CHAPTER 9

Origin of the idea of bodies
by means of the extrasubjective perception of touch

831. We have indicated two elements in acquired sensations:

1. A modification of the fundamental feeling, by which the affected part of our sense-organ is felt in a new way.
2. A sense perception of an external body.

Subsequent analysis of this extrasubjective perception also results in two elements:

a) A feeling of the action done in us.
b) Extension, in which we locate this feeling and which includes some extended thing outside us.

832. We can therefore conclude that when we have perceived something different from us, something extended, we have the perception of a body through acquired sensations. I must now explain how our exterior senses furnish us with a subject of these three qualities. I shall begin with touch.

833. Each of our senses receives an action.
An action done in us, of which we are not the author, indicates something different from us.(160) Therefore each sense perceives something different from ourselves.

834. In order to ensure clarity in our ideas, we must first note the distinction between what is different from us and what is outside us.
Something different from me means simply something different from myself.
Difference as a concept does not include any idea of extension nor any relationship with extension. On the other hand, the word 'outside' in its proper sense has a relationship with extension: one thing outside another does not occupy the place of the other. Thus, outside MYSELF means outside the parts and sentient organs of my body,(161) and only by transference is applied to our spirit.
While therefore 'different from me' indicates a relationship of difference from my spirit, 'outside me' correctly indicates a difference from my body in so far as my body is co-sentient through its intimate union with my spirit.
In order, then, to show that each of our senses perceives what is outside us, we must demonstrate that each sense perceives something different from our body perceived subjectively.

835. That this is the case results from what was said, when we showed that the fundamental feeling is produced by an activity different from the activity that changes it. Hence two kinds of activity: 1. my body which acts directly in my spirit; 2. external bodies which act on my body.
Thus in every sensation we perceive an active principle or body different from our body; every sensation is an experience we receive from something other than our body. Therefore each sense gives us something outside us.

836. The following observation will help to remove all doubt on the matter.
My body is felt in the fundamental feeling; what is felt outside this feeling is not my body.
Let us fix our attention on the four phenomena, colours, sounds, smells and tastes, and also on the various qualities of touch, like hardness. If we ask ourselves whether all these things are perhaps nothing more than our sense organs, we will see that the term of these sensations possesses something different from our organs. Smell, for example, does not have the slightest similarity to our nose, nor taste to the tongue or palate, nor sound to our ears, and so on for all other qualities. The sensations, therefore, cannot have only our body as their matter. Even if the sensation of our own body is included in them, our body is certainly not everything we perceive with them. They therefore indicate a principle external to our body, a term different from the term of the fundamental feeling.

837. When we are touched on a sensitive part of our body, we feel our body, that is, a certain pleasure or pain.(162) We also feel an action done in us by something foreign, that is, we perceive an agent outside us (cf. 834-836).
The action, different from a sensation in an affected part, is a feeling with an extended term and is diffused in a surface extension.
For instance, if a sharp point touches us we locate the discomfort at a point, at a very small surface; but if we are touched by a bigger surface, a coin for example, we locate the discomfort at points enclosed within that surface and feel nothing outside it. Suppose a piece of metal in the form of a cross is pressed to our arm. The sensation we have terminates in that particular shape, and is diffused throughout the whole area covered by the metal, to which it corresponds exactly.(163)

838. When we are touched on the surface of our body, we receive a sensation confined within a surface space.(164)
If we add the faculty of movement, we have the power to repeat at will the space in which the fundamental feeling terminates (cf. 803).
The same faculty enables us to repeat at will the surface felt by touch.
Thus, a surface moved by a motion outside the plane of the surface itself traces a solid space having three dimensions, length, height and depth.
The power to move ourselves, and other things with us, makes touch-sensation possible at any surface of solid space;(165) hence the idea we have of this possibility.
The idea of the possibility of indefinitely changing and repeating the surfaces which are the term of our sensations of touch is the idea of solid, indefinite space acquired by means of the sense of touch joined to movement.(166)

839. What we have said shows that the idea of extension or space is formed in two modes: 1. by means of the fundamental feeling accompanied by the faculty of spontaneous movement of our body; 2. by means of the sensations of touch aided by the same faculty.
The indefinite space in the first mode is produced by a movement in all directions of a solid space felt by us, that is, of our body; this movement is mentally conceived as indefinitely possible.
The indefinite space in the second mode is produced by the possible movement of a surface that is felt - a movement in all directions outside the plane of the surface itself.
This explains how people born blind perceive indefinite space and are able to understand mathematics.

