Welcome to the third lecture on general philosophy.
And now we're going to be going quite deeply into one of the topics one of the six topics we have already touched on several of them,
including particularly mind and body. But now we're going to spend an entire lecture and indeed a little bit more on induction.
The luminaries we have here are Pierro of Ellis at the left, who'll be introduced shortly.
Descartes. David Hume. Peter Strossen, who for a long time was Univ. and ended up spending many years at Maudlin.
And Simon Blackburn, who was fellow at Pembroke for quite a long time before moving to a certain unmentionable university in the Fenton's.
So Pierro of Ellis, we don't know very much about him.
What we do know comes from this chap, Diogenes Lazarus,
who enjoyed telling Uri Tales of the Great Greek philosophers and in particular, how they died often rather go orally.
In Pirro's case, however, he lived to a ripe old age,
apparently because he had lots of nice friends who followed him around, saving him from the consequences of his scepticism.
So he was a notorious extreme sceptic.
He saw no reason for supposing that precipice is dangerous or indeed hurrying chariots, but his friends kept him out of harm's way and he was OK.
So when you hear about tyranny and scepticism, for example, when reading Hume,
that's referring to this, this somewhat legendary extreme form of scepticism.
Now the works have loads of ancient Greek philosophers whom we typically know about only through Diogenes were lost.
As I mentioned in, I think the first lecture when Constantine converted to Christianity.
Basically, you had a sequence of Roman emperors who just destroyed the old pagan schools, burnt down libraries,
etc. But some of the ancient texts survived in the Byzantine Empire and in the Arabic world.
And with the downfall of the Byzantine Empire, a lot of scholars fled to the West, and that's standardly credited with kicking off the Renaissance.
I want to particularly focus on a few techs and in particular, the techs of sex empiric us,
who wrote a work called Outlines of Piron ism, in which he spelled out a lot of sceptical arguments.
And I mentioned in the first lecture why over this period, from about particularly 1500 to about 16 50, there was a lot of tumult in the West.
A lot of problems were being raised, not least thanks to the Reformation.
So people were debating things, questioning whether the things that they thought they knew were as solid as they were.
And into this came these sceptical manuscripts. Also, with the invention of printing, suddenly these works could be spread far and wide.
So works that had survived literally just one or two copies by chance had survived.
Of these hundreds of texts that we know about through Diogenes,
just a small number survived, but they were printed and reproduced and had a huge effect.
So the outlines of Paris apparent ism I've mentioned by Sixtus imperious.
He actually lived around 200 A.D. that was translated into Latin and printed in fifteen sixty two.
It had a major impact on Montaigne. He, in turn, influenced Descartes.
And but Bale PR Bale. Now, I've mentioned before that not only were there all these issues like the Reformation and so forth,
but also modern science itself invited scepticism.
And of course, still does. If you go back to the ancient Aristotle, the idea was that when you perceived something,
you actually mentally grasped the form of the thing that you were perceiving.
Your mind became, in a sense, like the thing that it was perceiving.
But for the moderns, it was quite different. They saw the world as composed of matter, whose form is quite different from what we see.
So in the case of Descartes, he thought everything, everything material was composed of pure extension of someone like Boyle.
You've got corpuscles in the void. But in either case, the perceptions that we have of things are very different from the things themselves.
So again, you get an invitation to scepticism. Now we've already seen some snippets from Descartes.
Here are a few more focussed, particularly on scepticism.
So his first meditation very famously presents sceptical arguments.
Now, Descartes is using this for a reason.
Scepticism is extremely convenient to Descartes because it enables him to sweep away the orthodoxy of Aristotelian ism.
He can say, I'm not going to accept anything unless it can withstand the arguments of the sceptics,
and an appeal to Aristotelian authority is not going to do that.
Now, Descartes thinks he actually has arguments that will withstand scepticism, and we're going to briefly look at those in a moment.
So famously, Descartes speculated that he might be dreaming that the world might all be an illusion,
or maybe that some kind of evil demon putting the perceptions into his mind.
So again, maybe the external world simply doesn't exist.
I'm an extreme variety of this kind of scepticism is is called solipsism,
and solipsism is the claim that the only thing that exists in the entire universe is me, my mind.
Everything else is as it were a figment of my imagination.
Now, Descartes himself, of course, is not a solipsistic, he is using scepticism, as I said, as a tool for getting rid of rival theories.
