Omitting the difficulties which attend an opinion which seems to

suppose the existence of what it denies, I will ask if geometry can

require more rigorous exactness than is found in the points to which

infinite power can come, if we suppose it to exercise its eternal

action in dividing the composite; or, in other words, can there be

any more strictly geometrical points than those seen by an infinite

intelligence in an infinitely divisible being? This not only satisfies

our imagination and our ideas of exactness, but goes even beyond.

Experience teaches us that to _imagine_ an unextended point is not

impossible; and to _think_ it in the purely intellectual order, is only

to conceive the possibility of this infinite divisibility, and to be

suddenly placed at the last limit,--a limit which must still be far

distant from that to which, not abstraction, but the sight of infinite

intelligence can reach.

If the geometrical point exists, the geometrical line also exists; for

it is only a series of unextended points; or, if we are unwilling to

acknowledge these, a series of extremes to which division infinitely

continued at last arrives. A series of geometrical lines forms a

surface; and a union of surfaces forms a solid, the ideal order

agreeing with reality in its formation as in its nature.

34. This theory of the realization of geometry extends equally to all

the natural sciences. It is an error to say, for example, that the

reality does not correspond to the theories of mechanics. It should

rather be said that it is not the reality that is at fault, but the

means of experimenting; the blame should not be imputed to the reality,

but rather to the limitation of our experience.

The centre of gravity in a body, is the point where all the forces

of gravitation in the body unite. Mechanics supposes this point to

be indivisible, and in accordance with this supposition, establishes

and demonstrates its theorems, and solves its problems. Here stops

the mechanician, and the machinist begins, who can never discover the

strict centre of gravity supposed in the theory. Experience disagrees

with the principles, and we ought to correct the former by adhering to

that which is determined by the latter. Is this because the centre of

gravity does not exist in nature with all the exactness which science

supposes? No; the centre exists, but the means of finding it are

wanting. Nature goes as far as science; neither remains behind; but our

means of experience are unable to keep up with them.

The mechanician determines the indivisible point in which the centre

of gravity is situated, supposing the surface without thickness,

lines without breadth, and the length divided at a determinate point

of space, which has no extension. Nature entirely fulfills these

conditions. The point exists, and the reality should not be blamed

for the limitation of our experience. The point exists in either of

the hypotheses mentioned above. The first, which favors unextended

points, admits the existence of the centre of gravity in all its

scientific purity. The other is not so decided, but it says to us: "Do

you see this molecule, this little globe of infinitesimal diameter,

the smallness of which the imagination cannot represent? Make it still

smaller, by dividing it for all eternity, in decreasing geometrical

progression, and you will always be coming nearer the centre of gravity

without ever reaching it. Nature will never fail; the limit will ever

retire from you; but you will know you are approaching it. Within this

molecule is what you seek. Continue to advance, you will never reach

it,--but what you want is there." In this case I do not see that the

reality falls short of scientific exactness; no mechanical theory

imagined or conceived can go farther.

35. These reflections place beyond all doubt that geometry with all

its exactness, and theories in all their rigor, exist in nature. If we

could follow it in our experience, we should find the real conformed

to the ideal order, and we should discover that when experience is

opposed to theory, it is not the latter which is wrong, but the

limitation of our means makes us lay aside the conditions imposed by

the theory. The machinist who constructs a system of indented wheels

finds himself obliged to correct the rules of theory, on account of

friction, and other circumstances, proceeding from the material which

he employs. If he could see with a glance the bosom of nature, he would

discover in the friction itself a new system of infinitesimal gearing

which would confirm with wonderful exactness those very rules which a

rude experience represents to him as opposed to reality.

36. If the universe is admirable in its masses of gigantic immensity,

it is not less so in its smallest parts. We are placed between two

infinities. Man in his weakness, unable to reach either one or the

other, must content himself with feeling them, hoping that a new

existence in another world will clear up the secrets which are now

veiled in impenetrable darkness.

CHAPTER VI.

REMARKS ON EXTENSION.

37. If extension is something as we have proved; what is it?

We find extension in bodies and also in space because in both we

find that which constitutes its essence, which is dimension. Is the

extension of bodies the same as the extension of space?

