Chapter 3

The essential relationships of extension and of what is extended

1126. If we consider an ens furnished with extension we shall easily realise that the concept of extension results from an essential relationship between the parts that we can assign mentally in a given continuum, or between as many points as we care to conceive in it. The essential relationship between the parts of which we are speaking is this: one part is outside another. The essential relationship between assignable points is this: there is, between one point and another, a given continuum of varying size prevents the points from ever touching. The concept of extended ens is the result of these relationships. Extension, therefore, involves possible relationship of one extended part to another, and of points to points. This relationship is distance.

1127. But if, on the contrary, we consider the relationship of the continuum with the sentient principle, we find this relationship altogether different. It is not a relationship of part to part or of point to point. The sentient principle is neither an extended part nor a mathematical point. I called this relationship between the extended element and the sentient principle relationship of sensility. It is evident that this relationship is non-extended precisely because it is not a relationship of part to part or of point to point, the only relationship which alone forms extension. Consequently, I concluded that the sentient principle apprehends what is extended in a non-extended way. When I say that the sentient principle apprehends what is extended, I mean that what is extended is in the sentient principle, but not as one part is in a greater part. As a result, the extended element is not in the sentient principle with the relationship constituting extension but in some other way, that is, in a non-extended mode.

This can be proved by another argument. When we say that one ens is in another in an extended mode, we mean that it is in the other according to the law of extension. This law states that one ens is in another as a lesser extension is in a greater, as part of a body is in the whole. A part of a body is in the whole in such a way that it is outside other parts. Properly speaking, no body is contained in another body, although it may be surrounded by some other body. The precise property of extension is that every single part is outside every other. This property when considered in bodies which enjoy extension is called impenetrability. On the other hand, if we consider how the extended sensible element is in sensation or in sensitive perception, it becomes clear that it is not present in the mode we described. Here, we certainly do not find two extensions of different sizes with the lesser comprised in the greater. We find that the whole extension is present to the sentient and perceiving principle, which is not a greater extension that embraces a lesser, but something different from extension (which is its term). The extended element, therefore, is not in the sentient principle according to the mode prescribed by the law of extension; it is there in an non-extended mode. All this is given to us by simple observation. It is an undeniable fact; we simply have to pay attention to recognise it.

Yet another proof of this truth, or another indication of how we can recognise this fact, is found in what follows. The phrase 'One body contains another, one extended element other less than itself' is improper, and strictly speaking is false. Extension and that which enjoys extension is impenetrable, as I said; one part cannot be within another without destroying its own extension. Now, if what is extended were contained in the sentient principle as one extended element is contained in another, it would follow that what is extended would never be contained in the sentient principle; the sentient principle would surround it, be next to it, but nothing more. In this case, the sentient principle would never feel what is extended because the latter would always remain outside it. This is, in fact, the case between every extended element; what is extended cannot feel what is extended. But the sentient principle does feel what is extended, and the whole of what is extended. It is necessary, therefore, that what is extended should be in the sentient principle according to some other relationship, according to a law different from that of extension. In other words, what is extended is present in an non-extended mode.

Moreover, if the sentient principle had extension and perceived what is extended by receiving the latter into its own extension, one of two things would follow: either the extension of the sentient principle would be the same as that of the extended things it feels, or it would be different. If it were the same, the sentient principle would feel only itself; it would never receive any new sense-experience. If it were different, that is, if another extension were added to that of the sentient principle, the new extension, in order to be felt, would itself have to become a sentient principle. This is manifestly absurd because in sense-experience and sensitive perception, the sentient element is one thing and the felt element another.

Finally, if the sentient principle were extended, each part of this extension could feel only an extended part of its own dimension. But however small the parts assigned mentally, they could always be diminished. This could go on indefinitely in such a way that the smallest parts could never be found. There are no absolutely small parts in an extended element. Consequently, the sentient parts would never be found because no part could be felt whole and entire by its corresponding part, which itself has other parts, each of which would not feel the whole, entire part. It would, therefore, be impossible to determine one whole, entire part that felt the whole of another part. There would be no sentient principle suitable for feeling the whole of some extended element, however small it were.(95)

The extended felt element would also be lacking, and for the same reason: there would be no sentient principle capable of feeling it as extended. Even if we supposed the sentient principle to be a mathematical point, such a point could still not feel anything other than a mathematical point; the extended element or point has no existence or action outside itself and could never feel what is extended. Indeed, the extended element would cease altogether because it cannot exist outside the sentient principle. If every part is outside every other in the extended element, every part, or better every smallest extended element, exists outside every other. If it exists outside every other part, its existence and its essence is limited to itself; it has no proper and essential relationship with any other part. But even the smallest extended element is a union of still smaller elements. This can go on indefinitely. The ultimate, extended elements cannot, therefore, be found, and thus extension itself vanishes. If extension supposes possible co-existing parts, if it supposes continuity (which has a single, simultaneous existence without any interruption), there must be a simple principle which can simultaneously embrace all possible parts.