He thinks he has an answer, which is going to refute scepticism.
And here I just want to sketch the form of that reply.
And to focus on its essential logical structure. So again, as with many of these slides, I'm going to be skipping over them quite quickly.
But you've got them there to read at leisure.
And I hope that they will give you a guide when you're reading the meditations to some of the highlights.
OK, so Descartes says I'm going to cast away anything that isn't completely certain.
That is how I am going to reply to the sceptic. I'm only going to hold on to things that are certain.
When I think about my own existence, I realise that there there is a source of certainty.
I'm aware of my own thinking. I could not be thinking without existing, so I'm absolutely certain that I exist.
I think therefore I am very famous.
More controversially, he says that by examining that particular case of certainty, he can see what is required in order for something to be certain.
Now, that's a very strange move, if you think about it, because he's identified this one unique special truth.
I think therefore I am. But then he goes on and tries to establish a general rule on the basis of that.
Now it may be that his knowledge of his own existence is somehow special and not just because he clearly and distinctly perceived it to be true,
but because it has other qualities like, for example, I cannot doubt without existing.
The very fact of doubting proves my existence. So that's the kind of thing that suggests that I think therefore I am special.
My own thinking somehow guarantees my existence.
That's not necessarily necessarily going to carry over to other claims that Descartes thinks that he clearly and distinctly perceives.
But at any rate, what Descartes does is quite clear, he says. What makes me sure that I exist is that I clearly and distinctly perceive it to be true.
So I can now draw a general rule that whatever I clearly and distinctly perceive is true.
Then he goes on and argues on the basis of things that he claims to clearly and
distinctly perceive that God exists in particular in the third meditation.
He notices that within his mind, he has an idea of God.
He sees that this idea of God has a sort of perfection to it.
And he claims that that perfection could only come about from a perfect cause.
So the effect that is the idea of God in his mind could not have been put there, except by perfect being.
And an example of one of the principles that he appeals to in this proof,
it is manifest by the natural light that there must be at least as much in the efficient and total calls as in the effect of that cause.
So if I get my idea of God is perfect, that perfection must have come from the cause of that idea.
So there must be a god. And a perfect God couldn't be a deceiver.
So if he's not a deceiver, then it must be that I who have been made by him must be capable of truth.
So when I clearly and distinctly perceive things, they must indeed be true because were that not the case, God would have been a deceiver.
And we know that God can't be a deceiver because God has got to be perfect.
OK, I've gone through that very quickly, but you may have noticed that there's a little bit of a circularity here.
Descartes seems to be appealing to his clear and distinct perception to prove the existence of God.
But then having prove the existence of God, he says,
now that I know that God exists and is not a deceiver, I can rely on my clear and distinct perception.
So it looks like he's relying on his faculties to prove the existence of God.
Then he's using God's existence to justify his faculties that looks circular.
And you might wonder in the light of this weather, actually, it's possible.
To defeat the sceptic without some such circular argument,
if the sceptic throws doubt on your very thinking faculties, how on earth can you justify them against him?
So I'm going to leave that hanging just for a moment and introduce the next big figure.
Probably these days, the most influential philosopher of the early modern period,
there are probably more people who think of themselves as humans in active in philosophy these days, certainly than Cartesian or Lacunes.
And probably even Campion's part of the reason that David Hume's influence is so great these
days is because he was a he was trying to establish a philosophical view of lots of things,
including ethics and philosophy of religion, as well as epistemology and metaphysics, but was completely independent of God.
And in the 20th and 21st centuries, that has become the standard way of doing philosophy.
So Hume was cold in his day, the great infidel, he's known as a notorious sceptic.
So unlike Descartes, who whose aim is to oppose scepticism, Hume often seems to be on the side of the sceptic.
Now we'll see that it's not actually so clear.
In many ways, he wants to respond to the sceptic, but he's certainly much more sympathetic to sceptical arguments than Descartes or Locke,
or indeed, any other great philosopher of this period.
So in your readings for general philosophy, there are two particular sections of Hume's first enquiry, which are relevant.
This is the enquiry concerning human understanding of 1748. One of them is Enquiry Section four.
That's where he presents his famous argument concerning induction, but the other is Enquiry 12, where he discusses scepticism.
And in this, in the next lecture, I'm going to be appealing to both of those.