I see and hold in my hand a pen: it is certainly extended. It moves,

and its extension moves with it. The space in which its motion is

executed remains immovable. At the instant A the extension of the pen

occupies the point A′; at the moment B the same extension of the pen

occupies the part B′ of space which is distinct from the part A′;

therefore neither the part A′ of space nor the part B′ is identified

with the extension of the body.

This seems to have all the force of a demonstration; but to make

it more clear and more general, I will put it into the form of a

syllogism. Things which are separated or may be separated are distinct;

but the extension of bodies may be separated from any part of space;

therefore the extension of bodies and the extension of space are

distinct. I said that this reasoning seems to have all the force of a

demonstration, but it is nevertheless subject to serious difficulties.

These difficulties cannot be understood without a profound analysis of

the idea of space, and therefore I shall reserve my opinion until this

has been treated of in the following chapters.

38. Is the extension of a body the body itself? I cannot conceive a

body without extension, but this does not prove that extension is the

same thing as the body. My soul has acquired a knowledge of the body

by means of the senses. These senses have _awakened_ in me the idea of

extension; but they have told me nothing of the intrinsic nature of the

body perceived.

In those beings which we call bodies we find the power of producing in

us impressions very distinct from that of extension. From two bodies of

equal extension we receive very different impressions, therefore there

is in them something besides extension. If extension was their only

quality, this being equal, the effect would be the same; but experience

teaches us that it is not so.

Moreover we conceive extension in pure space where there is no

body. The idea of body implies the idea of mobility, while space is

immovable. It implies the power of producing impressions; the extension

of space has not of itself this power.

Therefore the simple idea of extension does not include even in our

cognitions the whole idea of a body. We do not know in what the essence

of body consists; but we know that in the idea which we have of it

there is something more than extension.

39. When it is said that a body is inconceivable without extension

it is not meant that extension is the constitutive notion of the

essence of body. This essence is unknown to us, and therefore we

cannot know what does or does not belong to it. The true meaning of

this inseparability of the two ideas of extension and body is this:

As we have no knowledge _a priori_ of bodies, but whatever we know

of them, their existence included, we derive through the senses, all

that we think or imagine concerning them must presuppose that which is

the basis of our sensations. This basis, as we have already seen, is

extension; without it there is no sensation, and consequently without

it a body ceases to exist for us, or is reduced to a being which we

cannot distinguish from others.

I will explain my ideas. If I strip bodies of extension and leave

them only the nature of a being which causes the impressions which I

receive; this being is the same, so far as I am concerned, as a spirit

which should produce the same impressions. I see this paper, and it

causes in me the impression of a white surface. There is no doubt that

God could produce in my mind the same sensation without the existence

of any body. Then supposing that I knew that no external extended

object corresponded to my sensation, which was caused by a being acting

upon me, it is evident that there would be two distinct things in my

mind. First, the phenomenon of sensation, which under all hypotheses

is the same; and secondly, the idea of the being which produced it,

which is only the idea of a being distinct from myself, acting upon me,

which in relation to the external world, would involve two ideas; those

of distinction and causality.

I now take from the paper extension, and what remains? The same as

before. 1. An internal phenomenon, made known by consciousness. 2. The

idea of a being the cause of this phenomenon.

I do not know whether this must always be a body; but I know that

the idea of a body, as I understand it, includes something more than

this. I know that being is not in relation to myself distinguishable

from other beings, and that if there is any thing in its nature to

distinguish it from them, it is something unknown to me.[40]

[40] See Ch. I.

40. This is the sense in which I say that we cannot separate the idea

of extension from the body. But from this it must not be inferred that

the things themselves are identified; perhaps, even, a more profound

knowledge of matter would show us that instead of being identical, they

are entirely distinct. We have seen that it is so with their ideas, and

this is a sign that it is so in reality.

41. We have few ideas as clear as that of extension geometrically

considered; every attempt to explain it is useless; we know it more

perfectly by mere intuition than whole volumes could make it known to

us. It is so clear an idea, that on it is founded a whole science,

the most extensive and evident which we possess, that of geometry.

