Context

In Sections 1 through 3, the author presented his system explaining our ideas of space and time. In the previous Section, he defended the first of the two main parts of the system, that space and time are composed of indivisible parts. The present section will defend the second main part of the system, which is that human beings can form no conception of a part of space and time that is not filled with some existing thing.

Background

The question of the existence of a vacuum, void, or empty space was a topic of great controversy in ancient philosophy. The atomists were the most prominent advocates of the void, while Aristotle was the most significant defender of the plenum or matter with no void between its parts. There was a vigorous on-going debate as well among the modern metaphysicians and natural scientists.

Aristotle

Aristotle gives a thorough treatment of the state of the debate over the void in Book IV, Chapters 6 through 9. He describes the various ways in which the void was understood, analyzes the argument for and against the existence of the void, and draws his own conclusion that the void does not exist. The basic conception of the void is that of a place that contains nothing tangible in it. A place with color or sound would be said to be a void if it could receive something tangible and not a void if it could not receive something tangible. One of the main arguments for the existence of the void is that it is necessary for motion to be possible. The reason is that if the universe were full, the only way motion could occur is if the moving body could occupy the place of another body, (or penetrate the other body, as the author puts it), which is impossible. Aristotle’s solution to this problem was that bodies may simultaneously make room for one another, though there is no interval separate and apart from the bodies that are in movement. And this is plain even in the rotation of continuous things, as in that of liquids (Chapter 7). The author makes reference to this solution in paragraph 27 below.

Descartes

A key characteristic of the metaphysics of Descartes is his description of matter as extended substance. This view is described in the Principles of Philosophy, Part II, Article XI. [N]othing remains in the idea of body, except that it is something extended in length, breadth, and depth; and this something is comprised in our idea of space, not only of that which is full of body, but even of what is called void space. Therefore, so-called void space is not really empty because it is extended, but rather is filled with fine particles (Article XVII). A vacuum, space devoid of body, is impossible, because since there is extension in it there is necessarily also substance (Article XVI). Descartes claims that the non-existence of a vacuum is a necessary truth that cannot be violated even by God. A cavity in any object is extended and extension is an attribute of an extended substance—a body.

And accordingly, if it be asked what would happen were God to remove from a vessel all the body contained in it, without permitting another body to occupy its place, the answer must be that the sides of the vessel would thus come into proximity with each other. For two bodies must touch each other when there is nothing between them, and it is manifestly contradictory for two bodies to be apart, in other words, that there should be a distance between them, and this distance yet be nothing; for all distance is a mode of extension, and cannot therefore exist without an extended substance. (Article XVIII)

Newton

In Book III of the Mathematical Principles of Natural Philosophy, Newton pronounces his Theorem VI, That all bodies gravitate toward every planet; and that the weights of bodies toward any the same planet, at equal distances from the centre of the planet, are proportional to the quantities of matter which they severally contain. From this theorem he draws Corollary 4, If all the solid particles of all bodies are of the same density, nor can be rarified without pores, a void, space, or vacuum may be granted. By bodies of the same density, I mean those whose vires inertia are in the proportion of their bulks. Although no argument is given for this corollary, it seems to follow from the previous one, which states that All spaces are not equally full. The basis for this claim is that if all spaces were equally full, their weights would depend on their forms and textures, a claim disproved in the first corollary, which appeals to the theorem that it is the quantities of matter and their distances from the center are the only factors determining the weight or gravity of a body.

Leibniz and Clarke

In the celebrated correspondence between Leibniz and Samuel Clarke, the existence of a vacuum was asserted by Clarke on behalf of Newton and denied by Leibniz. None of the arguments presented there are relevant to the present Section.

Locke

Locke’s An Essay concerning Human Understanding contains a chapter devoted to the idea of space, Book II, Chapter XIII. He claims that this idea is obtained from 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. (Section 2)

The Treatise

1. The second part of the author’s system was that the idea of space or extension is nothing but the idea of visible or tangible points distributed in a certain order. [See Section 1.] From this it follows that it is impossible for us to form an idea of a vacuum or space, where there is nothing visible or tangible. There are three objections to this principle. All three objections will be stated together at first, because the answers to some of them depend on the answers to others.

2. The first objection concerns the history of the dispute between those who hold that space is entirely full (a plenum) and those who claim that there are gaps between objects in space. These disputes have never been resolved, the objection goes, and philosophers believe they are free to defend whichever side of the dispute they fancy. And no matter what the outcome of that dispute about the real existence of a vacuum, there is no disputing that we have an idea of it, because there could be no long history of a dispute over whether a vacuum exists without both sides having a notion of what it is they were disputing about.