So in the next lecture, we're going to go and see more about scepticism and about how human and a human can reply to scepticism.
So very early in Section 12, Hume attacks Descartes.
There is a species of scepticism antecedent to all study and philosophy,
which is much inculcated by Descartes and others as a sovereign preservative against error and precipitate judgement.
It recommends and universal doubt not only of all our former opinions and principles,
but also of our very faculties of whose veracity say they we must assure ourselves by a chain of
reasoning deduced from some original principle which cannot possibly be fallacious or deceitful.
He calls the antecedent scepticism because the scepticism is being raised even before we've applied our faculties,
it's casting doubt on our faculties right from the start. Now, Hume responds to that.
But neither is there any such a regional principle, which has a prerogative above others that are self-evident and convincing, or if there were.
Could we have advanced a step beyond it? But by the use of those very faculties of which we are supposed to be already diffident,
the Cartesian doubt there for wherever possible to be attained by any human creature as it plainly is not would be entirely incurable.
And no reasoning could ever bring us to a state of assurance and conviction upon any subject.
Now, personally, I have to say, this seems quite a strong counter to Descartes.
It's saying, look, if you start out distrusting your own faculties and requiring that your own faculties be justified, you've had it.
There's no way you're going to get to do it, except by using your faculties. And since you don't trust your faculties.
No chance. So what's the point of doing that? What is the point of pursuing that kind of sceptical philosophy?
You've simply dug yourself in a pit, you've thrown away the means of getting out of the pit.
You've had it. Futile. Now, let's go on and see an argument of Hume's, which is seriously sceptical,
but not a case of antecedent scepticism of the kind that he accuses Descartes of.
We'll be coming back, incidentally to this issue about antecedent scepticism, particularly in the next lecture.
Now Kim's most famous for his argument concerning induction, indeed,
it's probably the most famous and influential argument in all of English language philosophy.
It appears in three versions in the treats of human nature, the abstract of the treaties and the enquiry.
The version that you read for this course. The enquiry version is the best.
It's the fullest, the most polished. So you don't need to worry too much about the treaties in the abstract.
But if you, the abstract gives a very nice summary a sort of potted version of the argument.
It's considered as very widely being considered a dangerously sceptical argument, Broad called it the scandal of philosophy.
A lot of modern philosophy of science has been developed in response to this argument.
Its interpretation still remains controversial in various ways, but it continues to be extremely influential.
So quite unlike Descartes arguments that we've been talking about here is an argument which is alive and kicking,
which many people actually think is correct, despite the fact that its conclusion can seem wildly paradoxical or sceptical.
So I'm going to be following it broadly as it goes in enquiry for and enquiry section
four starts with the distinction between two different types of proposition. Relations of ideas and matters of fact.
Now relations of ideas are propositions that you can know to be true without consulting experience that a priori we've already come across that term.
You can know them to be true simply by thinking of the meanings of the terms they contain.
So they're necessarily true. There's no way you can conceive them to be false.
Hume gives examples of Pythagoras theorem and three times five equals half of 30.
An example. A very common example these days is all bachelors are unmarried.
An example of what is commonly called an analytic proposition, it's one such that the meanings of the terms determine its truth.
So those are relations of ideas.
A relation of ideas just tells you about the logical connexions between the words that you're using or the ideas that you associate with them.
It isn't telling you anything substantial about the world.
Now against that, we have matters of fact and matters of fact, our statements, but do tell you something about the world.
The things that cannot be known a priori.
You can't know them to be true just by looking at the meanings of the terms and their truth and falsity are therefore equally conceivable.
So here's an example of a matter of fact The Sun will rise tomorrow.
Here's another one. The Sun will not rise tomorrow.
Notice that when Hume talks about a matter of fact, he means if you like a question of fact, he doesn't mean it is actually true.
But it's a question of fact, whether it's true or false, or take this one.
This pen will fall when released in air.
Oh, that turned out to be a true matter of fact. So in modern terms, this is a synthetic proposition,
a proposition whose truth is determined by the facts of experience, not by the meanings of the terms.
OK, so that seems a very intuitive distinction.
It's been very, very influential since Kant.
It's been drawn more in terms of analytics, synthetic rather than relations of ideas and matters of fact, but it's essentially the same distinction.
OK, now it may seem straightforward to understand how I can know the truth of a relation of ideas.