Therefore there is reason to believe that we know the true essence of

extension, since we know its _necessary_ properties, and even base

a whole science on this knowledge. Yet we do not discover in this

idea, either impenetrability or any of the properties of bodies; but

rather on the contrary, we find a capacity indifferent to them all. We

conceive extension penetrable as easily as impenetrable, empty or full,

white or green, with properties by which it can be placed in relation

with our organs, as easily as without them. We can conceive extension

in a body acting on another body, or in pure space; in the sun which

enlightens and warms the world, or in the vague dimensions of an empty

immensity.

CHAPTER VII.

SPACE.--NOTHING.

42. It may have been remarked in the preceding chapters that the

idea of extension is always united with that of space, and when we

endeavor to determine the _real_ nature of the former, we encounter the

questions which relate to the latter. It is not possible to explain

one, while the other remains in obscurity. It is for this reason that

I have concluded to examine carefully the questions concerning space

under its ideal as well as under its real aspect; since only in this

manner is it possible to determine clearly the nature of extension.

43. Space is one of those profound mysteries which the natural order

presents to man's weak understanding. The deeper he examines it the

more obscure he finds it; the mind is buried in the darkness which

we imagine to exist beyond the bounds of the finite, in the abyss of

immensity. We know not if what we behold is an illusion or a reality.

For a moment we seem to have found the truth, and then we discover that

we have stretched our arms to embrace a shadow. We form arguments

which in any other matter would be conclusive, but are not so here,

because they are in direct contradiction to others equally conclusive.

We seem to have reached the limit which the Creator has put to our

investigations; and in endeavoring to pass beyond it, our strength

fails, for we find ourselves out of the element which is natural to our

life.

When certain philosophers pass rapidly over the questions relating to

space, and flatter themselves with explaining them in a few words,

we can assure them that either they have not meditated much upon

the difficulty which these questions involve, or else they have not

understood them. It was not so that Descartes, Malebranche, Newton, or

Leibnitz proceeded.

To descend this bottomless abyss is not to lose time in useless

discussion; even though we should not find what we seek, we obtain

a most precious result, for we reach the limits assigned to our

intellect. It is well to know what may be known and what cannot; for

from this knowledge philosophy draws high and valuable considerations.

Moreover, though we have small hope of success, we cannot pass over

without examining an idea that is so closely connected with all our

knowledge of corporeal objects, that is to say, extension. There must

be a motive of investigation since all philosophers have investigated

it, and who can say that after long ages of efforts the truth is not

perhaps reserved as the reward of constancy?

44. What then is space? Is it something real or only an idea? If an

idea is there any object in the external world which corresponds to it?

Is it a pure illusion? And is the word space without meaning?

If we do not know what space is, let us at least fix the meaning of the

word, and thus determine in some measure the state of the question. By

space we understand the extension in which we imagine bodies to be

placed, or the capacity to contain them to which we attribute none of

their qualities except extension.

Let us suppose a glass to be hermetically sealed, and the interior to

remain empty by the annihilation of what it contained; this cavity

or capacity which in our way of understanding it may be occupied by

a body is a part of space. Let us imagine the world to be an immense

receptacle in which all bodies are contained; let us suddenly make

it empty and we have a cavity equal in space to the universe. If we

imagine beyond the limits of the world a capacity to contain other

bodies, we have an unlimited or imaginary space.

Space appears to us at first sight, if not infinite, at least

indefinite. For in whatever part we conceive a body to be placed, we

also conceive the possibility of its moving, describing any class of

lines, or taking any kind of direction and departing indefinitely from

its first position. Therefore we imagine no limit to this capacity, to

these dimensions. Therefore space appears to us as indefinite.

45. Is space a pure nothing? Some philosophers maintain that abstracted

from the surface of bodies, and considered as a mere interval, it is

a pure nothing. At the same time they admit that it is only owing to

space that two bodies are really distant from each other, and add that

if we suppose the whole world, with the exception of one body only, to

be reduced to nothing, this body could move and change its place. I am

confident that this opinion involves irreconcilable contradictions. To

say _extension-nothing_ is a contradiction in terms, and the opinion of

these philosophers is reduced to this expression.