These individual parts no longer remain in their own single existence, but together are formed into a single existence, a single ens. The very nature of the continuum is that parts can be assigned in it that have individual and independent existence, although as a continuum it does not have these parts. The reason, therefore, for the continuum as a property of extension is not found in the individual existence of the single parts, but in a simple principle superior to these parts. This principle gives all the parts a single existence and by embracing them all abolishes them, because they cease to be parts of the continuum and become simply the continuum. This is done by the sentient principle to which the continuum is present without parts, although innumerable parts can be assigned in it. This explains why I said that an extended element can exist only in what is simple (cf. 440-452).(96)

1128. What has been said enables us to reason in two ways about the nature of extension and of bodies and thus, have two concepts of them. We can consider the nature of the extension of bodies

1. Under the relationship essential to extension, which consists in this: one part is outside another. This consideration does not move our thought away from extension and from what is extended. It simply makes us consider extension in itself and compare one part with another.

2. Under the other essential relationship of sensility. This consideration compares extension or the extended element with the sentient principle, and finds extension conditioned to the principle and in-existing in it.

Normally people consider extension and the extended element under the first relationship, in which they posit the essence of extension. The philosopher has to consider it under the second relationship. He must understand that the second relationship also forms part of its essence, and consequently that extension has an essential nexus with the sentient principle, a principle which is not extension. These connections between two entia (and essential to them both) are the foundation of ontological synthesism and the key to more sublime philosophy.

1129. Note that the first essential relationship is not destroyed in any way by the second. Indeed, the second supposes the first. If we consider continuous extension or the continuous extended element as existing in the sentient principle, there is no danger of confusing it with the sentient principle, to which it is opposed as co-relative term. This term is an ens in itself, constituted in such a way that it can be conceived without our needing to go outside it or add anything to it. The term is, therefore, a substance because 'substance has what is needed to be conceived, and therefore exists in itself.' Note that it is not at all necessary for a thing to have a cause or a constituent principle, in order to be conceived as a substance. It is sufficient for it to be conceived by itself. We may say more briefly that 'substance is that which has its own concept.' We simply add that the word substance involves, in addition, a relationship with accident as, for instance, in corporeal substance. This allows for different accidents which exist in and through the substance. They have no separate and independent concept because we cannot conceive of a corporeal accident as existing unless we first conceive a body, an extended element, in which it is. And it is precisely to this body that we give the name 'substance'. Substance, therefore, is 'an ens (or that which has a concept of its own) considered in relationship with other entities that exist in and through it.' This is the most complete definition of substance (cf. 52).

1130. But if the continuous extended element has existence in the sentient principle as its essential relationship, it would seem that this element cannot be conceived without recourse to the sentient principle in which it exists; everything essential enters into the concept of an ens. This difficulty can be overcome by noting how we insisted that an ens changes essentially in our concept through the addition or subtraction of an essential relationship. As we said, the beings of which we are speaking are those we conceive. But the essential part added to them does not change the first part.

1131. We also need to consider that the concept of the continuous extended element, although thought of without the sentient principle, nevertheless presents in itself continuity, produced by the simplicity of this principle. It is precisely by reasoning about the nature of this continuity that we later induce the necessity of a sentient principle. This induction, although founded on the first concept of the extended element, pertains to a reasoning posterior to the conception of this element. Such reasoning is not necessary for the conception of an ens which as we said is posited with the first concept.

1132. Until now, we have spoken indiscriminately of extension and the extended element because our reasoning was valid for both. But before going on to speak of the unity which the sentient principle gives to its term, it will help to clarify and eliminate all doubt in the mind of readers if we distinguish extension from the extended element.

By extension, I understand the same as space, considered independently of bodies. By extended, I understand a body which occupies a part of space, that is, of extension. Extension, that is, total or empty space, exists whether occupied or not by bodies. It is certainly not nothing, as some would have us believe. Nothing cannot be occupied by anything, nor can thought assign parts to nothing as they can be assigned in space.
This space, however, is boundless [App., no. 5], immobile, indivisible, that is, continuous and unmodifiable. Only body is measurable, mobile, divisible and modifiable. But the presence or absence of the body in a given space does not modify space or extension in any way. This remains as it was previously.

