Okay. Now we're going to move on to Hume's theory of space and time.
Where we'll see that the theory of abstract ideas plays quite a significant role.
So the theory of space and time comes in. Book one, part two of the Treaties.
Now this part is very often ignored.
If you look at books on HUME, you will often find that no mention of this is made at all, or it's treated rather dismissively.
I actually think that's probably fairly justified.
But you will find plenty of HUME scholars who will argue the reverse, and I'll be referring to some of them.
Now, what you seems to be doing in this part of the treatise is applying his theory of ideas to draw
conclusions about the nature of both our ideas of space and time and of space and time themselves.
Now, you might think that the former is reasonable enough.
He's looking at our ideas, investigating them, drawing conclusions about how we conceive of space and time.
What seems a little bit more puzzling is that in this part of the treatise,
he seems often to be drawing conclusions that go beyond that, that talk about space and time in themselves independently of our ideas.
So the burden if the first part of part two is to argue that space and time,
both our ideas and space and time themselves, are not infinitely divisible.
So in the very first section entitled of the Infinite, The Visibility of our Ideas of Space and Time.
Now again we find humour saying that something is very obvious.
It is evident from the plainest observation that the capacity of the mind is limited and can never attain a full and adequate conception of infinity.
Okay. Well, that seems reasonable enough, right?
Our minds aren't infinite. If you try to imagine something that's infinite, you try to imagine the infinite sequence of numbers.
Or the infinite number of fractions or imagine infinitely dividing a line.
We do give up pretty quickly. It follows that the idea which we form of any finite quantity is not infinitely divisible.
We must ultimately therefore reach a minimum.
Now notice that there's a little bit of a an assumption here.
HUME seems to be assuming that because we cannot go on dividing our ideas infinitely,
we must hit rock bottom, as it were, with a particular minimum size.
It's not absolutely clear that that's the case. And one could imagine.
Trying to divide up one's image of something.
And succeeding to different extents on different occasions.
Perhaps sometimes we tire. Sometimes we feel more acute.
And so we're able to go farther. But HUME has an argument or an illustration to back this up.
So here's what we're supposed to do. Imagine an ink spot drawn on a board.
And imagine retreating from it further and further and further.
So the ink spot gets smaller and smaller. Until you just stop seeing it, it disappears.
Then go back just a tiny bit so you can just see it.
That is the minimum visible quantity.
So what you will see, HUME thinks, is a coloured point, a coloured extension list point, because it will be indivisible.
It will just be a point. You won't be able to distinguish the left side from the right side of it, but you will just see that point.
So what we have here is a kind of visual atom.
And we will see that HUME uses this atomic theory of our perceptions to draw quite significant conclusions.
Now. In a recent article in Human Studies, Rolf George has made what I think is a very interesting speculation.
The severability principle we've already met, and we'll see later Hume's various applications of it.
But an intriguing fact about Hume's philosophy is that the severability principle is
not mentioned at all after the treatise in the inquiry concerning human understanding.
It doesn't come up at all. Some people claim that it's there implicitly in certain of the arguments.
Personally, I'm not convinced. But what's also interesting is that a number of other things seem to disappear from the inquiry,
which at least seem to be connected quite closely with the severability principle.
For example, HUME drops the simple, complex distinction, or at least he puts much, much less emphasis on it.
And the distinction between simple and complex ideas seems to be very much wrapped up with
the theory we're talking about now about the simple visual atoms and atoms of other senses.
Likewise in the inquiry, we get almost no discussion of space and time.
We get a little bit when he talks about the sceptical arguments and we get a little footnote where
he refers to his theory of abstract ideas and suggests that might possibly provide a solution.
That said, there's a bit of a mystery there. We don't really know why HUME left this stuff out of the inquiry to obvious theories.
One He wanted to make the inquiry more simple and palatable.
He was addressing a different audience,
an audience who wouldn't be interested in all the intricacies of infinite visibility and his discussion of space and time.
So he saw no need to put in the severability principle.
Maybe. That's right. But an alternative explanation is that he'd lost confidence in it.
And Rolf George speculates a particular reason why this might be so.
So in 1738, James Durin published an essay upon distinct and indistinct vision.
And Georgie's hypothesis is that this, as it were, awoke David HUME from his dogmatic slumbers.