46. If every thing in a room be reduced to nothing, it seems impossible

for the walls to remain distant from each other; for the idea of

distance implies a medium between the two objects; and nothing, being

nothing, cannot be the medium required. If the interval is nothing,

there is no distance. To attribute properties to nothing, is to destroy

all ideas,--to affirm that a thing may be and not be at the same

time,--and consequently to overthrow the foundation of human knowledge.

47. To say that if the contents were annihilated, a negative space

would remain, is only to play with words without touching the

difficulty to be solved. This negative space is either something or

nothing; if it is something, the opinion we are opposing is false; if

it is nothing, the difficulty remains the same.

48. But, it may be said, although nothing remains between the surfaces,

they still retain the capacity of containing something. To this I

reply, that this capacity is not in the surfaces themselves, but in

their distance from each other; for if it were in the surfaces, they

would still preserve it, no matter how they may be placed, which is

absurd. We have not therefore advanced a single step. We must explain

what this capacity, or this distance, is; and this is still untouched.

49. Perhaps it may be said that annihilating all that is contained

between the surfaces, does not destroy the volume which they form, and

the idea of this volume implies the idea of capacity. But I reply, that

the idea of volume involves that of distance, and there is no distance

if this distance is a pure nothing.

50. In our efforts to surmount these difficulties, another seemingly

specious solution offers, but if we examine it we shall find it as weak

as the others.

Distance, it might be said, is a mere negation of contact, but negation

is a pure nothing; therefore this nothing is what we seek. I say

this solution is as weak as the others; for, if distance is only the

negation of contact, all distances must be equal, because negation

cannot be greater or less. The negation of contact is the same whether

the surfaces are a million leagues or only the millionth part of an

inch distant from each other. This negation, therefore, explains

nothing, and the difficulty still remains.

51. Not only is the idea of distance not explained by the idea of

contact, but on the contrary, the idea of contact can only be explained

by the idea of distance. Contiguity is explained by immediate union

of two surfaces; we say that they touch each other because there is

nothing between them, or there is no distance. The idea of contact does

not involve the qualities which relate to the senses, nor the action

which one body may exercise upon another which touches it, as impulse

or compression. Contiguity is a negative, and purely geometrical,

idea, and implies only the negation of distance. Contiguity cannot be

greater or less; it is all that it can be when there is a true negation

of distance. Two objects may be more or less distant, but they cannot

touch more or less, with respect to the same parts. There may be

contact of more points, but not more contact of the same points.

52. If we attribute distance and capacity to space, the argument in

favor of its reality becomes still stronger. Let us suppose an empty

sphere two feet in diameter. Within there is only space; if space is

nothing there is nothing in it.

Is motion possible in this empty sphere? It does not seem that there

can be any doubt of this. There is a movable body, an extension

greater than the extension of the body, and a distance to be passed

over. We may add to this, that if motion were not possible, it would

not be possible to make the sphere empty, or after making it empty,

to fill it. Neither emptying nor filling the sphere can be done

without motion of bodies in the interior of the sphere, and motion of

a body in another body is only possible in space, because bodies are

impenetrable, and also because, when the sphere is filled after it is

empty, the body which enters does not meet another body; and when the

sphere is made empty, the body which passes out, moves over the space

which it abandons, and in which nothing remains after it has passed out.

Therefore, supposing the sphere empty, there may be motion in it. But

if the space contained in the sphere is a pure nothing, the motion also

is nothing, and consequently does not exist. Motion can neither exist

nor be perceived without a distance passed over. If, therefore, the

distance is nothing, there is no motion. If we say that the body has

passed over half of the diameter, or one foot, what does this mean? If

the space is nothing, it can mean nothing. I see no reply which can be

made to these arguments, which are all based on the axiom, that nothing

has no properties.