840. We have seen, on the one hand, how hard it is to think about and be aware of the fundamental feeling and, on the other, how easy to be aware of acquired sensations (cf. 710-721).
For the same reason, indefinite space perceived by the possibility of the movements of our body easily escapes our reflection. On the other hand, because sensations of touch are acquired, they and their movement attract our attention more easily.

841. The term of the external sensation of touch is a more or less extended surface (cf. 837).
This surface is identical with the external surface of our body because the sensation is felt only in the nerve endings where we are touched.(167)
The same surface(168) is also the term of both the subjective sensation we feel in our organ and the action done in us from outside. Consciousness of this action constitutes what we have called the extrasubjective perception of the senses. Because the external agent is called an external body, the surface, when touched, is not only the term of our body but also of the external body. Now if we think of this surface (felt and perceived by us and common both to our body and the external body) as being moved in all directions (cf. 839), we arrive at the origin of the concept of indefinite space.
Indefinite space is therefore perceived by us in two ways: either by moving the organ felt by us through a modification of the fundamental feeling or by moving the surface perceived in the external agent. In both cases it is always one and the same surface.
Space, therefore, whether perceived in the two subjective modes or the extrasubjective mode, is one and the same, because any modification of the fundamental feeling (an acquired sensation of our organ) has the same extension as the fundamental feeling.

842. Our body, when considered in association with its sentient subject, shares the same extension with the external body, which is simply the agent we feel.
The communion of these two bodies in the same extension provides the step from the idea of one to the idea of the other; it is the communicating bridge we were looking for. The very act by which we perceive the mode of our body's existence is the same act by which we perceive the mode of existence of an external body.

843. This consequence (cf. 842) is of the greatest importance.
We have established two elements necessary for the essence of a body: 1. an action done on us; 2. an extension in which that action is diffused and terminates.
Our own body exercises a continuous, internal action on us, occasioning the fundamental feeling, and this effect of the agent spreads throughout an extension. Here we have therefore the two elements forming the essence of body. Hence the perception of our body is undeniable, and its essence is as certain as the fact of consciousness.

844. The perception of an external body is brought about when we first feel an action done on us, although the immediate effect of this action is simply a modification of our fundamental feeling.
This effect alone does not draw us out of ourselves. We still feel our body as we did before, but in a new way (with an accidental sensation).
But we are then easily led to argue to a cause, which is unknown because the action is still indeterminate. This alone would not suffice to make us perceive a body outside us. For this, the action has also to be extended. We would perceive an agent in extension, which is the notion of a body.

But how are we able to perceive the extension of an agent? The author of nature, in his wisdom, provides the answer: we feel extension habitually, that is, the diffusion of the fundamental feeling. Consequently, we are able to feel the extension of the external agent when it diffuses its action in the same extension as our fundamental feeling.
This explains why the surface of the extension of our fundamental feeling and the surface of the extension of an external body should unite to form a single surface in which we experience two feelings. Hence the action of an external body takes place in and extends over the very same surface in which the fundamental feeling is diffused and terminates. Consciousness itself tells us that the action comes from outside and takes place in an extension already felt by us naturally.

We perceive: 1. an external action; and 2. the surface in which this external action functions or terminates. Thus we perceive the two essential properties of body, common to our own and external bodies, and confirm for ourselves the existence of two bodies, each having the same corporeal nature, although their effects upon us are quite different.