I simply look at my own ideas, I think through the consequences of the meanings of my terms and I work out that it must be true.
But how can I know a matter of fact? Well, you may think in some cases, that's very straightforward.
I can know there's a glass in front of me because I see it. I can know that there's a glass behind me because I remember seeing it.
OK, so let's not worry about that.
We're not going to do what Descartes was doing. We're not going to raise sceptical questions about perception or about memory.
What are we going to ask is how can we know any matter of fact which we are not either currently perceiving or remembering?
So, for example, how can I know? That that pin will fall when I let go of it.
OK, let's take a paradigm example of this kind of inference, and Hume chooses billiard balls.
So suppose we see a yellow billiard ball moving towards a red one and colliding with it?
We expect the red one to move, don't we?
Why? Well, Hume says that we suppose a causal connexion, a causal connexion between the impact of the yellow ball and the movement of the red one.
OK, fine. But how do we learn what causes what, how do we learn about causal relations?
And here Hume brings in a thought experiment involving Adam.
Adam is the very first man, he's just been created by God.
He's a perfect specimen of a human being. All his faculties work just as they should because God's just made him.
OK. So, Adam, sitting there and God up comes up to him and says, Look, Adam, here's a billiard ball.
Oh, what's that? Never seen one of those before. No, you haven't. But here's one anyway.
Here's another one. Now I'm going to roll, says God.
One of the billiard balls towards the other. What do you think will happen, Adam, when that billiard ball hits that one?
And Humes thought experiment is actually Adam would not have a clue.
Adam's never seen this before.
He doesn't have the faintest idea what will happen when one hits the other because he can imagine lots of different things that might happen.
One might just stop. It might go through right through it. One might jump in the air or go backwards or all sorts of things.
How could Adam, without experience, possibly know what was going to happen when one billiard ball hit the other?
He couldn't. And that does indeed seem a plausible result of that thought experiment.
OK, now, suppose God did this a number of times. So, Adam, that by now he's seen 100 billiard balls and every time the second one is moved.
And now God says to Adam What will happen when this ball, when the yellow ball hits the red one and Adam says, Oh, the red one will move.
OK, well, what makes the difference? Why, why does Adams experience of one believable hitting another?
How does it help him in making a prediction about others?
Well, it must be because he's able to extrapolate, he's able to extrapolate from the experience he has had to the experience he's going to have.
So Hume claims very plausibly all inference to matters of fact beyond what we perceive or
remember is based on causation and all our knowledge of causation comes from experience.
But we can only learn from experience on the assumption that observed phenomena,
the billiard balls we've seen in the past provide a guide, some sort of at least vaguely reliable guide to unobserved phenomena.
The billiard balls we're going to see in the future.
So we have to be able to extrapolate from observed to unobserved on the basis that the unobserved will resemble the observed.
OK. Do we have a rational basis for making that assumption?
Now, that assumption is commonly called the uniformity principle, it's not Hume's term.
But Hume scholars normally use it to refer to this principle. Here are a couple of ways in which she expresses it in the enquiry.
All our experimental conclusions, he just means conclusions from experience.
All our experimental conclusions proceed upon the supposition that the future will be conformable to the past.
OK. How then, can we know that the future will be conformable to the past?
What possible means of justification do we have for the principle of uniformity?
OK. Spoiler alert. We don't have any.
Hume is going to claim, by the way, I think he's right that we don't have any source of independent justification for the uniformity principle.
OK, so I now need to take you on a little detour to look at the various sources of evidence
that Hume thinks might conceivably be available for the uniformity principle.
Or somebody might think were available for the uniformity principle.
So here's a little snippet from a document that Hume wrote in 1745 that's three years before he published the enquiry.
It's a shame he doesn't say anything quite this clear in the enquiry.
It is common for philosophers to distinguish the kinds of evidence into intuitive, demonstrative, sensible and moral.
OK. So when he talks about intuition, he means things that are self-evident.
So if something's an intuitive truth, it's self-evident. When he talks about sensible evidence, he means what we would call sensory evidence,
evidence from the senses and when he talks about demonstrative and moral reasoning,
or sometimes he uses the term probable rather than moral reasoning.
He means two different types of inference, which were distinguished by John Locke.
So again, I'm brief detour. Here's an example from lock of demonstrative reasoning.
