Context

In the opening Section of Part II, the author argued for the negative claim that the ideas of space and time cannot be divided infinitely. His aim in the present Section is to give a positive account of the ideas of space and time.

Background

Locke

According to Locke, we have a number of different kinds of simple ideas (or perceptions, in the terminology of the author). Ideas of colors are produced by vision, and the idea of solidity is produced by touch (An Essay concerning Human Understanding, Book II, Chapter 3). Another kind of simple idea is that of space or extension, which we get from the two senses of sight and touch (Chapter 5). Locke comments on this idea:

[W]e get the idea of space, both by our sight and touch; which, I think, is so evident, that it would be as needless to go to prove that men perceive, by their sight, a distance between bodies of different colours, or between the parts of the same body, as that they see colours themselves: nor is it less obvious, that they can do so in the dark by feeling and touch.

Berkeley

In the New Theory of Vision, Berkeley treated extension as magnitude, either of what is visible or of what is tangible. The components of extension are visible and tangible points, the minimum perceivable units of the senses of sight and touch (Section 54). In the Principles of Human Knowledge, Berkeley regarded extension to be an idea or sense-impression (Section 5). It cannot be separated or abstracted from color (Section 99). There is no idea of time that can be abstracted from the succession of ideas in the mind (Section 98).

The Treatise

1. The author lauds his own discovery that the origin of all ideas in the mind are prior impressions. The virtue of impressions is that they are all so clear and evident, that they admit of no controversy. Ideas, on the other hand, are often so obscure, that ’tis almost impossible even for the mind, which forms them, to tell exactly their nature and composition. This principle that ideas are derived from impressions will be applied here to the ideas of space and time in order to discover farther the[ir] nature.

2. The idea of extension is formed in the following way. When my eyes are open, I perceive many visible objects (such as a table in front of me), and when I close them again, I form an idea of extension. Because every idea is derived from an impression or impressions, there must be some impression or impressions from which the idea of extension is derived. [Since the idea of extension is formed as the result of the use of vision], the precedent impression, if sensible, must be derived from sight. Otherwise, the impression(s) would have to be an internal one that arises from one or more impressions of sight. [Internal impressions are also called secondary impressions or impressions of reflection.]

3. Our internal impressions are our passions, emotions, desires and aversions. [These are the subject of Book II.] The author recognizes that no one would take these to be the model, from which the idea of space is deriv’d. So the origin of the idea of space must lie in sensation. The question then becomes what impressions of the senses give rise to the idea of space. This is the principal question, and decides without appeal the nature of the idea.

4. The answer is that if the impressions are visual, as when a table is viewed, they are sufficient to supply an idea of extension, which is borrow’d from them. The visual impressions are nothing more than of colour’d points, dispos’d in a certain manner. The author asks the reader to point out anything else that enters into the impressions of sight. If this cannot be done, we may conclude with certainty, that the idea of extension is nothing but a copy of these colour’d points, and of the manner of their appearance.

5. Consider now the first formation of the idea of extension from the visual impressions of the extended object. If the visible points were all of the same color, say, purple, then whenever the idea formed of that object is repeated, the points would lie in the same order and be of the same color. With repeated experience we discover objects of different colors, which are arrayed in many different ways. If we find a commonality in the arrangement of the points, we then omit the peculiarities of colour, as far as possible, and found an abstract idea merely on that disposition of points, or manner of appearance, in which they agree. [The nature of abstract ideas is the topic of Part I, Section 7.] The abstract idea may even represent the disposition discovered by the sense of touch which resembles the disposition of colored points. The reason is that [as claimed in Part I, Section 7] abstract ideas are particular ideas that are consider’d in a certain light, which can represent many objects, even those very different from themselves, when they are attached to general terms [such as ‘extended’].

6. The abstract idea of time, while likewise a particular idea, represents objects with even greater differences, as it is derived from the succession of both impressions of sense and impressions of reflection. [Thus, the succession discovered in motion of physical objects and in the changes in our emotional states are both represented by the abstract idea of time.]

7. A succession of impressions is required for the generation of the idea of time. It is not possible for time alone ever to make its appearance, or be taken notice of by the mind. Someone in a deep sleep does not notice the passage of time, nor does someone concentrating deeply on a single matter. Moreover, the appearance of time in the imagination varies with speed with which one’s impressions are changing. A great philosopher has remarked that there are certain natural limits to the speed at which our impressions change, and that nothing in the objects of the impressions can over-ride these limits.

[Footnote. The great philosopher is John Locke. See above.]

For example, a burning object at the end of a swiftly rotating rod will appear to describe a circle because we cannot generate impressions fast enough to correspond to the different positions occupied in succession by the object as it twirls about. Further, if there is no perception of succession, there is no idea of the passage of time, even if there really is succession in the objects of the perception. From these phænomena, as well as from many others, we may conclude, that time cannot make its appearance to the mind, either alone, or attended with a steady unchangeable object, but is always discover’d by some perceivable succession of changeable objects.