845. What we have said explains how the extrasubjective perception of bodies is founded on the subjective perception.

The first element in extrasubjective perception is a force modifying us. We perceive this force in its action according to the kind of impact it has on us, and with it perceive a subjective modification of our fundamental feeling.
The second element is extension, and in particular the extension of the fundamental feeling, which we feel naturally. But because the fundamental feeling is changed in extension by an external force applied to each part of the extension, we perceive this force as extended in its term. This explains why the criterion for the perception of an exterior body is ultimately the perception of our own body (cf. 843-844).

846. Before continuing, I must give some attention to the real extension I have sometimes attributed to a body; it is a very important matter, discussed by others at various times. I will show that the extension we perceive in a body is real, not apparent and illusory [App., no. 30].

847. Many thinkers have considered multiplicity essential to corporeal nature.
But it is easy to see, as Leibniz pointed out, that the concept of multiplicity cannot be the concept of an individual nature but of the coexistence of several natures. It is a relative concept, presupposing and based on an absolute concept. In short, where the many is, there must be the one; multiplicity is merely the aggregate of many unities. Thus the nature of things must be sought in unity(169) and not in a multitude, which is only several natures joined together.

848. The essence, therefore, of a body or of anything else will never be multiplicity, which is purely a mental entity. Only idealists, especially transcendentalists, who suppose that bodies are an emanation of our mind,(170) are content to posit corporeal nature in multiplicity.

849. Certain conditions are required for our organs to feel, one of which is communication with the brain.
We may conclude from this that the sensitivity of each part of our sensitive organ depends on the form of the whole sentient system, that is, on a division and organisation of parts whose harmonious result is a single whole, sensitive in all its parts. Thus the parts composing the organ are sensitive because of this single whole, or rather because of a unity rooted in the whole.
We can say that our body, in so far as it is sensitive, enjoys a certain composite unity which makes it one because it has in itself an order or harmony of parts.

850. This truth remains valid even if we cannot say whether there is a centre in the brain, and if there is, whether it consists of a single particle or several in which all the nerves end. For even independently of the intelligent spirit, the unity of the human body is sufficiently established by its need of a certain disposition if it is to be vivified and inhabited by the spirit, and its different powers be, as Dante says, 'organated.'

851. Let us imagine we possess two bodies. In this case we would then have two fundamental feelings and extensions, because these are the two essential elements of our body. Our consciousness, therefore, which indicates one fundamental feeling only, diffused in a definite extension, indicates the unicity of our body.
Let us imagine that we feel we have two bodies. In this case we could not have one only because in our sensation the two constitutive elements of our body would be perceived as doubled. Thus we still could not err in judging whether our body is one or two [App., no. 31].

852. Because our body is one through the harmony of its parts, we perceive its unicity. Anything outside this harmony and foreign to us is not felt. However such unity and unicity does not exclude multiplicity from our body, as I must now explain.
Through the organisation of the body, my spirit feels all its sensitive parts by means of the fundamental feeling and of the adventitious sensations in its sensitive parts. This makes it possible at least to conceive multiplicity.

853. If we keep to sensation, because the same reasoning can easily be applied to the fundamental feeling, we have to ask what can and cannot be affirmed about the multiplicity of sensation?
Let us suppose that we experience a sensation of touch and that its impression has a certain extension. If the extension is sufficient, we feel it and generally advert to it. But if the extension is small, it escapes our attention.
The smallest extension we can be aware of may be called the minimum extension.
Now if this minimum is regarded as the basic element of an extended sensation, it is certain that one element is not another because in each we find two separate things: 1. sensation; and 2. extension, which are the two constitutives of body.
Thus we can consider these elements as tiny bodies, subsisting separately and outside each other, which cannot be confused nor take one another's place. In our body therefore we perceive with equal certainty both multiplicity and unity.

854. A similar argument can be applied to external bodies. When an external body is so minute that its extension is less than a certain limit, it entirely escapes our attention.
If we take this minimum (that is, the smallest noticeable body) as the basic element, it can safely be said that in the perception of a larger body we can mentally distinguish and separate minimum perceptions as possible, and even as really distinct when considered individually.
Furthermore, because the two constitutive elements of body are present in each of these minimum perceptions, we can mentally distinguish minute bodies, whether they are divided or not.
They can also have an independent subsistence because they have separate and incommunicable action. As we have seen, in each of these minimum spaces that we have distinguished, there is an extension outside every other extension. Thus each agent is outside every other agent and is a substance that, while it can be contiguous with another substance, appears separate and isolated in its own existence. In this way we perceive multiplicity in external bodies also.