It's a proof that the angles within a triangle add up to the angles on a straight line,
and the claim is that we can see intuitively we've got two parallel lines.
We can see intuitively, it's self-evident that Angle A is equal to an angle e.
It's self-evident that angle B is the same as angle D,
and it's self-evidently follows from the first two propositions that a plus B policy is equal to E plus d plus c.
So the sort of idea of a demonstrative argument for Lock, which Hume takes over,
is an argument where every link in the inferential chain goes with absolute and complete certainty.
So we've got what we would call a deductive argument and argument where if the premises are true,
you simply could not possibly doubt the truth of the conclusions as following,
because there's no way the premise could be premises could be true without the conclusion being true.
Now, probable reasoning or what Hume calls moral reasoning notice, by the way, when he talks about moral reasoning, it's nothing to do with ethics.
All right. This is an old use of the term. It's still retained.
When people talk about moral certainty, they don't need ethical. They mean certainty for the purposes of human life or something like that.
So improbable reasoning. You have an argument where the links of the chain are not infallible.
So in demonstrative reasoning, you go from the premises through the steps of the argument to the conclusion with absolute certainty all the way,
the sort of thing you do in maths, the sort of thing you do in logic. Improbable reasoning the links of the chain are not so certain.
And this is lock talks about this, but gives very little in the way of example, an example he gives is this one telecom tree gentlewoman.
The wind is southwest and the weather flowering, unlike to rain,
and she will easily understand it is not safe for her to go abroad thin clad in such a day after a fever.
She clearly sees the probable connexion of all these these south west wind and clouds, rain wetting, taking cold relapse and danger of death.
Well. A bit dramatic, but you get the idea.
These are not demonstrative Connexions. The woman is drawing probable connexions from one thing to another.
OK. And I mentioned a point there at the bottom, which I'll come back to a little later.
So Locke's distinction between demonstrative and probable reasoning pretty much corresponds with what we call deductive and inductive reasoning,
deductive reasoning is where the premises guarantee the truth of the conclusion.
An inductive argument is one that draws conclusions about typically about the unobserved on the basis of the observed by extrapolation.
OK, so now let's come back. Remember, we were asking what justification could one possibly have for the uniformity principle?
And we've got four possible sources of evidence, according to Human, and Hume says this is quite standard as it is in his day.
Is it self-evident that the future will resemble the past?
No, it's not self-evident. Can it be proved demonstratively by deductive reasoning?
Can you prove that the future will resemble the past?
That because billiard balls in the past have acted in such and such a way that you can logically prove that the next one will act that way?
No, you can't. Both of these are clearly impossible because we can easily imagine things turning out differently.
And if we can consistently imagine things turning out differently, that's enough to show that we haven't got a logical or demonstrative proof.
What about sensory knowledge, could we know through the senses that future billiard balls will operate in the same way as past billiard balls?
Well, no, we can't think of the atom thought experiment.
Adam, by looking at the billiard balls, didn't have a clue what was going to happen until he actually saw it.
And by the same reasoning, he couldn't have had a clue that the billiard balls would act consistently.
Just looking at the superficial qualities of the billiard ball didn't tell him
anything about how it's going to behave or whether it will behave consistently.
So that's no good. What about what Hume calls moral reasoning or probable reasoning,
and I'm calling factual inference for short because he often calls it reasoning concerning matter of fact.
Well, the problem there is that if we use that to justify uniformity, we're just going in a circle.
We have said that all arguments concerning existence again,
he means all moral probable reasoning or factual inferences are founded on the
relation of cause and effect that our knowledge of that relation is derived
entirely from experience and that all experimental conclusions proceed upon
the supposition that the future will be conformable to the past to endeavour.
Therefore, the proof of this last supposition by probable arguments or arguments regarding existence, which suggests just the same thing,
must be evidently going in a circle and taking that for granted, which is the very point in question.
Okay, so we cannot justify extrapolating from past to future.
Either on the basis that it's self-evident, it isn't or with a deductive argument, because there isn't one or on the basis of sensation,
because that doesn't tell us that the future is going to resemble the past, nor on the basis of inductive argument,
because inductive argument takes for granted that the future will resemble the past.
So we've got absolutely no justification, apparently, for the assumption that the future will resemble the past.
And since all of our influences is beyond what we immediately observe or remember depends upon this assumption,
or at least the assumption that the unobserved will resemble the observed we act.