53. However great may be the difficulties opposed to the reality of

space, they are not so great as those which are brought against the

opinion, which, while granting extension to space, still regards it

as a pure nothing. The former, as we shall soon see, are produced by

certain inaccuracies in our way of conceiving things, rather than by

arguments founded on the nature of things; whilst those objections

which we have brought against the opinion denying the reality of space,

are founded on the ideas which are the basis of all our knowledge,

and on this evident proposition: nothing has no properties. If this

proposition is not admitted as an established axiom, the principle of

contradiction falls, and all human knowledge is destroyed. For, it

would be a plain contradiction, if nothing could have any properties

or parts; if any thing could be affirmed of nothing, or could be moved

in nothing; if a science like geometry could be founded upon nothing;

or if all the calculations which are made on nature are referred to

nothing.

CHAPTER VIII.

DESCARTES AND LEIBNITZ ON SPACE.

54. If space is something, what is it? Here is the difficulty. To

overthrow the opinion of our adversaries was easy, but to maintain our

position is more difficult.

Can we say that space is only the extension of bodies; that conceived

in the abstract it gives us the idea of what we call pure space; and

that the different points and positions are mere modifications of

extension?

It is easy to see that if space is the extension of bodies, where

there is no body there can be no space, and consequently vacuum is

impossible. This consequence is unavoidable.

This has been the opinion of celebrated philosophers like Descartes

and Leibnitz; but I cannot understand why they both gave the universe

an indefinite extension. It is true that by this means they avoid the

difficulty of the space which we imagine beyond the limits of the

universe; since, if the universe is not limited, there can be nothing

beyond its limits, and therefore, whatever we can imagine, must be

within the universe. But our object is not to avoid difficulties, but

to solve them; and it argues nothing for the soundness of our opinion

that it escapes difficulties.

55. According to Descartes, the essence of body is in extension, and

as we necessarily conceive extension in space, it follows that space,

body, and extension, are three essentially identical things. Vacuum,

as it is generally conceived, that is, an extension without a body, is

then a contradiction; for it is a body, because it is extension, and it

is not a body, because we suppose that there is no body.

Descartes accepts all the consequences of this doctrine. He does not

admit the supposition that if God should annihilate all the matter

contained in a vessel, this vessel could still retain its form.

"We shall observe," he says, "in opposition to this serious error,

that there is no necessary connection between the vessel and the body

which fills it; but such is the invincible necessity of the relation

between the concave figure of the vessel and the extension contained

in this concavity, that it is not more difficult to imagine a mountain

without a valley, than to conceive this concavity without the extension

contained in it, or this extension without a thing extended. Nothing,

as we have often said, cannot be extended. Therefore, if any one should

ask, what would happen if God should destroy the matter contained in a

vessel, without replacing it, we must say that the sides of the vessel

would come so closely together as to touch each other. Two bodies must

touch each other, when there is nothing between them. It would be a

contradiction to assert that these two bodies were separated; that is

to say, that there was a distance between them, if this distance were

nothing, or did not exist. Distance is a property of extension, and

cannot exist without extension."[41]

[41] Descartes, _Principes de la Philosophie_. P. 2, § 18.

56. If Descartes had gone no farther than to maintain that space,

because it contains real distances, cannot be a mere nothing, his

reasoning would seem conclusive. But when he adds that space is body,

because space is extension, and extension constitutes the essence of

body, he asserts what he does not prove.

Because we cannot imagine or conceive a body without extension, it only

follows that extension is a property of bodies without which we cannot

conceive them,--not that it is their essence. To be able to say this,

it would be necessary for us to have the idea of body as we have that

of extension, in order that we might see if they are identical. But all

that we know of bodies is derived through the senses; we are not able

to penetrate into their more intimate nature.

Whence arises the inseparability of the ideas of body and extension?

It arises from the idea which we have of bodies being a confused

idea, since we conceive it to be a substance in certain relations to

ourselves, and causing in us the impressions which we call sensations.

But since the basis of sensations is extension, as we have demonstrated

in a former chapter, this is the only medium by which we are placed in

relation with bodies. When we suppress this basis, by abstracting it,

we retain nothing of body beyond a general idea of being or substance

without any thing to characterize it, or to distinguish it from others.