8. The claim just made, that time is perceived only as the result of a perceivable perception of succession in objects, is now confirmed by a new argument, which to me seems perfectly decisive and convincing. The first evident point is that time must have parts, since we conceive of lengths of times (durations) as different from one another. [An hour is longer than a minute, containing minutes as parts.] The second evident point is that the parts of time do not exist simultaneously [as claimed in the previous Section]. An object that is not changing produces only impressions that co-exist. [There is no succession in the impressions of the object, assuming that the visual set-up remains constant. Co-existence must be understood in this way, since it cannot mean existence at the same time because the disposition of the impressions is supposed to be the basis of the very idea of time.] So there are no parts in the impressions that do not co-exist, in which case there is no basis for the idea of time, and consequently . . . the idea must be deriv’d from a succession of changeable objects, and time in its first appearance can never be sever’d from such a succession.

9. The conclusion just drawn, that the idea of time requires a succession of impressions of changeable objects, is restricted to the first appearance of that idea. This raises the question of whether time can be conceived without the conception of succession, and thus whether the idea of time can be distinct from all other ideas.

10. In general, we may wish to know whether we can have separate ideas of objects that are joined in a single impression. [For example, the color and shape of an object are joined in the impression of a colored figure, and we may wish to know whether the idea of color is separable from the idea of shape. See Part I, Section 7.] The answer is that if the objects are different from each other, then the ideas of them can be separated. The author here repeats his two criteria of identity and difference: What is different is distinguishable, and what is distinguishable is separable in conception. Conversely, what is not different is not distinguishable, and what is not distinguishable is not separable in conception. [From this it follows that objects are different if and only if they are separable in conception.] The author claims that time is not different from a succession of perceptions, in which case it is not distinguishable from them and therefore cannot be conceived separately from them. The reason time fails to meet these criteria of separability is that it is not a further perception in addition to the successive perceptions. Rather, it arises altogether from the manner, in which impressions appear to the mind, without making one of the number. An example of successive impressions giving rise to an idea of time is the hearing of five notes played on a flute. There is no sixth impression of time conveyed by any of the senses. Nor is there an additional impression of reflection [a passion or emotion] produced by the five notes so as to yield an idea of time. But such an impression of reflection is needed to produce an idea of reflection [as the separate idea of time would be in this case]. Moreover, given the constitution of our minds, we cannot produce a new idea by revolving over a thousand times impressions of sensation, since this procedure does not produce any new impression [and all ideas are derived from impressions]. Our contemplation can only reveal the manner, in which the different sounds make their appearance [and not a new sensation or impression of reflection]. This manner may be considered later apart from the heard sounds and applied to any other objects. The mind must have the ideas of some objects to have an idea of time, since that idea of time does not arise from any primary distinct impression, it must be based on some other ideas. What is required is nothing but different ideas, or impressions, or objects dispos’d in a certain manner, that is, succeeding each other.

11. The author acknowledges that the common opinion among both the philosophers and the unlearned that the idea of duration is applicable in a proper sense to objects, which are perfectly unchangeable. This opinion is refuted by the observation that the idea of duration is always deriv’d from a succession of changeable objects, and can never be convey’d to the mind by any thing stedfast and unchangeable. Since the idea of duration cannot be derived from perception of an unchangeable object, that idea cannot be applied to such an object in any propriety or exactness. Thus, nothing that does not change can be said [properly] to have duration. The only way in which an idea can represent or apply to either an impression or an object from which it is not derived is by a fiction of the imagination. The author will later discuss the type of fiction we produce in our attempt to attribute duration to unchanging objects and to use it to measure rest as well as motion.

[Footnote. See Section 5.]

12. A further very decisive argument in support of the author’s thesis is based on the principle that our ideas of [space and time] are compounded of parts, which are indivisible. [This principle was defended in Section 1.] This argument will be examined in the case of space in the next four paragraphs and in the case of time in the concluding paragraph.

13. Since every distinguishable idea is separable, we may separate from the compound idea of extension one of the simple indivisible ideas making it up. Considering it by itself, we can try to discover its nature and qualities.

14. This simple indivisible idea cannot be the idea of extension, since the latter consists of parts and it has been supposed that the former does not. But it is not nothing either, since together with other ideas of the same sort it makes up the idea of something, extension. To think that something can be composed of non-entities is absurd. So we are left to ask, What is our idea of a simple and indivisible point? As the question has scarce ever been thought of, it is no wonder that the answer will appear somewhat new. What has been debated is the nature of mathematical points, but what has not been considered is the nature of the idea of a point.

15. There are two senses that convey the idea of space: sight and touch. None of the remaining senses can produce the appearance of extension. The components of the compound idea representing extension are several lesser impressions, that are indivisible to the eye or feeling, and may be call’d impressions of atoms or corpuscles endow’d with colour and solidity [if they are impressions of sight or touch, respectively]. Further, just as these atoms must be colored or solid in order to be perceived by senses, they must retain their color or solidity to be comprehended by our imaginations. There is nothing but the idea of their colour or tangibility, which can render them conceivable by the mind. If these qualities are removed, the conception is annihilated.

16. The qualities of the parts apply to the whole. There can be no idea of a point that is not colored or solid, and since points are the components out of which extension is formed, there could be no idea of extension composed of points that are not colored or solid. We are conscious that the idea of extension does exist, and so the parts of extension must exist as well, and for them to exist, they must be colored or solid. So there is no idea of space or of extension unless these are considered to be an object of sight or touch.

17. This general line of reasoning applies to time. If there is to be an idea of time based on a succession of perceptions, the moments of time must be fill’d with some real object or existence, whose succession forms the duration, and makes it be conceivable by the mind.

The Enquiry

There is no discussion in the Enquiry of the topics covered in the present Section.

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