It looks like we haven't got any justification for any belief about anything,
any matter of fact that goes beyond our immediate perceptions and memory.
That's a serious worry. And notice that Hume here, he's not doing things like doubting the external world.
He's not doubting our perception. He's not doubting our memory. He's simply saying, what justification do we have for going beyond those?
And his answer seems to be, we have none. We have to depend on this principle of extrapolation for which we can give literally no reason, whatever.
What's particularly scandalous is I cannot give you an answer to this, which is going to show that Hume is wrong.
He may well be right.
OK, so the upshot is that our empirical reasoning, all of our empirical reasoning, wherever we reason from observed to unobserved.
It's based on a brute assumption of uniformity for which we can't give any ground.
It's not based on any insight into the nature of things.
Hume draws the conclusion that human reason basically differs only in degree from animal reasoning.
It's just like, you know, the dog. When he hears the door go, he expects to be taken for a walk or given food or whatever.
It's just animal habit. Well, basically, we're the same.
We see one billiard ball going towards another. We expect the second one to move by habit.
Look, as I mentioned in the earlier slide, attributed probable reasoning,
as well as demonstrative reasoning reasoning to the perception of Connexions.
Hume says that's nonsense that we don't perceive any connexion between one billiard ball moving and the other one moving.
It's just habit. And no causal interactions are really intelligible.
They're all based on this familiarity, what Kim calls custom.
You can see why Hume became very popular in the 20th century.
I talked in the last lecture about quantum mechanics, general relativity and so on.
People became aware that actually the world is rather weird and our intuitions do not provide a good guide to it.
In previous generations, people may have thought that they had rational insight into the way the world works.
In the 20th century, we were disabused of that complacent assumption.
We discovered actually that the only way we can find out how the world works is by experiment and observation.
But what humans shown is that even relying on experiments and observation,
we have to take for granted this basic assumption that the unobserved will resemble the observed.
OK, the general philosophy reading list includes several attempts to justify induction to answer him or any of these successful.
Well, let's take a little look at them. I've listed some there.
We'll be talking a little bit about the Van Cleave and Reichenbach moves next time.
But for now, I want to focus on the first two.
So the analytic justification of induction is basically saying that induction is rational by definition, right?
If you ask how can we justify extrapolation from observe to unobserved?
Well, that's just the rational thing to do if you don't extrapolate from observe to unobserved, you're being irrational.
So the gambler who says, Yes, I've lost this game 100 times in a row, I'm bound to win next time.
That's just irrational. OK? By definition.
So we don't need any argument to justify it. That's enough.
Probabilistic attempts to justify induction appeal to mathematical probability.
And there's quite a variety of those, we'll be looking at one of those.
The inductive justification of induction is basically saying induction has worked in the past.
It will work in the future. Now Hume obviously says that's just circular.
All right. Well, some philosophers have tried to find ingenious ways to get around that circularity.
And the pragmatic justification of induction says we are pragmatically justified in relying on induction.
We can't prove that it'll work or even that it's likely to work, but we've got good practical reason for relying on it.
Maybe we can give some theoretical argument to back that up by showing that induction will work in giving us predictions, if any method will.
That's the line that Reichenbach takes. So let's have a quick look at a couple of these.
So the analytic justification, as I say, says that induction is just rational by definition, what we mean by a rational method of inference.
Is one that infers the same about the future as has been observed in the past.
So suppose somebody relies on astrology or reading tea leaves.
Well, if you investigate these things, it finds out you find that they're hopelessly unreliable.
So we do not consider those rational methods of inference because they've proved not to be reliable.
That shows that we are judging methods of inference inductively.
We are treating those that yield truth consistently over time.
That's attribute the same properties to things over time as rational.
So induction is arguably constitute constitutive of what it is to be rational.
You can only be rational by definition if you think if you reason inductively.
OK, well, maybe that's plausible. But does it actually touch you?
I don't think it does. Because what Hume will say is this we do, of course, take for granted that the future will resemble the past.
We all do it all the time. We couldn't survive if we didn't. It's absolutely built into us to take for granted that the future will resemble the past.
And so obviously, we think of that as constitutive of human rationality.
And we people who think differently, we're going to treat as mad.
So, well, that's just a question of how we judge it. It doesn't mean we've got any independent justification for it.
That just shows that we are indeed taking it for granted.