We find all this in the order of our ideas, but we cannot infer from

this that bodies have no other reality than extension.

57. The same reasoning destroys the opinion of indefinite or infinite

extension. Descartes, explaining his doctrine on the idea of extension,

says: "We shall also know that this world, or the extended matter which

composes the universe, is without limits; for, no matter how far off we

place these limits, we can imagine spaces indefinitely extended beyond

them; and we not only imagine these spaces, but we conceive them as

really existing such as we imagine them, and containing an indefinitely

extended body, as the idea of extension which we conceive in every

space is the true idea which we ought to form of a body."[42]

[42] Descartes, Ibid., § II, p. 21.

In this passage, besides the error in relation to the essence of

bodies, there is a gratuitous transition from a purely ideal or rather,

imaginary order, to the real order. It is certain that wherever I may

imagine the limits of the universe, if I consider them as an immense

arch surrounding it, I still imagine new immensities of space beyond

this arch; but to conclude that the reality is as I imagine it, does

not seem conformed to the rules of good logic. If it is as clear as

Descartes supposes, if it is not only an imagination, but a conception

founded on clear and distinct ideas, how happens it that so many

philosophers see in all this only a play of the imagination?

58. Leibnitz thinks that space is "a relation, an order, not only

between things existing, but also between possible things as if they

existed."[43] He also believes vacuum impossible, but not for the

reason which Descartes gives. These are his words:

[43] Leibnitz, _Nouveaux Essais_. L. II., C. XIII., § 17.

"_Philalethes._--Those who take matter and extension for the same

thing, pretend that the sides of a hollow empty body would touch each

other. But the space which is between the two bodies is enough to

prevent their mutual contact.

"_Theophilus._--I am of your opinion; for, although I do not admit a

vacuum, I distinguish matter from extension, and concede that although

there were a vacuum in a sphere, the opposite poles would not on that

account unite. But I do not believe this is a case which the divine

perfection would permit."[44]

[44] Leibnitz, Ibid., § 21.

59. Leibnitz seems to me to commit what logicians call _petitio

principii_, or, "begging the question." He says that in the case

supposed, the sides would not touch each other, because the space

between them would prevent it; but this is what he had to prove,--the

real existence of this space. This reality is what Descartes denies.

60. If we compare the opinions of Descartes and Leibnitz, we shall see

that both agree in denying to space a reality distinct from bodies, but

basing their denial on very different reasons. Descartes places the

essence of body in extension; where there is extension there is body;

where there is space there is extension; consequently, there neither

is nor can be a vacuum. Leibnitz does not believe an empty capacity

intrinsically absurd, and that he does not admit it is solely because,

in his conception, it is repugnant to the divine perfection. The two

illustrious philosophers started from very different principles, but

arrived at the same conclusion. Descartes rests upon metaphysical

reasons, founded on the essence of things. Leibnitz bases his opinion

on the absolute essence of things only in its relations with the

divine perfection. Empty capacity is a contradiction in the opinion of

Leibnitz, only inasmuch as it is opposed to optimism.

61. It is very remarkable that three so distinguished philosophers

as Aristotle, Descartes, and Leibnitz, should agree in denying the

existence of this capacity which is called space, considered as a being

distinct from bodies, and with the possibility of existing by itself.

The difference of their opinions only proves that at the bottom of

the question there is a difficulty more serious than some ideologists

believe, who explain the idea of space and its generation with the same

ease as though they were treating of the simplest matters.

CHAPTER IX.

OPINION OF THOSE WHO ATTRIBUTE TO SPACE A NATURE DISTINCT FROM BODIES.

62. The preceding considerations seem to me to establish beyond any

question, that space and nothing are contradictory terms. If space is

a capacity with dimensions that can be really measured, it has real

properties, and therefore is distinct from a pure nothing. We have the

idea of space, on it is based a certain and evident science, that of

geometry; this idea is also necessary for the conception of motion. A

pure nothing cannot be the object which corresponds to this idea.

Is space something distinct from the extension of bodies? It is

objected to the opinion which maintains this, that space must be either

body or spirit, and if not body it must be spirit, which is absurd,

since that which is essentially composed of parts, as space is, cannot

be a spirit, which is a simple being.