1133. For me, pure space is a term of the fundamental perception of the soul (cf. 554-559).
This primal space is not a form in Kant's sense, a law of operation as it were and a production of the soul itself, but the distinct term of a natural perception. The term, however, has successively two states, the primal state devoid of any quantitive distinction or relationship, or of any other nature (pure, indistinct space); and reflective space which is brought about by the mind which compares primal space, also perceived intellectually, with various dimensions of bodies and with the possibilities of such dimensions (ideas of pure distinct space, that is, space relative to bodies). This pure, distinct, reflective space with its quantitative relationships is of another genus; it is the idea of interminable space, whose origin we have indicated in A New Essay.(97) For me, one of the terms of the fundamental feeling is an extended body and thus a distinct extension limited as the body is limited. But the animal has power to move itself, and movement means simply transporting the body into another part of space.

If, therefore, some trace of the previously occupied space remains, the distinct space remains enlarged in the sentient principle in proportion to the movement and retentive faculty of the principle. When movement takes place in the human being, who is furnished with intelligence and possesses the concept of what is possible, he understands the possibility of indefinitely multiplying and extending the space of his and other bodies through motion. He thus forms the concept of reflective, distinct, pure or immense space.(98) This concept is lacking in animals, who have no concepts; it is acquired in human beings, although the indistinct space of sensitive and rational perception is innate. The instinct of motion does indeed suppose the fundamental perception of immense, indistinct space, but not the idea of distinct space. This instinct is only the bodily feeling with its limited space, of which, however, it does not feel the exterior confines. As such, the instinct tends to adapt itself in the most comfortable and pleasing way without the animal's feeling, as full and distinct, the new space to which it is to move. The animal transports itself through its activity to this space which, however, it feels as distinct, that is, occupied or occupiable, only when it has already moved itself there, provided of course that it has some way of preserving in itself the traces of the preceding space.

Space connected with one's own body is therefore distinct space because it is occupied space, but it is not marked by limits. These cannot be distinguished because as yet nothing corporeal is felt outside the space that limits one's own body, the space of which is absolutely limited, but not measurable by the animal. Measurement supposes a relationship with some other extended quantity which is lacking until the animal exercises its locomotive power and receives new sense-experiences.

1134. This, therefore, is simply space, unmodifiable and immobile. It has no accidents, and although it can truly be called an ens because its concept (after the human being has obtained it) is self-sufficient and without need of body, it cannot be called a substance. The concept of substance is relative to other entities which exist in and through an ens, that is, relative to accidents. Here again, we see how unfounded is the affirmation: 'There are no entia, other than substances and accidents.' It pertains to false, material ontology.(99)

1135. Space, with or without corporeal force, is the term of feeling. This shows that space is an ens, not nothing. However, while it is only this force which changes (space remains immobile), it must be said that space is an ens having only a first act by which it is in the sentient principle it informs as term. Space has no other activity or second acts and hence no accidents. That is why those who fail to acknowledge anything until they see accidents and second acts, make the mistake of calling space nothing.

Again, in considering pure space (extension) as the immediate term of the spirit, we consider it in the very act by which it is constituted because it has no other activity beyond the activity which it demonstrates as the natural term of the sentient principle. The concept of body (of the extended element), however, as term of the sentient principle involves in addition some passivity possessed by corporeal nature relative to both the spirit whose term it is and to other powers or external forces which move and modify body independently of our spirit. In other words, we can acquire the concept of distinct space, that is, of several spaces, simply by abstracting it from body.

But acquisition of the full concept of body requires the kind of experience which shows that the body is an ens acting in our spirit, which in turn reacts on the body by modifying it. Other foreign forces and powers also act on the body by producing movements and modifications in it. From all this information, the result of experience, the human spirit draws conclusions about the kind of force which, expanding in extension, is called 'body'.(100)

1136. From what has been said, we can draw the following important corollary: the unity found in extension and in the corporeal, extended element is constituted by the unity and simplicity of the sentient principle, that is, by the soul.
In fact, the only unity of which we are aware in extension and the extended element consists in continuity. If we remove continuity, by splitting it up successively with our mind, space and body are multiplied. This multiplication goes on ad infinitum because the continuum always remains; division and multiplication ad infinitum never provides us with a space and a body that have no continuum. Imagining this is absurd. If, then, we sweep away the continuum immediately, not successively, all extension and every phenomenal body perishes.(101)
But we have seen that the continuity of the extended element can only be conceived if we have an ens which, remaining identical, is simultaneously in all the assignable parts of the continuum. This can be affirmed of the spirit, when the continuum is considered as its undivided and indivisible term.