3. The second objection does not depend on the first and so may be raised even if the first objection is contested. It consists of an argument for the reality of the idea a vacuum, or at least for the possibility of such an idea. [A version of this argument is found in Locke, as noted above.] The argument begins with the principle that every idea that is an infallible and necessary consequence of ideas that are possible is itself possible. The next step is the claim that the idea of the world’s being deprived of motion is a possible idea, even if the world is a plenum. Another possible idea is that of the annihilation of any part of matter by the omnipotence of the deity, while the other parts remain at rest. The reason that this idea is possible is that the ideas of two parcels of matter are distinguishable, and hence are separable in the imagination, in which case they may be conceiv’d to be separately existent. From this conception of their separate existence it follows that the existence of no parcel of matter depends for its existence on any other, any more than a square figure in one body implies a square figure in every one. The author now asks what results when we put together the ideas of bodies being at rest and being annihilated. Suppose there is a chamber within which all the air and smaller bodies are annihilated, while the walls remain motionless. What must we conceive will happen? Some metaphysicians [such as Descartes, as described above] identify matter with extension and hence claim that annihilating matter annihilates extension. As a result, there can be no distance between the walls, and they touch each other; in the same manner as my hand touches the paper, which is immediately before me. The author now challenges this reasoning because it appears that the touching of the walls implies their motion, but they are presumed to be at rest and [therefore] stand in the same spatial relation to one another. Suppose that two walls run north and south, while the other two are oriented east and west. How can the north and south walls touch while preserving their relation to the east and west walls? The same question can be asked about the floor and ceiling. How can the floor meet the ceiling without disrupting their relation to the four walls? If you change their position, you suppose a motion. Or, if something is conceived as lying between the six surfaces, it must have been created in the wake of the annihilation. So, if we adhere strictly to the notions of rest and annihilation, the idea resulting from their combination is that of a vacuum, rather than the contact of the surfaces.

4. The third objection goes farther and asserts not only that the idea of a vacuum is a real or possible idea, but that it is also necessary and unavoidable. The basis of this claim is the fact that we observe motion in bodies. It is claimed that this observed motion could not take place or be conceived unless a displaced body had a vacuum into which it could move. The author will not comment on this objection, as it lies primarily with in the scope of natural philosophy and not the science of man, or moral philosophy, which is the topic of the Treatise.

5. Answering the first two objections requires taking the matter pretty deep, in order to understand perfectly what the dispute is about. This will require considering the nature and origin of several ideas. We begin with the idea of darkness, which idea is not positive, but rather the negation of light, or more properly speaking, of colour’d and visible objects. A person born blind would have no idea of light or darkness, and a sighted person sees no more when completely deprived of light. [So, even with the power of sight, a person understands what darkness is only in a negative way.] The conclusion drawn by the author is that the impression of extension is not received from the mere removal of visible objects, and that the idea of utter darkness can never be the same as that of a vacuum.

6. A second example concerns tangible impressions. The author has us consider a person who is supported in the air, and . . . softly convey’d along by some invisible power. [That is, the person is floating and moving forward by a force that cannot be seen or felt.] Such a person perceives nothing that would give him the idea of extension, or in fact of any [tangible] idea. This is the case even if he were to flap his arms and legs about. This may give him a succession of impressions, which might be the basis of an idea of time. But these perceptions certainly are not dispos’d in such a manner, as is necessary to convey the idea of space or extension.

7. Neither darkness with the removal of everything visible nor motion with the removal of everything tangible can give us the idea of extension without matter, or of a vacuum, as can be seen from the preceding two paragraphs. This raises a new question: can darkness or motion give us an idea of extension when they are mixed with visible or tangible perceptions, respectively?

8. Philosophers [such as Berkeley] commonly hold that it is primarily reason, rather than the senses, that discover distance, since all objects appear to the eyes as if they were painted on a flat surface. [Ordinarily,] we see objects separated by other objects, but they are also separated by the blue color of the sky. [So, if we want to discover whether darkness can afford us] the impression or idea of a vacuum, we must consider the case in which two luminous bodies are separated by utter darkness, with no impression of any visible objects.

9. A parallel question can be asked concerning the tangible idea of extension. Can it be formed from the feeling of one object, followed by no feeling, and followed again by the feeling of another object. The question is, whether these intervals do not afford us the idea of extension without body?

10. Here is a way of explaining how we can form an idea of extension from the impressions of bodies separated by total darkness. Take any two luminous bodies. We can perceive whether they are conjoined to each other or separated, and this by a grate distance or a small distance. Moreover, we perceive variations in these distances as the bodies move. Because the distance is not something colored or visible, it may be thought that here is a vacuum or pure extension, not only intelligible to the mind, but obvious to the very sense.