There are strong arguments against the opinion which attributes to

space a nature distinct from bodies, but I do not attach much weight to

the above objection; for it is only necessary to deny the disjunctive

proposition and the whole argument falls to the ground. How can it be

proved that there is no medium between body and spirit? We know the

essence of neither body nor spirit, and shall we arrogate to ourselves

the right to assert that there is nothing in the universe which is not

comprised under one of two extremes, the nature of which we know not.

63. It may be replied, that there is no medium between the simple and

the composite, any more than between yes and no; and therefore there

is no medium between body which is composite, and spirit which is

simple. I concede that there is no medium between the simple and the

composite, and that whatever exists is one or the other; but I deny

that whatever is composite is body, and whatever is simple is spirit.

These two propositions: every composite is a body, and: every body is

composite, are not identical. There may, therefore, be composites that

are not bodies. Composition, or the possession of parts, is a property

of bodies, but does not constitute their essence, or, at least, we do

not know that it does. If it were so, we should be obliged to embrace

the opinion of Descartes, that extension constitutes the essence of

bodies. How do we know that there may not be things which have parts,

and yet are not bodies?

64. Even the state of the question makes us suppose space to be a

substance, that is, a being subsisting by itself without requiring

another being in which to exist. The difficulty once overcome on this

supposition, it is solved in its most essential and inaccessible point,

and therefore in all others. If we suppose space to be distinct from

bodies, and at the same time a true reality, we must consider it as a

substance, as it exists in itself without any other being in which it

inheres.

65. I said that a simple being is not necessarily a spirit. To explain

this, I need only observe, that to say every spirit is simple, is not

the same as to say every simple being is a spirit. Simplicity is a

necessary attribute of a spirit, but does not constitute its essence.

The idea of simplicity expresses only the negation of parts, and the

essence of spirit cannot consist in a negation.

66. The argument of those who object to this opinion which attributes

to space a nature distinct from bodies, making it an extended

substance, that it must also be infinite, is equally inconclusive.

For even on this hypothesis, there is no reason why a limit may not be

assigned to space. What is there beyond this limit? Nothing. We may, it

is true, conceive a vague extension, but imagination is not reality. We

also imagine an epoch prior to the Creation; if, then, imagination were

an argument in favor of the infinity of the world, it would also be an

argument for its eternity.

The arguments with which I have fought against the opinion that space

is a pure nothing, are not founded on our imaginations, but on the

impossibility of nothing being extended, or having any properties. This

is the principal argument which I have used against those who, while

they hold space to be a pure nothing, maintain the possibility of the

conception or existence of the properties which they attribute to space.

CHAPTER X.

OPINION OF THOSE WHO HOLD SPACE TO BE THE IMMENSITY OF GOD.

67. Overwhelmed by these difficulties, and unable to reconcile the

reality which space offers us with nothing, or to conceive in any thing

created the immobility, infinity, and perpetuity which we imagine in

space, some philosophers have put forth the opinion that space is the

immensity of God. At first sight this seems an extravagant absurdity,

but if we wish fairly to prove the falsity of this opinion, we must

do justice not only to the right intention of those who have defended

it, and the sound explanations which they brought to their assistance,

but also to the reasons which forced them to this extremity, and

which, though certainly not weighty or solid, are far from being so

contemptible as one may imagine.

68. The argument in favor of this opinion may be put in the following

form. Space is something. Before God created the world space existed.

It is not possible to conceive bodies as existing without space in

which they are extended. Before they exist, we conceive this capacity

in which they may be placed, as already existing. Therefore, space is

eternal. There is no motion without space; and in the first instant of

the creation bodies could move and be moved. Though we suppose only

one body in the world, it could be moved; and this motion could be

infinitely continued. Therefore space is infinite. Annihilate now this

body also, and the extension in which it moved will remain; in it new

bodies, new worlds may be created. Therefore space is indestructible.

But an eternal, infinite, and indestructible being cannot be created.