How could it do that? Well, here we have a line and here we have a dot.
And you will notice that the dot is wider, a greater diameter than the line is across.
Now, imagine retreating further and further away from that until the dot cannot be seen.
Nevertheless, you will still be able to see the line.
Now, that's an empirical claim. What James Durian was doing was making empirical investigations into human acuity.
But you can see that's a little bit of a problem for him.
If you think that there are minima in our visual field of a certain fixed size that as you go smaller and smaller,
you hit a limit like a computer pixel, just like the pixel on a computer screen.
You cannot represent any image which is smaller than that.
Well, at the point when that dot has disappeared, there should be no pixels at all left representing the line.
So the line should disappear too. But it doesn't. So as I say, that's an interesting speculation.
We don't know whether it's true. But the dates are very suggestive.
We have this investigation being published in 1738.
The treatise was published in 1739, a highly plausible that HUME between then and 1748 came across this, and George gives relevant evidence.
Okay. But let's now proceed and see what he does with his theory.
Well, having established that there are these minima.
HUME considers. Those.
Now, if we hit a minimum, if we actually think of a minimum possible point, it's extinction less.
You cannot distinguish the left from the right. It's as small as anything could be.
It follows that nothing can be more my Newt than some ideas which we form in the fantasy that the fancy remember is another name for the imagination.
And images which appear to the senses, since these are ideas and images perfectly simple and indivisible.
The only defect of our senses is that they give us disproportionate images of things and represent as my Newton unkempt.
What is really great and composed of a vast number of parts.
So take that dot that we've drawn on a board and maybe it's quite big, but we go further and further and further away until we can only just see it.
And at that point it looks to us completely simple and on compounded.
We just see the dot. Now we might therefore have the erroneously draw the conclusion that the thing itself that we're seeing is totally simple.
But what we can do at that point is pull out our binoculars or our telescope and take a look.
And we see, oh, it's bigger. So it's clear that there are a lot of light rays coming.
And if we use instruments, we can see the thing in more detail.
It ceases to be so simple. But what HUME wants to say is that that simple idea that we get correctly represents the smallest part of anything.
Nothing can be smaller than that. So we get a famous image of a flea from Hooke's Micrographia, 1665, and HUME is clearly alluding to this.
This, however, is certain that we can form ideas which shall be no greater than the smallest
atom of the animal spirits of an insect a thousand times less than a mite.
The animal spirits think of what goes through the nerves,
and we ought rather to conclude that the difficulty lies in enlarging our conception so much as
to form a just notion of a mite or even of an insect a thousand times less than a might for.
In order to form a just notion of these animals, we must have a distinct idea representing every part of them.
So what's going on here?
You might think that, you know, when we look at something from a distance, as it were, we're making an error in seeing the thing as simple.
Our idea as it were is misrepresenting it. And him saying, we think thinking that way around it is the wrong way, actually.
We can form ideas which are adequate to the tiny parts of things because our ideas are pure and simple.
They just aren't compounded. So they form an adequate idea of the very smallest parts of anything.
What's actually difficult is forming an idea adequate to a whole might.
That's vastly complex. Or even a creature.
A thousand. Part of that sort. Thousandth part of a mind. Okay.
So HUME has drawn here an important conclusion,
and it's one that he's going to use now to conclude about space and time in themselves rather than just about our ideas.
So we get that right at the beginning of treatise one, two, two.
Wherever ideas are adequate representations of objects, the relations, contradictions and agreements of the ideas are all applicable to the objects.
Okay, that seems reasonable. If our ideas are faithful representations of the way objects are.
Then inevitably any conclusions that we draw from the ideas will be applicable to the objects.
And I realise you're all wondering where the handout for this is.
It'll come next week with stuff for next time.
Because what didn't make up a complete end up. Okay.
So fair enough. If we've got adequate ideas, the ideas, as I say, faithfully represent what they are ideas of.
Then in reasoning about the ideas and drawing conclusions about those,
those conclusions will inevitably follow to the things that the ideas represent.
But here comes the crucial claim, the one he's been arguing for.
But our ideas are adequate representations of the most mind parts of extension.
And through whatever divisions and subdivisions we may suppose these parts to be arrived at.
They can never become inferior to some ideas which we form.
So the ideas are so simple, so un compounded that no part of extension can possibly be less than those.