11. Although this way of thinking [i.e., taking perceivable distance to be the foundation of an idea of extension] is common, it will be corrected by a little reflection. Suppose that in the midst of perfect darkness, two bodies were to appear to the vision. The only thing that changes in this situation is the appearance of the two bodies, and all the rest continues to be as before, a perfect negation of light, and of every colour’d or visible object. This holds not only of what lies in a direction away from the bodies, but also for the interval between them—the distance—which is nothing but darkness or the negation of light; without parts, without composition, invariable and indivisible. Because the distance is perceived by a sighted person no more so than by a blind one, or by sighted people in the darkest night, the distance itself must have the same properties, [being without parts or composition, invariable and indivisible]. So, since we get no idea of extension from blindness or the darkness presented to both the blind and the sighted, it is impossible that the dark and undistinguishable distance betwixt two bodies can every produce that idea [of extension].

12. When two luminous objects appear in utter darkness, the only difference there presence makes, the author has contended, is in the objects themselves, and in the manner they affect our senses. The only way we can judge of the distance is by [this manner,] such as the angles formed by the light flowing from them, the motion needed by the eye to look from one to the other, and the different parts of the organs of sight that are affected by the two bodies. [T]hese produce the only perceptions, from which we can judge of the distance. However, the perceptions themselves are simple and indivisible and hence cannot afford the idea of extension [which is complex and divisible].

13. This conclusion is now illustrated for the corresponding case of our idea of tangible extension. Suppose there are two tangible or solid objects, separated by an imaginary distance. [The distance must be imagined, because it is not perceived.] Two cases are supposed by the author. In the first, a person is supported by the air, and moving his limbs to and fro, without meeting any thing tangible. The second is that of someone who feeling something tangible, leaves it, and after a motion, of which he is sensible, perceives another tangible object. The author asks what is the difference between the two cases. He thinks that everyone will agree that the only difference is the perception of the objects in the second case, while the sensation of motion is in both cases the same. In the first case, the sensation of motion cannot give us an idea of extension, and since the sensation is not altered by the presence of the objects, adding the perception of the objects to the perception of the motion does not yield an idea of extension, either.

14. Although neither darkness nor motion (with or without separated objects) can produce an idea of a vacuum or extension without matter, they do cause us to imagine falsely that such an idea is produced by them. For there is a close relation betwixt that motion and darkness, and a real extension, or composition of visible and tangible objects.

15. Three aspects of this close relation are given in this and the next two paragraphs. The first aspect is the fact that our perception works the same way when we perceive an extended array of sensible objects and when we perceive two objects with nothing sensible between them. The relations noted in paragraph 12 hold in both cases. The angles formed with the eyes, [the motion of the eyes in shifting the gaze from one to the other, and the effects on the optical organs,] are the same whether the interval between the two bodies is perceivable or not. In the case of feeling, we feel the same motion whether there there are bodies between the two felt bodies or not.

16. The second sameness in the relations between the bodies and the perceiver is the way in which we convert an invisible and intangible distance into a visible and tangible one, without any change in the objects which lie at a distance. Experience shows that we can assign the same distance between two bodies that are separated by darkness as we can to those separated by visible objects, without any sensible impulse or penetration, and without any change on that angle, under which they appear to the senses. Experience also shows that the same motion will allow us to feel two separated objects as to feel two objects that are linked to each other by other tangible objects.

17. The third relation between real and imagined distance is that the physical effects on each other of two bodies separated with nothing in between and two with objects interposed between them are virtually the same. Such properties as heat, cold, light, attraction and so forth diminish with distance, and there is but little difference observ’d whether this distance be mark’d out by compounded and sensible objects, or be known only by the manner, in which the distant objects affect the senses.

18. The conclusion is that there are three relations in which there is little difference resulting from the presence or absence of perceived bodies in between two bodies. The distant objects affect the senses in the same manner, whether separated by the one distance or the other; the second species of distance is found capable of receiving the first; and they both equally diminish the force of every quality.

19. The existence of the three relations provides an easy explanation of the fact that we confuse the idea of a visible or tangible distance with the imaginary idea of an invisible or intangible extension. For we may establish it as a general maxim in this science of human nature, that wherever there is a close relation betwixt two ideas, the mind is very apt to mistake them, and in all its discourses and reasonings to use the one for the other. The author finds this kind of mistake so widespread that he will take the time to examine what causes it to be made. He cautions that uncertainties based on conclusions drawn about the causes of the ideas do not necessarily introduce uncertainties about what they cause, i.e., the ideas. The phænomenon may be real, tho’ my explanation may be chimerical. So even if the explanation is false, it does not imply the falsehood of the other. [Since the phenomenon and its cause are closely related by causality,] the belief that the falsehood of an explanation implies the non-existence of what it is supposed to explain is very natural. And because this natural tendency to confusion is the result of a close relation of ideas, it is an evident instance of the very principle, which I endeavor to explain.