855. We 'name things according to the way we intellectually perceive them' (cf. 647 [678]).
To investigate what a body is, is to investigate the notion given by the human race to the word 'body' (cf. 653-656).
We found this notion was the result of two elements, an agent acting on us and an extension in which this action and our own experience of it were diffused.
However if the agent effected nothing in us, we could neither know it nor name it, since we know it and name it in so far as it acts on us. So the word 'body' is determined by the immediate effects of the agent on us and by the laws governing its action.
But the agent could have powers and laws unknown to us, different from but not contrary to those we experience. If all possible or unknown effects and their laws were like this, they would be neither known nor named by us. The name 'body' therefore cannot be applied to these qualities as long as they remain unknown: 'Words may not be used with a sense wider than that for which they were devised' (cf. 648-652 [679]).

Suppose however that the order of things were changed. We might discover new effects with new laws dependent on the same principle as the effects now determining the meaning of the word 'body'. In this case the common use of the word would change.
But while we continue to use the word in the present condition of things, it has a meaning limited by its immediate effects or actions and by the laws according to which bodies present themselves to us.

856. For this reason I prefer to distinguish corporeal principle from body and include the former in the definition of body only in so far as body is accompanied by effects and laws enabling us to know the principle. But I would also grant to the corporeal principle all that it has in addition to and different from what its nature reveals to us.

857. Speaking therefore about body in this sense, I have no hesitation in affirming that
we know with certainty the multiplicity of bodies.(171)

858. Let us suppose that the surface of our body where sensations take place is continuous, or at least that there is in it some continuous space.
It seems to me that a body producing an extended, continuous sensation must also be extended and continuous.(172) This is a corollary of what has already been said.

I have said that 'bodies are the proximate cause of our sensations' (cf. 639-645 [667]). I have explained that 'proximate cause' means an ens receiving its name only from the immediate effect it constantly produces. I concluded that the constant sensations (the fundamental feeling and its modifications) are not produced by a power of a body but by a body's substance, by a body itself; the word 'body' indicates only those immediate effects which are its total meaning.

The result of these findings was the recognition that in each space where we experience a sensation diffused in extension, we must acknowledge an agent possessing all the characteristics required for what we call 'body'. Hence we must acknowledge a multiplicity of bodies obtained from a multiplicity of sensations in a multiplicity of spaces. I can always imagine a sensation ending in one space while continuing in another, or beginning here while ending there, so that all I know about sensations in different spaces indicates their mutual independence.

This essential difference of effects compels the acceptance of a substantial difference of causes, and therefore a multiplicity of causes. This in turn shows that, granted a continuous sensation, there must be a continuity of extension in the body producing it.

859. We have imagined various small spaces as divisions of a larger space in which sensation is diffused. We saw how a force or a minute body is present, producing a sensation in each small space.
Now if we fuse all these small spaces together, they become one large, continuous space. But this fusion does not affect our argument; nothing is altered. Provided the spaces are distinct, a corresponding minute body is necessary for each of them whether the spaces are distant, near or even contiguous with one another. However, their continuous contiguity, resulting in one large, continuous sensation, must also give one continuous body.

The whole force of the argument lies in this one principle: wherever there is sensation, there is also an acting force. So if a sensation is continuous and equal in every assignable point of a space, an acting cause, the body, is present throughout the same space. Hence if there is no interval in the sensation, there is no interval in the body. Granted a continuous sensation, the body producing it is continuous.

The need for such a conclusion is found in the wonderful, mysterious but undeniable nature of continuous extension. No space, however small or wherever present, can be assigned in continuous extension unless it has its own entity outside and fully independent of other spaces. Every smaller space can be at least mentally separated from the whole, giving us the indefinite limitability of the continuum we have noted. The fact that each space is outside every other means that the action confined to one space cannot operate within any other; the smallest space presupposes an agent outside the agent acting in the next space. In the external body therefore we must be able to identify as many contiguous parts acting on our body as there are identifiable contiguous spaces in our own body felt by us.