1137. If, therefore, the simplicity of the material world consists solely in continuity, and if continuity possesses such a concept or nature that it cannot be posited outside the sentient principle (we cannot even think it outside the sentient principle), the simplicity and the unity of the material world comes about as a result of this essential condition and relationship. In other words, the material world is the term of the animal- sentient principle, that is, of the sensitive soul.

1138. Here I trust that no one who has followed the argument will object that 'being contiguous or non-joined is a condition proper to two bodies, not to feeling'. This would show that the objector had not considered that:

1. Immobile extension is the foundation of the continuum even in bodies. Bodies are only forces diffused in extension which has its seat in the sentient principle.

2. The continuity of bodies is nothing relative to the individual bodies themselves. None of these has in itself any relationship of proximity or contiguity with another. This relationship, therefore, is extraneous to the concept. It is simply a relationship that each of them has with the term of the sentient principle, that is, with immobile and unmodifible extension. Hence, the contiguity of bodies is a relationship with the sentient principle, which feels them in the space by which, as by its term, the principle itself is informed.

Notes

(95) When in the last century D'Alembert asked about the bridge of communication between the spirit and external things, his question was posed absurdly. This way of asking the question presupposes as given and agreed that there is a relationship of extension between the spirit and things, just as there is a relationship of extension between one bank of a river and another, between one body and another. But once the error of this presupposition is identified, the question itself ceases to exist. It is seen to be one of those questions to which no reply can be given because the questions themselves do not truly exist. The relationship between spirit and things is not a relationship of distance but of sensility; it is not the relationship of one corporeal part to another, but of body to spirit, of felt and sentient. An important principle of logic can be drawn from this: 'All questions proposed in such a way that they include or presuppose something absurd are non-resolvable, and are annulled when the truth has been discovered.' Simultaneously with the truth we find how the state of the question has been changed, and the true question solved.

(96) This truth was seen in some way by the Scholastics when they asked if the intellective soul were the single form of the human being. This is St. Thomas' opinion. He says: 'Through the soul this being is body and organic and a potency having life' (S.T ., I, q. 76, art. 4, ad 1). Cajetan, a celebrated and very subtle commentator, when explaining how the soul as a single form also produces corporeity, says: 'This question is only about quantity and what is extended per accidens , that is, SUBJECTIVELY.' He does not reflect, however, that the extended element, although existing in the subject is distinct from the subject; nor does he note that the principle which directly causes the existence of the extended element is the sensitive, not the intellective principle; nor is he aware that the extended element vanishes when outside the subject. Nevertheless, the commentary of this illustrious Cardinal deserves attention.

(97) NE , vol. 2, 820-830.

(98) Here we have to add that this mental operation with which we conceive interminable space would be impossible for us unless we had some movement other than absolute movement, which cannot be felt. We need relative movement. We are helped in retaining this space through which we have moved above all by surface sensations, and by sight which marks their limits so clearly. Once we know these limits, we soon think of the possibility of going beyond them again (once the limits have been passed, and we know through experience that they can be expanded indefinitely). Indeed, the concept of limit or term of space contains virtually the immensity of space in the same way as a condition is contained virtually in what is conditioned. Reasoning enables us to draw the former from the latter.

(99) Rinnovamento , bk, 3, chap. 47.

(100) These reflections enable us to confute the error of the Cartesians who confused space with body by positing the essence of body in extension. Errors of this kind result from an inability to discover any corporeal quality outside extension. As a result, they considered extension as the substratum of corporeal accidents, that is, as the first thing conceived in bodies, but failed to reflect that the extension of bodies is not perceived distinctly except by feeling. Extension, therefore, is never conceived alone, but in the company of extended sensations in which some force is always perceived. Hence, in the order of concepts, the force which acts in us is prior to the extension of bodies. Extension, therefore, is not the first thing that we conceive in them. Rather, we conceive contemporaneously force as cause, and extension as effect. These two things do not perhaps differ relative to time, but they certainly differ relative to logical order. I grant, however, with the Cartesians that the concept of extension should be clear and sharply delineated. Cardinal GERDIL'S work Della immaterialità dell'anima contro Locke is helpful on this point, but does not prove that extension is the substance of bodies.

(101) One of the properties of an ens is simplicity . This truth was known and taught by the Scholastics, who held as a principle that esse substantiale cuiuslibet rei in indivisibili consistit [the substantial being of anything whatsoever consists in an indivisible element], as St. Thomas says (S.T. , 1, q. 76, art. 4, ad 3). This means: 'Where simplicity cannot be found, there is no being'. An accident is not, properly speaking, an ens, but an entity, that is, an appurtenance of an ens.