The plain consequences that whatever appears impossible and contradictory upon the comparison of
these ideas must be really impossible and contradictory without any farther excuse or evasion.
Now notice that HUME here is not using what might seem seem to be his conceive ability principle.
He's arguing from inconceivable bility to impossibility.
That's different from arguing from conceive ability to possibility.
We saw the conceived policy principle last time. We'll be seeing lots more of the conceive ability principle.
HUME thinks quite generally that to conceive of something distinctly.
Implies its possibility. You cannot distinctly conceive of something that's impossible.
Okay, so conceive ability implies possibility. But here he's saying that inconceivable bility implies impossibility.
But he only wants to say that that applies where ideas are adequate.
Now that's quite important. Remember humans and empiricist. He thinks our ideas are derived from impressions.
He thinks, for example, that a blind man has no visual ideas.
So he surely doesn't want to say that. Inconceivable, as he quite generally implies, impossibility.
There may be all sorts of things which we cannot conceive because we don't have the ideas.
And he said that our minds are finite. There may be all sorts of things that we can't conceive of because we're just not capable of it.
We don't want to conclude, in general, that that implies impossibility.
But when our ideas are adequate, that's a different matter.
So he's already said that our ideas are adequate representations of the most minor parts of extension.
We've seen that our ideas are not infinitely divisible and it follows that the same is true of space.
I first take the least idea I can form of the part of extension and being certain that there is nothing more my newt than this idea.
I conclude that whatever I discover by its means must be a real quality of extension.
I then repeat this idea once, twice, thrice.
So imagine that tiny little atomic idea. And now put another one next to it and another one next to that.
And if it helps, think of them as differently coloured. You start off with a blue dot.
Remember, it's extension lists. You can't distinguish its parts. But now you put a red dot next to it, maybe a yellow dot next to that.
And what you do now is build up extension. The idea of extension comes to you as soon as you've got more than one of these.
So each of our minimal ideas is indivisible and therefore not extended.
But as soon as you put two together, you've got the minutia part of extension.
Add another one, you've got a bit more extension. Add another one.
You've got more. Carry on to infinity.
Where do you get? Well, you're going to have an infinitely large extension. No way round it.
Although each individual, indivisible atom, as it were, is unexpended.
As soon as you put lots of them together, you get a finite extension.
If you put an infinite number together, you will get an infinite extension.
So he goes as far as saying that the idea of an infinite number of paths is the same idea with that of an infinite extension.
So he's proved. To his satisfaction.
At any rate, that space is not infinitely divisible because we've got these little ideas that are adequate to the minimalist parts of space.
And if space were infinitely divisible, then you'd have to be able to have an infinite number of these tiny parts within a finite amount of space.
But you can't, because as soon as you get an infinite number of these little atoms, you get an infinite extension.
Now. If you're familiar at all with mathematics, an objection is likely to come to your mind.
Imagine something that's finite, extended. Imagine dividing that extension into and taking half of it.
Then divide that in two and take half. Divide that in two and take half and go on and on and on and on and on.
You start with a half, then a quarter, then an 1860.
On and on and on. Without stopping, apparently. So what's wrong with that?
Why can't you divide things infinitely? Well, Jim actually addresses this objection.
In a footnote, he distinguishes between proportional and adequate parts.
It's a proportional part where you're dividing up again and again and again like this, adequate parts, all of equal size.
And he just seems rather dogmatically to say, Well, that doesn't deal with my argument.
Because nothing I've prove nothing can be inferior to those main parts we conceive.
When I think of this idea of a simple, nothing can be smaller than that.
So divide up as much as you like. You cannot get smaller than that.
And if you can't get smaller than that, then an infinite number of those is going to give you an infinite extension.
So there you are. My argument stands. Later into the intersection, HUME again comes back and deals with a potential mathematical argument.
So there are various mathematical arguments that seem to tell in favour of infinite visibility that seem to try to prove it.
And HUME says these can't be right. Now, he is appealing to the conceive ability principle.
He's saying, I have this notion of space made up of all these little atoms.
That's a conceivable picture of the way space could be.
Since it's conceivable, it's possible. So any attempted proof that it's impossible must be fallacious.
So he's attacking the mathematical objection to his own view and he's attacking himself.
The argument of mathematicians that he's claimed as a positive proof of infinite visibility.