860. Someone might object: when an external body wounds some part of our feeling faculty, it produces pain more extensive than itself, as the pain spreads, by sympathy, to other parts. There is no necessity therefore for the extension of a sensation to correspond exactly to the sensation of the body causing the sensation.

I reply as follows:

1. I note that in all the places where the pain extends by sympathy there must be sensitive parts. The argument given above must be applied to these parts; if the pain extends in a continuous space, the injured parts producing it must be continuous.(173) Now if the parts of our body are continuous, there is a continuum in bodies, which was to be proved.

2. Diffused sensation, propagated sympathetically, follows the same law as all other sensations: 'A force is felt at the spot where it is applied.' A sensation spreads precisely because the force changing the state of the parts in the sensitive organ spreads. Let us suppose that the movement of the organ which gives rise to the pain (it does not matter whether the pain is produced by a mechanical, physical or chemical force) spreads from one part to another part of the limb, let us say from one layer to another. The third layer receives the movement from the second. It feels only the pressure or action of the second layer, not the external body. The pain present by sympathy or communication in the sensitive material does not indicate an external body. Only the limb is perceived more acutely, that is, those parts of it causing the pain actively and immediately. But in this case, the sensation produced directly by the external body is indeed detected and indicates the existence of the body; we are conscious of feeling a disturbance at the place where the body is acting. Thus the principle I began with, to demonstrate the continuity of bodies, is valid also for sensations diffused sympathetically. It is always true that 'in every place where we feel a sensation, there is a force in act, a body acting.'

861. This truth has been demonstrated in the preceding paragraph. It is also proved by the definition of the sensitive parts of our body.
Because we feel a sensitive part only where we feel and confirm a sensation, sensations therefore do not extend outside the sensitive parts, and vice versa.

862. This follows from the preceding proposition.
The size of an external body is measured by sensations, especially touch. We have already seen that the extension of our body, perceived subjectively, is the measure of the extrasubjective extension of external bodies.
Therefore the extension of external bodies is neither greater nor less than the extension of the sensations produced in us by the contact of external bodies.

863. When we touch a very smooth surface with a part of our body, we are unable to notice any break in the sensation we experience.
The sensation, spread throughout the surface, seems to be continuous, that is, the continuity is phenomenal.
However if we look at the surface through a microscope, it is seen to be uneven and rutted. This would seem to contradict what we have just established, that a sensation of touch produced by an external body does not extend outside the size of the body itself. But we must always bear in mind the real, necessary distinction between a sensation and our awareness of that sensation.(174) We must convince ourselves by observation that there are very minute sensations which entirely escape our awareness. This explains why we think a surface is even and smooth, because in the sensation of the surface we do not advert to the tiny corruscations and intervals. Hence a large sensation is not in fact continuous; we think it is because we do not advert to its very minute intervals.

864. There is no perfect continuity, therefore, in a notably extended sensation (like the surface we have discussed); there are intervals and irregularities in its parts.
The large sensation is broken up by intervals, so to speak, into small, elementary sensations, next to each other but not contiguous on every side.
It is my opinion that these tiny, elementary sensations are diffused in a truly continuous extension, as I will now show.
We begin by supposing the opposite, that is, they have no continuity and are therefore merely mathematical points.

865. Mathematical points would necessarily have between them spaces of various minute sizes which would always be continuous, and also contiguous because a mathematical point does not break contiguity.

But here we must note a law governing sensations: 'If our body has two or more sensations located in quite different places, we notice the space separating them', because we refer the sensations to different points. When these spaces are noticeably extended, we feel them, especially by comparing the places affected and unaffected by sensation.
Now if we were to feel the sensation only in many unextended points, would it be possible for such a sensation to be phenomenally continuous, as it is in fact? It would not, as the following reasons will show:

I. If we were capable of adverting to sensations that have no extension, we would be much more capable of adverting to the tiny spaces separating them, for these have an extension infinitely greater than mathematical points. Thus the total sensation could never seem continuous. If it were continuous, we would have to advert to it as something composed of unextended points, distantly separated from each other. In such a case it would be impossible to explain the phenomenon of continuity in sensations.

