CHAPTER 8

Origin of the idea of space

820. I have defined body as 'a substance capable of producing in us an action which is a feeling of pleasure or pain having a constant mode we call extension' (cf. 749-753).
Extension, therefore, when derived from body, is a mental abstraction, like pure time and movement. It is the particular mode of the feeling which body causes in our spirit. Once this abstraction has been formed, it can exist independently of bodies, like all abstract ideas.

821. Extension, or space, taken in this abstract way, or in any other, is limitless, immeasurable and continuous.
We must now examine how our concept of space, taken only from bodies, acquires these undeniable characteristics. We shall begin with limitlessness and immeasurability.
The potency for moving our body (cf. 672-692 [800-802]) means simply changing or reproducing the mode of feeling of our body. In other words, we reproduce the extension our body occupies.

But we can reproduce acts of our potencies indefinitely; and even when our limited energies prevent our reproducing them any further, we can still imagine ourselves reproducing them indefinitely. This capacity is given us by the idea of possibility, continually present to our mind, which we can join to anything we mentally conceive (cf. 403).
We have already explained, through the idea of being, how our spirit can add the idea of what is possible to any event or object it conceives and, with the help of this idea, imagine the indefinite reproduction of the event or object (cf. 469 ss.).
Thus our capacity for imagining or thinking of the indefinite reproduction of our body's extension enables us to acquire the idea of limitless extension. This idea is, in fact, only 'the possibility of reproducing indefinitely the mode of our feeling that we call our body's extension by abstracting in thought and imagination from the body itself.'

822. In this way we draw the idea of limitlessness of extension from extension perceived subjectively.(156) At the same time, extension perceived subjectively can also be perceived extrasubjectively, that is to say, in external bodies, because the exteriority of a body is only the extrasubjective mode with which we perceive bodies.
Granted this perception of bodies, we have by abstraction the perception of their extension.
Hence the limitlessness and immeasurability of extension conceived in this way, which can in general be defined as 'the possibility of thinking the indefinite reproduction of the extension of bodies.'

823. As we have seen, the idea of unending space which first lends itself to analysis is an abstract idea, expressing the possibility of limitless, successive change to the extension of a body.
It is true that in dealing with this we have been paying more attention to our own body than to that of external bodies, because until now we have spoken intentionally only of subjective perception. However, what we shall say about space perceived subjectively, the reader will be able to apply for himself to external bodies, that is, to bodies which we perceive extrasubjectively.
Dealing with our present question, 'Does the concept of space contain perfect continuity?', we must be careful not to confuse feeling as it actually exists with the possibility of its other states. We could indeed raise an extremely difficult problem connected with the fact of feeling: does the actual feeling of our body include the feeling of the perfect continuity belonging to our body?
To answer this question through experience would not only require very accurate and extremely shrewd observation and insight; it would in the end be impossible. Only conjecture or very acute philosophical reasoning would perhaps provide a solution. What we are asking is whether sensation could be stimulated along the nerves in such a way that sensitive parts are mathematically contiguous. Now observation can tell us nothing about such a problem because it cannot attain such depth.(157)

However, this kind of research is not necessary for our present question.

An explanation of the continuity of extension is not furthered by knowing whether all the mathematical points encountered in a nerve passage are truly sensitive. We are not dealing with a factual truth, but with an abstraction or idea resulting from the clear possibility of locating the sensation we experience at any of the points along the nerve. If the nerve we feel has pores and gaps in its delicate texture, it is entirely accidental whether these gaps come in one place rather than another. We can think of a nerve full of them, although it may in fact be devoid of them; mentally we can change the place of any of the sensitive particles of the nerve, just as we can for the empty spaces found along it. This power of the intellective imagination is sufficient to explain how we can fully conceive 'the possibility of locating a feeling at any assignable point whatsoever', that is, how we are able to conceive the idea of continuity.

This possibility for locating a feeling at any assignable point in a space arises from the neutral disposition of the nature of space which receives feeling indifferently at any point. Because of this indifference, a sensation may terminate in any point within the confines of the body. The possibility of locating the feeling indifferently at any point or place includes, and is, the idea of the continuum in abstract space.