What Hume is asking or challenging is the thought that we've got some kind of insight that justifies extrapolation.
He's not questioning that we use the word reason in a particular way.
Because the way in which we use that word actually builds in our assumption that induction is a reasonable way to go,
that we've got good evidence for it. Humans argued that actually that complacent assumption is false.
We don't have any good reason for supposing that the future will resemble the past.
So the analytic justification, you know, may be plausible as an account of how we use words, it doesn't touch him.
What about probabilistic justification? Now, Hume in his argument.
Take something for granted, which could be questioned he takes for granted that all probable arguments,
all arguments that aren't demonstrative in force have to rely on experience.
Right. Because remember, he said. You can't have a demonstrative argument that the future will resemble the past for the following reason.
We can imagine the future not resembling the past. We can coherently conceive of the future being different.
That's enough to show that you can't demonstrate that the future will be the same.
And then with regard to probable argument, the reason you can't justify the future resembling the past by inductive or probable reasoning,
Hume says, is that all such reasoning takes for granted that the future will resemble the past.
So you'd be reasoning in a circle. But maybe humans overlooked something.
Maybe it is possible to have probabilistic reasoning, which is a priority where your reasoning from basic probabilistic principles
that we see intuitively to be true rather than on the basis of experience.
And if such an argument were possible, then Hume's argument has not ruled it out.
OK, so there is a gap in Hume's argument. So probabilistic justifications aim to get through that gap.
Now, a lot of attempts have been made, I've listed a few of them there.
Roy Harrod. Came up with an ingenious argument, which was later developed by Simon Blackburn,
and we're going to be looking a little bit at that, that this is on your reading list.
OK, so here's the ingenious argument. Suppose I'm crossing a desert, I don't know how big the desert is.
And I'm making predictions about how long the desert will go on.
So I'm sitting out on a straight path across the desert, and I'm making predictions about how long my journey will continue through the desert.
And suppose I make predictions like this,
the desert ahead will extend for at least 10 percent as long as the distance I've already travelled through it.
OK, now imagine I I make such predictions again and again and again, so I'm walking along.
I say the desert will last for 10 percent more. The desert will last for 10 percent more, the desert will last for 10 percent more.
So I'm making lots and lots of these predictions.
And of course, as I go further and further through the desert desert, my predictions are predicting yet more desert.
So if I go for 10 miles, I'm predicting another mile. If I go for 20 miles, I'm predicting another two miles.
If I go for 30 miles, I'm predicting another three miles. And so on.
OK, now at some point. The desert hands.
And so the predictions I make towards the end of that journey will have turned out false.
It will not, in fact, have been true that the desert had another 10 per cent to go beyond what it had already gone.
And the dividing line, the point at which the predictions will stop being true will be 10 11.
So the way through the journey? OK. So if I've gone, let's let's suppose that the desert is 110 miles wide.
Then after 100 miles, I will be making the prediction. The desert will go on for another 10 miles.
And that prediction will be right, but the very next one I make will be wrong.
Agreed. OK, so imagine that I'm making these these predictions sufficiently frequently that
we can ignore rounding error 10 11 months of my predictions will come out,
right? OK, if I make, well, let's call them one tenth extrapolations i.e. the journey is going to go go on for another tenth as long as it's gone.
So far, 10 out of 11 of those will turn out true.
OK, so maybe this justifies making such predictions.
If I make such a prediction, I've got a 10 11 chance of being true.
So I can justify extrapolation, at least to that limited extent and humans wrong.
Well, that's not quite right. It's not quite right, because imagine that I've imagined that I've travelled 100 miles through the desert.
And I'm making a prediction the desert will go on for another 10 miles.
I've no idea how long it's going to go on, all right, but I make that kind of prediction.
When I say to myself, well, look, what I know is that no matter how long it goes on, 10 11 of these predictions will be right.
So I've got a 10 11 chance that this particular prediction will be right.
Hang on a minute. That's not right, is it because a load of predictions that I made in the past have already been fulfilled, right?
All the predictions, for example, that I made up to 90 miles.
They've already come and gone. Right?
When I passed the 99th mile that confirmed the prediction that I made it 90 miles, that it would go on for another nine.
So loads of the predictions have already been fulfilled.
So now when I ask, what is the chance that this prediction will be fulfilled,
I can't go by this 10 11 chance because that a large proportion or significant
proportion of those 10 11s that are going to come out true have already come out true.
