Summary: A Treatise of Human Nature (page 4)

Part 2: Ideas of Space and Time

In this first movement of thought, Hume has determined the nature of ideas, their origin, and the way in which they associate.

He now turns to the study of particular ideas, beginning with those of space and time—two fundamental ideas that must be examined in the light of the empiricist conception he has just developed.

Where do the ideas of space and time come from? What is their nature?

First, we must clear up a difficulty: we must resolve a paradox that has confronted all thinking about space and time since the dawn of philosophy—the paradox of infinite divisibility.

It was Zeno of Elea who formulated it: space is infinitely divisible since we can always conceive of half the expanse we are considering. The arrow will never reach its target, since it will always have to cover half the distance remaining, and so on ad infinitum.

This paradox reveals the impossibility of movement; more broadly, it undermines the very notion of space, for what is space if it consists of an infinite number of parts ¹?

To resolve this paradox, Hume follows this path:

Rather than looking at space itself, let us examine the idea of space in our minds. How is it formed? What are its characteristics?

For Hume, thought cannot be an infinite process; it must necessarily come to an end—namely, finite ideas, simple and indivisible:

The idea which we form of any finite quality, is not infinitely divisible, but [..] by proper distinctions and separations we may run up this idea to inferior ones, which will be perfectly simple and indivisible. In rejecting the infinite capacity of the mind, we suppose it may arrive at an end in the division of its ideas ².

The same applies to things extended in space: when we mentally divide space, we necessarily reach a simple idea:

’Tis therefore certain, that the imagination reaches a minimum, and may raise up to itself an idea, of which it cannot conceive any sub-subdivision, and which cannot be diminish'd without a total annihilation ³.

He takes the example of the grain of sand: The idea of a grain of sand is not distinguishable, nor separable into twenty, much less into a thousand, ten thousand, or an infinite number of different ideas ⁴.

Now that the principle of a finite, simple, and indivisible idea is assured, what about space itself?

Using the same method, Hume describes what happens in our mind during the formation of the idea of space: if I start from the least idea I can form of a part of extension, and I then repeat this idea once, twice, thrice, etc. this one, I find the compound idea of extension, arising from its repetition, always to augment, and become double, triple, quadruple, etc. ⁵.

It eventually grows to a considerable size, but let us note that it remains finite. At no point have we encountered the infinite: we started from a finite idea, the simplest and indivisible one, and we arrive at another finite idea. The infinite appears only in the following way: Were I to carry on the addition in infinitum, I clearly perceive, that the idea of extension msut also become infinite ⁶.

Summing up: the idea of space is neither infinite nor infinitely divisible, any more than our abstract ideas are general. In both cases, they appear general or infinite to us because we consider them in a certain way that seems to extend them.

The same applies to time.

Hume multiplies the arguments to show that all the pretended demonstrations for the infinite divisibility of extension are equally sophistical ⁷.

As we can see, this approach sheds light on and resolves paradoxes that had resisted thought for centuries.

He is delighted by this:

No discovery cou'd have been made more happily for deciding all controversies concerning ideas, than that above-mention'd, that impressions always take the precedency of them, and that every idea, with which the imagination is furnish'd, first make its appearance in a correspondent impression ⁸.

When, therefore, we encounter a difficulty in our examination of an idea, we shall seek to reduce it, in a genetic approach, to the impression from which it originates. Indeed, are all so clear and evident, that they admit of no controversy; tho' many of our ideas are so obscure, that ’tis almost impossible even for the mind, which forms them, to tell exactly their nature and composition ⁹.

Here, then, is the origin of the idea of space:

Upon opening my eyes, and turning them to the surrounding objects, I perceive many visible bodies; and upon shutting them again, and considering the distance betwixt these bodies, I acquire the idea of extension ¹⁰.

In reality, I have no experience of space itself. All things considered, all you see are colour'd points, dispos'd in a certain manner ¹¹.

Other impressions reveal to us points of another colour, arranged in a different way, and from this we forge the abstract idea of extent—that is, of space.

Abstract ideas which, let us remember, are really nothing but particular ones, consider'd in a certain light; but being annex'd to general terms, they are able to represent a vast variety, and to comprehend objects, which, as they are alike in some particulars, are in others vastly wide of each other ¹².

Similarly, I have no experience of time itself.

In fact, as ’tis from the disposition of visible and tangible objects we receive the idea of space, so from the succession of ideas and impressions we form the idea of time, nor is it possible for time alone ever to make its appearance, or be taken notice of by the mind ¹³.

To summarise, according to Hume, the ideas of space and time:

a) Derive essentially from experience, from some of our impressions.

b) Derive indirectly from it, and are therefore derived, secondary. What experience reveals to us is merely a succession of coloured points or the succession of our impressions—an observation that radically calls their status and legitimacy into question.

Here is an idea that will leave its mark on Kant, and against which he will protest from the very beginning of the Critique of Pure Reason, arguing the opposite: space and time are not empirical concepts provided by experience, but the forms of sensibility—the conditions of possibility of experience itself—and thus recover their primary and original status.

Hume devotes lengthy developments to examining and refuting possible objections, which leads him once again to consider the doctrine of infinite divisibility. We will not examine these in detail but go straight to Part Three.

¹ 1.2.1, p.23
² Ibid.
³ Ibid.
⁴ Ibid.
⁵ 1.2.2, p.25
⁶ Ibid.
⁷ P.27
⁸ 1.2.3, ibid.
⁹ Ibid.
¹⁰ Ibid.
¹¹ Ibid.
¹² P.28
¹³ Ibid.