20. In Part I, Section 4, the author had introduced the three principles of union among ideas,

• Resemblance,
• Contiguity,
• Causation.

21. Mistaking resembling ideas is the source in large part of nearly all error. Not only are the resembling ideas themselves related, but the actions of the mind regarding them also resemble each other so much that they are not distinguishable for each other. This fact is very important, and the author observes that in genera, wherever the actions of the mind in forming any two ideas are the same or resembling, we are very apt to confound these ideas, and take the one for the other. He notes that many instances of this will be uncovered later. [Examples from Part IV are:

• (Section 2) Perfectly resembling but interrupted impressions of objects are mistaken for uninterrupted impressions,
• (Section 5) Ideas of qualities of objects related causally and sequentially are mistaken for ideas related by spatial contiguity,
• (Section 6) A succession of connected perceptions is mistaken for an idea of an identical self.

22. At this point, the author is prepared to counter the objections given in paragraphs 2 through 4 above. The first two objections are from metaphysics and the third from mechanics. [The first objection was that the fact that we are free to take either side in the dispute over whether a vacuum exists, so we must have an idea of a vacuum. The second objection was the only way to make sense of the result of annihilating everything between walls that are at rest is to suppose that there is a vacuum between them. The third objection was that we cannot explain motion without supposing a vacuum.] As for the first objection, our ability to take sides in the dispute over whether there is a vacuum (or extension without matter) does not imply that we have an idea of such a thing. We frequently deceive ourselves in believing that our words are attached to ideas, and particularly so when we actually have an idea [of invisible and intangible distance] that is closely related to the would-be idea of a vacuum.

23. Almost the same response can be made to the second objection deriv’d from the conjunction of the ideas of rest and annihilation. The appearance of a room in which all matter has been removed from existence resembles very much its appearance when it is filled with air that is invisible. What we would see is a fictitious distance due to the angles at which light from the remaining walls strike the eye and to the variations in light and shade. There is also a fictitious tangible distance which is the result of the [unimpeded] movement of the hand or some other part of the body. In vain shoul’d we search any farther. These are the only impressions we could get in this scenario, and the only we ideas we can gather from it are resemblances of those impressions, since all ideas are copies of impressions, as argued in Part I, Section 1. [Thus, since we can have no impression of a vacuum, we can have no idea of it, either.]

24. The third objection is met in the following way. It has already been granted by the proponent of the idea of a vacuum that we can suppose that a body standing in the distance between two others can be annihilated with no change in those other bodies. It is easy to conceive the opposite: that the annihilated body could be re-created without any change in the contiguous objects. The author now observes that the motion of a body has much the same effect as its creation. If a body moves between the two others, it is very much like a body being created between them. In neither case are the two other bodies affected. So since we can imagine the creation of a body between the two others, we can imagine the motion of a body between them as well. [This motion is imaginable without our having to conceive of something’s being moved out or displaced in order to make way for the body moving in.] Now that it has been shown that we can consistently imagine the motion of one body between two bodies distant from each other, we turn to experience to see whether they really have such a capacity of receiving bodies betwixt them, as well as that we can convert the invisible and intangible distance into a distance that can be seen and felt. While it may be natural to suppose that this conversion can be made, we do not know whether it is practicable, before we have had experience of it.

25. While the author has given answers to the three objections, he recognizes that many will not find them to be satisfactory, but will immediately propose new objections and difficulties. He raises one such objection himself, that all he has done is to explain only the manner in which objects affect the senses, without endeavouring to account for their real nature and operations. There are two parts to the explanation. The first is that by experience we find that the appearance to the eye and to the touch of the distance of bodies is the same whether or not they have visible or tangible bodies placed between them. The second part of the explanation is that the idea we have of an invisible and intangible distance is also found by experience to contain a capacity of receiving body, or of becoming visible and tangible. But there is no attempt here to explain the cause, which separates bodies after this manner, and gives them a capacity of receiving others betwixt them, without any impulse or penetration. [We do not know whether there is an empty space between the bodies or how it is that an occupied space between them could be filled without either the occupying bodies being moved out of the way or by another body occupying the same space with them at the same time, by penetrating them.]