So it's a bit like I mean, imagine if I clicked the tickets from one supposes a weekly lottery.
All right. And I clicked the tickets from the previous nine lotteries.
OK. And then on the tenth week, I buy a lottery ticket and I put it into a bag together with those the nine previous winning tickets.
And I say there's a nine 10 chance of me winning this lottery because I've got it's one of 10 tickets and nine of them are winners.
No, can't do that. The nine winners have already been and gone.
I'm interested in whether this particular ticket will win, so I can't I can't load the dice as it were like that.
Well, Harrods suggests that there's a way of correcting for this.
Basically, you average over all the different positions that you could be on your way through the through the desert,
and he suggests you get a slightly more modest prediction of 100 over 121.
Let's not worry about that. I mean, it's a it's a reasonable point.
But Blackburn points out that it doesn't actually solve the problem,
because even if I average for all the different positions that I could be through my journey.
The fact remains that at 100 once I've got to 100 miles, there is still the fact that I know that all these previous predictions,
the ones I made up to 90 miles and indeed beyond 90 miles.
All those have already been gone. So averaging over every possible predict place, I could be within the that within the overall desert,
you know, am I in the first half of it or the first quarter or the last 10th or the last 11?
I just don't know. All I know is that a lot of predictions that I've already made have been and gone.
I don't know what proportion of those already successful predictions.
I don't know what proportion they form of the whole unless I know how big the desert is.
So what Blackburn does is he says, well, here's a way of saving Harvard's argument,
rather than focus on the believer, focus on the sceptic and say to the sceptic, Look, you are denying.
That we can justifiably rely on these one extrapolations.
But look, Howard's argument still holds that in general, if people make inferences of this kind extrapolations of this kind.
10 out of 11 of them will be successful. So you, as a sceptic, are casting doubt on something which 10 out of 11 will be successful.
How do you justify that? Well, it's a neat effort, but I don't think it works.
Let's, first of all, a couple of general points.
First of all, I want to suggest that the the focus that Harold introduces and Blackburn retains on the proportion of
extrapolations that will come out true is simply giving a false impression of the logic of the situation.
It's like with those lottery tickets that you put into a bank. The extrapolations are sequentially ordered.
They're not a random group. It's not like you've got a load of predictions and you randomly pick one out of it, and 10 out of 11 of these are true.
The extrapolations come strictly in order they are made in order and they are fulfilled in order.
And the extrapolation that I make now can only be true with all of the ones before were true.
So thinking in terms of choosing one from a group is just a misleading way of representing the situation.
Another important point against Blackburn is that appealing to a general practise of making this kind of inference is hopeless for a different reason.
And that is that the 10 out of 11 proportion applies to every individual uniformity, every journey you make.
If you make these 10 11 extrapolations sufficiently frequently, 10 out of 11 of them will be true.
All right. Sorry. I think I need to repeat that, Steve.
Any journey at all.
If you make one tenth extrapolations sufficiently frequently, then 10 out of 11 of them will come out true in that individual journey.
So it's not like you've got 10, 11, it's true in some large sample,
some large group from which you are picking an individual example rather than every individual journey you do.
The proportion is 10 out of 11. So when I ask, is my next extrapolation likely to come out true, statistically,
the only sequence that matters is the current one, the current journey.
What what may be true about other journeys just is not relevant despite Blackburn.
And the only extrapolation that matters is the one I'm about to give appealing to the statistics of extrapolations in general won't help.
As I say, they're sequentially ordered. It's not like choosing one from a set.
Unless I know how far I am through the desert or the period of uniformity, if we're applying this to induction.
I can't know what proportion of extrapolations have already been fulfilled, so I can't apply the statistics anyway.
So unless I can justify extrapolation from observed to unobserved, it seems I'm no better off than when I started out.
So it's an ingenious attempt to justify induction.
It's trying to show that one tenth extrapolations, modest extrapolations from experience are justified statistically.
If that were true, we would be able to justify induction, at least to some extent.
We could say the world has been uniform for at least, you know, 100 or a thousand or maybe 13 billion years.
Therefore, it's likely to continue to be uniform for a tenth as long again.
But sadly, it doesn't work.
Next time, we'll be looking more at scepticism and briefly considering a couple of other attempts to respond to Hume's scepticism.
Thank you.