics, we won't necessarily accept his authority elsewhere.
So he's got to be not only an expert, but an expert in the particular area of the argument.
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.
There was a chap who was put forward as an expert, wasn't there?
And you might ask, well, how much are they paying him to do this advertisement when he gives his recommendation
for this particular product and it's an area in his area of expertise?
Could he be biased? Could it be that we shouldn't listen to him?
And finally, we might ask whether he's representative because physicists differ on a lot of things.
Perhaps this expert is is an expert who holds a minority view.
So whenever the BBC gets to get people together to talk about climate change,
for example, you'll often have a scientist who speaks against climate change.
Yes, he's an expert. He may or may not be biased, let's say he's not biased, but is he representative?
Again, you've got to ask yourself, perhaps he's he's a dissenter on this particular opinion.
And here's an inductive generalisation and on the other side, a causal generalisation.
This is an inductive generalisation whenever I've tried to ring, but it's taken me hours to get through.
Therefore, when I ring Beattie today, it'll take me hours to get through.
So I'm inductively inferring from this premise to this conclusion perfectly reasonable.
I think you'll agree this is a causal generalisation. Statistics say that married men live longer than single men.
In other words, there's a correlation between being married and living longer between men who
are married and therefore being married if male causes you to live longer.
So here we're inferring from a correlation to a causal relationship.
Let's have a look at how to evaluate these. So, again, first question always, is the premise true?
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,
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.
But I think you'll agree that the fewer the number of occasions on which I've tried to ring Beattie,
the less credence we should attach to the conclusion of that argument.
And we might also ask, is the sample typical?
I mean, what I tried to ring Beattie at two o'clock in the morning, rather, at two o'clock in the afternoon.
If I was, then maybe again, I shouldn't infer from that premise to that conclusion.
And evaluating causal generalisations finally start off, of course, with is the premise true?
A second question we ask is how strong is the correlation? OK, this correlation between men being married and men living a long time.
But how I mean, is the correlation only about 60 percent of men who are married live longer or is it stronger than that?
And the stronger the correlation, the better the argument here.
Could the correlation be accidental? And sometimes correlations are accidental.
When I was an undergraduate, we always talked about striking a match and a pineapple falling from a tree.
You think? Well, even if there was a perfect correlation throughout the whole history of the
universe between somebody striking a match and a pineapple falling from a tree,
on the whole, you still think that correlation is accidental.
You can't see how there would be a mechanism to underpin a causal relationship between those two types of events.
You might also ask, could the causal relationship work the other way around?
Could it be that men who live longer or sorry, men who are going to live longer get married?
Perhaps there's something genetic that genetically inclines people to get married and also inclines them to live longer.
That's the third one. So could the correlation be caused by a third thing that's attached that causes both the other two,
which explains why the other two are correlated rather than that?
There's, of course, the relation between those two.
So, OK, they are that's induction and that's quickly for different inductive arguments and how to evaluate each of them.
And there's the slide telling us a bit more about how to find out more.