26. The author responds by stating that he indeed gives no explanation of the hidden causes of the separation of bodies or their capacity to receive other bodies between them. Not only does this discussion fall beyond the scope of the plan for the present work, but it also seems impossible to bring to a satisfactory conclusion, due to the limitations of the human understanding, so that we can never pretend to know body otherwise than by those external properties, which discover themselves to the senses. The author cannot approve of attempts to take the matter farther until he sees at least one case in which it has been successful. He is content with knowing perfectly the manner in which objects affect my senses, and their connexions with each other, as far as experience informs me of them. This is all that is needed for the conduct of life and all that is needed for my philosophy, which pretends only to explain the nature and causes of our perceptions, or impressions or ideas.

[Footnote from the Appendix. We can avoid all difficulties in any question so long as we confine our attention to the appearances of things and not attempt to understand their real nature and operations. In the case at hand, one might ask whether the invisible and intangible distance, interpos’d betwixt two objects, be something or nothing. The answer is easy: it is something, but only a property of the objects to affect the senses in a certain way. A second question is whether two objects with an invisible and intangible distance between them touch. The answer is that it depends on the definition of ‘touch.’. One sense of the word is that there is no sensible thing lying between the two objects. In that case, the objects may be said to touch. Another sense of the word is that the images of the objects strike two parts of the eye that are contiguous or the objects are felt successively when the body moves over them. In this case, the objects are said not to touch. There is no inconsistency in the appearances of the objects, so that there is no danger of problems arising unless we use our terms obscurely.

On the other hand, it seems that carrying the controversy beyond the senses to the objects themselves will give rise to conclusions that are full of scepticism and uncertainty. One might ask, for example, whether the unseen and unfelt distance between two bodies is filled with other bodies that might be discovered were our senses more acute. The author finds no decisive argument on either side of the issue. He states his inclination toward the contrary opinion [that the space is not filled with potentially perceivable bodies] because it is more suitable to the vulgar and popular notions. The correct understanding of the assertion of a vacuum in the Newtonian philosophy of nature is simply that bodies are plac’d after such a manner, as to receive bodies betwixt them, without impulsion or penetration. But how this is possible remains unknown, as [w]e are only acquainted with its effects on the senses, and its power of receiving body. The author asserts that what is most suitable for Newtonian physics is a modest scepticism to a certain degree, and a fair confession of ignorance in subjects, that exceed all human capacity.]

27. The examination of extension, which has occupied Part II to this point, is concluded with a paradox that can be solved easily given the author’s account of our idea of extension. Suppose that it be conceded that invisible and intangible distance (that is, the capacity to become a visible and tangible distance) is a vacuum. It will follow that while there is a vacuum, extension and matter are the same thing. On the other hand, suppose that it is claimed that invisible and intangible distance is not a vacuum. Then there may be motion in a plenum (space with no gaps or vacuum between bodies) without there having to be some mechanism that has traditionally been used to explain how this is possible. There need be no impulse in infinitum, no circular motion, and no penetration of objects. These difficulties are avoided if we confine our notion of extension to what is filled with objects and whose parts are visible or tangible.

28. Having completed his examination of extension, the author turns to time, which he explains as nothing but the manner, in which some real objects exist. [This account of time is developed in Section 2, paragraphs 6 through 11.] He notes that his explanation of the idea of time is open to the same objections as his explanation of the idea of space. There is debate about whether time exists without there being any change in objects. But the author finds no impression of such a thing, whether of sensation or of reflection. But if you cannot point out any such impression, you may be certain you are mistaken, when you imagine you have any such idea.

29. On the other hand, we can find out the appearances which give us the mistaken belief that there is such an idea. We observe that there is a continual succession of perceptions in our mind. For this reason, the idea of time is always with us. So suppose we are consider an unchanging (steadfast) object, first at 5:00 and then at 6:00. We apply the idea of time to it in much the same manner as if either it was changing its position or otherwise being altered. The first and second appearances of the object, being compar’d with the succession of our perceptions, seem equally remov’d as if the object had really chang’d. There are two further considerations. First, we learn from experience that the object could have been changing constantly between its two appearances. Second, the fictitious duration of the unchanging body has the same effect in increasing or diminishing any quality as does the real succession of perceptions. From these three relations we are apt to confound our ideas, and imagine we can form the idea of a time and duration, without any change or succession. [Note that these three relations are the same as in the case of extension, described in paragraphs 15 through 17 above. There is a resemblance between a real duration, which requires continual succession, and a fictitious duration, we can easily convert the idea of the fictitious duration of an unchanging object into the idea of a real duration of a changing one, and the effects of increase and diminution are the same for the fictitious and real duration.]

The Enquiry

The topic of the possibility of an empty space or time is not raised in the Enquiry.

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