866. II. An infinite number of mathematical points placed together could not cover a surface or even a line. They cannot give the extension they do not possess. Thus, if we were to join together all the supposed unextended points we feel, the size of the surface in which they are spread would not be covered in any way. We would have to feel on the one hand the sensation of the unextended points, and on the other, the surface exactly as it was previously felt by our fundamental feeling, or indeed feel no continuum at all. All the tiny spaces that as a result had no sensation would, taken together, form an extension as large as the extension existing prior to the sensation of the points. If therefore the whole extension we felt in the points were non-existent, we would have to be aware of the extension remaining between the points. This extension would be exactly the same as it was before we received the impression that has only unextended points but no extension. In this case we could never have a perception or idea of any continuum.

867. III. Again, if we felt simple points, we would feel a composite of non-corporeal sensations because such sensations would not terminate in extension (cf. 754 [755]), which is of the essence of corporeal sensations; nor would sensation of this kind supply matter for the idea of a body.

868. IV. Finally, let us suppose we feel only unextended points. It would be possible to locate them at different places in the body's periphery. This can be done only by measuring in some way the distance between one point and another. Now either we feel these distances, or we do not. If we do, we will feel a continuum; if we do not, we will have no means of locating the points at the places we do locate them. In this case, they would be sensations, foreign to every place, located perhaps in the simplicity of our spirit but nowhere else. There is no doubt that only the continuum can be a measure of distance; a simple point is no measure because entirely devoid of extension. But granted we perceive a continuum, we can measure the interval between one point and another. The size of these intervals is only a projection we make of their ability to repeat a certain number of times the continuum we use as a unit of measure.

We have to recognise therefore that small, elementary sensations, whether acquired or forming the fundamental feeling, are extended, that is, terminate in a continuous extension.

869. We cannot affirm or deny the simplicity of the corporeal principle because the principle may (cf. 855-857) in part be unknown.
But it is clearly false that bodies can be a composite of simple points, as Leibniz maintained.(175)
We have seen that: 1. elementary sensations are extended and continuous; 2. the size of bodies, which are the proximate causes of sensations, is equal to the size of the sensations.
We therefore conclude that elementary bodies have a continuous extension.(176)

870. Points escape our senses. We can never perceive unextended points which, therefore, cannot be bodies. We cannot give a name to what we do not know; names indicate things only in so far as things are known.(177) Thus the word 'body' must indicate things known, things falling under our senses that we touch, see and perceive with our other organs. The word does not mean unextended points, of which we have no experience at all.
Wherever there is a sensation, there is an experience relative to ourselves, and an action relative to the agent, a force in act that we call body. Now if there are continuous sensations in some of the little spaces, the force must be diffused in the whole space, be present in every point, and be extended and continuous. Hence elementary bodies must possess real continuity and cannot be simple points, if we use reason, not imagination, as our guide for the data provided by observation.(178)

871. Having established that continuous extension is real in bodies, we can now perfect the definition of body(179) by adding to it this quality of extension: 'A body is a single substance(180) endowed with extension, and producing in us a pleasant or painful feeling terminating in the same extension.'(181)

872. If a body is a force whose act terminates in a solid, continuous extension, we must investigate how we perceive a body by touch.
Extension has three dimensions, length, breadth and height, which we first perceive in our body through the fundamental feeling (cf. 692 ss.).
In the action of external bodies on the surface of our body, we cannot feel and perceive more than a surface, that is, two dimensions, length and breadth. Our body alone does not allow us to perceive the dimension of depth in an external body.(182)
But if we consider the external surface, perceived by our touch, in relationship with the faculty we have of moving the surface, we obtain the idea of a solid body.
Just as we obtain the idea of solid space by conceiving a body movable in all directions outside its plane, so the idea of a solid body comes from the movement we partly experience and partly expect or think as possible, of a corporeal surface moving outside its own plane.