Our potency for movement facilitates the attainment of this idea because it indicates in fact the indifference of every part of space relative to the diffusion of our feeling. Let us imagine that we have a microscope powerful enough to show us the nerves in our hand. Such an instrument would reveal how the molecules composing them cling together, and how there are tiny spaces between the molecules where the nerve lacks feeling because it is insensitive. But now we move our hand slightly, and find that the spaces previously occupied by the molecules have been left empty while empty spaces have been filled. In the new position of the hand, feeling is now located at places which were empty. Movement, therefore, enables us to dispose our feeling in any mathematical point of space, and such a possibility makes us conceive space as an absolute and perfect continuity.
It is true, of course, that the feeling of the organ acquired through movement remains unchanged (granted that movement is per se unfeelable, cf. 806). This, however, does not prevent the mind, assisted especially by the external sensation of bodies, from arriving at the idea of the continuity of extension in the way described.

824. So far, by mentally placing together various possibilities we have arrived at the idea of a continuum. But does the continuum really exist in corporeal extension?
I shall have to answer this question later, when I deal with the extrasubjective perception of bodies; this provides an easier approach to the problem and throws greater light on it. In the meantime, it is enough to know that continuity of bodies and of space is not repugnant.

825. Continuum means that which has no gap or division or split.
The continuum, therefore, cannot have parts, because parts presuppose separation amongst themselves.

826. So far, we have defined the continuum as 'the possibility of a body's terminating simultaneously in any assignable point of a given extension.'
The idea of limitless continuous space has been defined as 'the possibility of a body's reproducing indefinitely its continuous extension.'
But we can also restrict our thought to the possibility of some, rather than all, possible changes.
In this way, there arises within us the idea of something continuous, yet limited, for example, an area measuring a thousand square metres, or something similar.
Because it has no parts in itself, this area although limited is also continuous.
While I can imagine as many of these areas as I please, each of them, whatever its size, remains continuous, that is, without parts.

827. All these ideas of continuous limitations are, therefore, potentially comprised in the idea of what is unlimitedly continuous, that is, unending space.(158) Each one, moreover, has a relationship of size with every other (one may be twice, or three times the size of another, and so on). In other words, it has yet another of the characteristics assigned by mathematicians, whether this characteristic is actually measurable or not.

828. In this way, we come to consider lesser continuous things as parts of those which are greater, although this depends on various acts of our mind and its capacity for limiting in different ways its conception of the continuum. Lesser things, as parts of larger, are only mental, not actual things.

829. Consequently, these mental parts do not form one continuous thing while they are conceived as parts; they are lesser continuous things and nothing more. When we want to consider them altogether as a single continuous thing, we have to remove the idea of parts and division completely, running them together with our imagination so as to eliminate even mental confines. The concept of continuum is clean contrary to the concept of part.

830. The continuum can be said to be infinitely divisible only in the sense that we can limit it indefinitely.(159)
This indefinite reduction arises from the nature both of the continuum and of our faculties, which can always repeat what they have done previously. This is especially the case with our power of thought which, by means of the concept of possibility, can imagine and think as possible all that is not contradictory.

Infinite divisibility, therefore, is only the possibility of repeating indefinitely the limitation of the space we think of. Hence St. Thomas' teaching: 'The continuum has infinite possible parts (in potency), but none in reality.'

(156) Extension is something in exterior objects. It is also something in the fundamental feeling in which, and related to which, it has the nature of matter and term. Moreover, extension is common to our sensations and to external bodies. In our sensations we call it their matter; in external bodies we call it the external term.

(157) However, there is no absolute repugnance, rationally speaking, in the thought of such observation.

(158) That which is in potency cannot truly be said to be. In what is continuous, therefore, we find only the limitations we ourselves put there, and nothing more. The infinite number of ideas imagined by Malebranche as possessed by our mind in the conception of space and shapes - his infinite number of infinites (Book 3) - is fallacious. The idea of the continuum is a single idea which, when limited by us, produces other ideas but always in a limited number because our mental effort finally comes to an end without ever arriving at an infinite number of limitations.

(159) The continuum is improperly said to be divisible because what is divided is no longer continuous.