Now, these arguments don't seem to be.
Ideal. Particularly his argument against infinite visibility, against proportional parts.
Because when he says My idea is as simple as can be, this atomic idea of a visual atom.
Must correctly represent the smallest parts of space because nothing could possibly be smaller.
Therefore, when you finally get down to the ultimate bits of space, they're going to be simple.
My idea is simple. Therefore, the two must match.
That must be an adequate idea. The obvious response is to say, well, I'm sorry, who if space is infinitely divisible?
You never do. Get down to an ultimately simple part.
So I went in claiming that the ultimate parts of space must match with this idea.
You're begging the question you're taking for granted that you do actually get two ultimate simples.
And that's just assuming that space isn't infinitely divisible.
So there's a bit of a puzzle here. I mean, humans generally are pretty acute philosopher, as I've said,
but one part two is probably, well, almost certainly the weakest part of treatise.
But what? The arguments aren't that great. And maybe HUME just imagined himself to be better at mathematics than he really was later in life.
He did actually produce a treatise on geometry, and he was persuaded by Lord Stanhope, a noted mathematician, not to publish it.
Sadly, it disappeared without trace.
It'd be great if it turned up at some point, but at any rate, when he wrote the treatise, he seems pretty confident, doesn't it?
Is evident this is absolutely clear, etc.
So is something going on that brought it about that he didn't see the problems that we see in his arguments?
Well, here we reduced really to speculation. Tom Holden, a book published in 2004.
He suggests that HUME is presupposing an actual part's metaphysic,
whereby anything that is divisible must in advance consist of the actual parts into which it is divided.
So contrast to different possible accounts of visibility, you've got the Aristotelian idea of potential infinities.
So suppose I take an extension, divide it up. Divide that again.
Again and again and again. Like, however much I divide it, I can go on dividing further.
So in that sense, there's a potential infinity. It's like saying, give me any number.
I can always add one. You can always go further.
So there's a potential infinity. But that's different from saying that there's an actual infinity.
You can say that the the line is potentially divisible without claiming that it is already divided into parts,
that those separate parts already exist, as it were, prior to the division.
But Tom argues that at the time the actual part, metaphysic was very strongly in the air.
The thought that if some things divisible, the parts already have to be there.
They have to exist prior to the division. Now that suggestion is somewhat supported by an argument that HUME uses in treaties.
One, two, two, three. He borrows it from Nicholas.
The militia is evident that existence in itself belongs only to unity and is never applicable to number.
But on account of the unities of which the number is composed,
it is therefore utterly absurd to suppose any number to exist and yet deny the existence of unities.
And as extension is always a number and so on.
The thought is if a group of people exist, they exist only in virtue of the existence of each one of them.
Take any number of things. The ultimate existence are always the unities of which the group is composed.
Now apply that to an extension. The thought would be that unless there are ultimate parts of extension.
Nothing exists. So if if if you always can divide further, you never hit the ground.
Then ultimately, metaphysically, there's nothing. Another possible account of what's going on is due to Don Baxter.
He's written an article in the Cambridge Companion to HUME quite recent.
And he suggests that HUME is pursuing a somewhat Kantian agenda.
So what Immanuel Kant wanted to do was to say that our knowledge of space and time,
our knowledge of space and time in the phenomenal world, in the world that we experience, not in the world as it is in itself.
And.
So Baxter suggestion is that Hume's aim is to find out about objects as they appear to us, by examination of the ideas that we use to represent them.
So it's less ambitious. The thought is Hume's concern is with space and time.
Within, as it were, the experienced manifold. And within that realm, the limits of space and time are given by the limits of our ideas.
I'm not persuaded, but it's an interesting suggestion.
Finally notice that HUME draws the same conclusions about time that he draws about space.
All this reasoning, he says, takes place with regard to time, and he adds an extra argument.
It's the essence of temporal moments to be successive.
Time is of its nature, successive in a way that space isn't.
So if time were infinitely divisible, you'd get coexisting moments.
And that's not possible. So time can't be infinitely divisible.
And then as soon as you think of motion something moving in time through space,
you can see that if infinite visibility of time is impossible, infinite the visibility of space must be as well.
Okay, we'll continue next time with a little bit more on space and time.
And then we will be getting on to book one, part three, which is the most important part of the entire treatise.
See you then.