873. As we consider this movement, we conceive as possible that all the surfaces imaginable within a solid space can be felt, that is, they can be terms of the action done in us by a body.
To help us understand this, let us imagine a body formed as a perfectly hard cube. If I touch all six faces of the cube of very hard material, pressing as firmly as I like, I perceive simply the limits of a solid space shaped like a cube, that is, corporeal surfaces. This gives me only an imperfect idea of body because all I have perceived are surfaces enclosing and terminating a solid space; I have perceived only the body's limits, not its solid extension.

Next I take a cube of soft material, such that I can change its form or break it into parts. If I shape or divide it, there is only one result: more and more surfaces are revealed, which I did not feel before because they were not uncovered from within the cube and were certainly not surfaces.
As I continue to divide it up, I have to conclude that the solid cube presents not only a corporeal surface externally, but has the ability to present more and more surfaces internally. Experiments and thoughts like this lead me to the concept of corporeal solidity, completing my idea of solid body, that is, of a substance diffusing its activity in solid extension according to certain laws.

874. The previous experiment taught me that, by applying force to the cube sufficient to change its form or divide it, I can obtain more surfaces from within the space enclosed by the corporeal surfaces of the cube.
Examining this fact, I cannot find any reason why the exposed surfaces should be in one particular part of the cube and not
in another.
There is no repugnance in thinking that these corporeal surfaces are equally present in all parts, that is, in every plane assignable within the cube. Now the possibility of thinking of the corporeal surfaces dividing the volume of the cube in any plane, is the idea of mathematical body, which is always conceived as perfectly continuous.

875. As long as I think the possibility of finding a corporeal surface in any imaginary plane within a cube, I have the idea of a mathematical body (cf. 874). But if, instead of this simple possibility, I try as well as I can to determine the forms of a particular, real body with my touch or other senses (even with the use of instruments), I become aware of irregularities, ridges and spaces between one section and another. In this case I form the idea of a composite of tiny parts, not in perfect contact, differently shaped and interspersed with intervals and links so strongly bonded together in some places that they cannot be forced apart. I call this physical body.
All this explains how people born blind can form the idea of both mathematical and physical bodies by means of touch, movement and intellect.

(160) Cf. 672-691. The distinction which Royer-Collard attempted to establish between the senses cannot be accepted. He considered some senses merely as instruments of sensations, others as instruments of both sensations and perceptions (cf. parts of Lezioni del Royer-Collard printed by Jouffroy). All senses however perceive and all have their extrasubjective part which is more distinct in some, less distinct in others, as we shall see.

(161) Every part of my body, whether sentient or not, can be said to be outside me in so far as it is perceived extrasubjectively. In such a perception we consider what the part has in common with all external bodies; as such, it is outside the subject, that is, the perceived part is perceived as outside the perceiving part.

(162) There are feelings essentially different from pleasure and pain. For example, the sensation of tickling seems to be wholly sui generis, and the same can be said of many other feelings. It is not my intention to investigate this matter but it seems to me beyond doubt that all the feelings we experience are accompanied by some level of pleasure or pain, or are themselves modes of pleasure or pain. So I say 'a certain pleasure and pain' or else 'corporeal pleasure and pain' where 'corporeal' indicates the differences not investigated in this work.

(163) It is really the ends of the nerves that are touched and hence the contact takes place at the surface, which is true for external touch.

(164) I am speaking of adventitious sensations, not the fundamental feeling of which, I am convinced, there is a continuum in the parts where it terminates.

(165) This solidity need not be known to our senses. Of itself, motion is not sensible, as we have observed, but is a means for us to form the thought of sensible solidity.

(166) Spontaneous movement is the principal cause of the information we acquire about distances and measured spaces. Touch (by means of time) and sight do nothing more than make us perceive exactly the termination of the distance. A delicate sense of touch, therefore, is not necessary for measuring great distances. Birds are an example: they fly and measure immense distances, having only the weak sense of touch of their claws. The vulture, for instance, measures the space, time and the speed necessary to catch its prey. But all it needs for this is its weak sense of touch and its powerful eye-sight together with its great power of movement.

(167) The sensation of our body must always be distinguished from the perception of an external thing in the same surface. Although we feel the same surface, we feel two things: 1. our body, a subject that feels and is felt; 2. an external agent that is felt but does not feel.

(168) The unity of this surface determines the nature of touch, and of the mysterious unity of agent and recipient in every kind of action, as we have already pointed out. [Cf. App., no. 22]

(169) If corporeal nature is to be found in the elements from which composite bodies result, such elements cannot be thought of as unextended. Continuous extension is sufficient because the continuum is one, as we saw (cf. 825).

(170) I mean actual multiplicity, although the nature of what is extended always involves the idea of a potential multiplicity, which however is not yet multiplicity.

(171) No new properties would falsify former properties, whatever might be discovered in bodies or whatever change they might undergo from a force above nature. Hence the extrasubjective qualities we now perceive in bodies are not deceptive; they are true even if they were to be changed.

(172) The same would be true if the fundamental feeling were diffused in a surface or solid continuum, that is, without any interruption.

(173) We can sometimes wrongly locate a sensation, as in the pain of an amputated limb; but here our habitual judgment is deceived, not our feeling (cf. 762).

(174) On many occasions I have distinguished between feeling and awareness of feeling. I am certain and will show that, although a corporeal stimulus acting on our spirit may produce a sensation, the stimulus needs to be quite intense for it to produce a sensation capable of drawing our attention with relative ease. The weaker the sensation, the more difficult is it to advert to it, even if it exists. Hence, a very weak sensation must be totally unsuited to making us aware of itself or of its extension.

(175) Leibniz's error seems to consist precisely in his desire to speak about the corporeal principle rather than bodies; in other words, about the unknown rather than the known. But who can speak clearly and accurately about something he does not know?

(176) Besides having a certain continuous extension, elementary bodies must have certain regular forms, like crystals, and must be perfectly hard and unchangeable.

(177) Cf. 647-652. However we must always remember that words indicate the real thing, although only in the limited way we know it.

(178) If the action of simple points terminated in one point only, these agents would pass from one part of our body to another without causing the least disturbance. But if they are granted a tiny sphere by which they are surrounded and into which their force extends, they are no longer simple forces; on the contrary, this tiny sphere of force is precisely the extended body. To verify that the points were of this form, we would need to show that the force of elementary bodies acts like rays emitted from a centre. This research, which has not yet been made, may need to be carried out. If it is not proved, there would be no difference between the centre and the sphere because the force is in every point of the sphere without exception. If the centre is something ideal in the extended part, we have a mental postulate, which constitutes no nature. Again, the forms of primal bodies would have to be spherical if we suppose that the centre emits a force, but this cannot be the case for all bodies. On the other hand, if they are not spherical, the law of the centre of gravity is at odds with the centre of the force. But whatever the case, the only meaning possible for body is that of a force endowed with some extension.

(179) I first defined bodies imperfectly, basing the definition on common sense (cf. 635). I say 'imperfectly' not 'falsely' because it contained the entire essence of bodies without analysis of their elements. Analysis of the definition has allowed me to perfect it (cf. 749-753), especially here. The progress of knowledge, I believe, must be something like this, and begin with natural, composite ideas (popular understanding), which are analysed and then scientifically synthesised to form knowledge. Hence those who deny the necessity of starting from definitions, fall into the opposite error. If anyone wishes to be understood, he has to begin with definitions; but there are scientific definitions and popular definitions, and both are true. We must begin with the popular to finish with the scientific.

(180) It is single because it is continuous, nothing more.

(181) This was demonstrated earlier.

(182) Sometimes an external body seems to act simultaneously in all the points of a solid space of our body, for example, a penetrating, acidic substance. Granted this, we would indeed perceive our own body's solidity but not the solidity of the external body. This observation can help us to distinguish our body's extension from the extension of the external body; the two bodies can easily be confused because we perceive them united in our sensation of touch. A relationship that distinguishes two agents differs relative to each agent.