Therefore, space is uncreated. Therefore it is God himself. But it

must be God inasmuch as we conceive him in relation to extension; and,

therefore, space is the immensity of God. Immensity is the attribute

by which God is in every part; it is an attribute which relates to

extension. Space is, therefore, the immensity of God. Only by adopting

this theory can we reasonably admit that space is eternal, infinite,

and indestructible.

69. The objection to this opinion is that it destroys the simplicity of

God. If space is a property of God, it is God; for, whatever is in God,

is God. Therefore, as space is essentially extended, God too must be

extended.

Clarke saw the force of this argument; he was made to feel it by the

arguments of his adversary, Leibnitz; but he answers it very weakly.

He says that space has parts, but they are not separable. But, however

this may be, it is certain that space has parts. True, in the idea

of space we distinguish parts without separating them; but we really

conceive them in it, and we cannot conceive space without them.

Besides, if we should admit this theory, what would become of the

proofs of the immateriality of the soul? If the infinite wisdom is

extended, why may not the human soul with much more reason be so?

Carried away by his favorite idea, Clarke went so far as to write

what we should not have expected from such a man, that: "In questions

of this nature, when we speak of parts, we mean parts that are

_separable_, composite, and disunited like those of matter, which for

this reason is always a compound and never a simple substance. Matter

is not one substance, but a composition of substances. This is why, _in

my opinion, matter is incapable of thinking_. This incapacity does not

proceed from extension, but from the parts being distinct substances,

disunited, and independent of each other."[45] This explanation tends

to destroy the simplicity of thinking beings; for by simplicity has

always been understood the absolute wanting of all parts and not the

absence of this or that kind of parts. Inseparability does not destroy

the existence of parts; it merely asserts the force of cohesion.

[45] Fragment of a Letter.--(I do not know what letter the author here

refers to, but the same opinion in almost the same words may be found

in Clarke's fourth and fifth letters to Leibnitz, _Tr._)

70. It is also to be feared that this doctrine opens the door to

pantheism. It was even objected to Clarke that it made God the soul of

the world, and although he defended himself from this charge, there

still remains an objection which was not proposed to him, and which

is a very serious one. If we say that God is space, or that space is

a property of God, what hinders our saying that God is the world, or

that the world is a property of God? The world is extended; but so is

space. If God and space are not contradictory ideas in the same being,

why are God and the universe contradictory? Clarke says that bodies are

composed of different substances, that they are not one substance; but

it is certain that all we know of bodies is that they are extended, and

that they cause certain impressions in us. Since, then, extension is

not repugnant to God, and much less so the causality of impressions,

there can be no reason against saying that what Clarke calls distinct

substances, are only the parts, or, if he prefers it, the properties

of the infinite substance. Newton went so far as to say that space

was the sensorium of God, and even Clarke maintained against Leibnitz

that Newton's expression might bear a sound interpretation, as it was

intended only as a comparison. But Leibnitz insists so strongly on this

charge that it is plain that he had very great objections to this word.

71. Whatever tends to confound God with nature, or to place him

in constant communication with it, otherwise than by pure acts of

intellect and will, places us on a very slippery declivity, where we

can hardly help being precipitated to the bottom, and at this bottom is

pantheism, which is but a phasis of atheism.(30)

CHAPTER XI.

FENELON'S OPINION.

72. Clarke's opinion is very similar to that of Fenelon, who in his

_Treatise on the existence and attributes of God_, explains immensity

in a very surprising manner. He says: "After considering the eternity

and immutability of God, which are the same thing, I ought to examine

his immensity. Since he is by himself, he is sovereignly, and since he

is sovereignly, he has all being in himself. Since he has all being

in himself, he has without doubt extension; extension is a manner of

being, of which I have an idea. I have already seen that my ideas upon

the essence of things, are real degrees of being, which actually exist

in God, and are possible out of him, because he can produce them.

Therefore, extension is in him; he can produce it outside of himself,

only because it is contained in the fulness of his being."

To a certain extent the words of Fenelon may be explained in a sense

which most theologians would not reject. They distinguish two classes

of perfections; those which involve no imperfection; such as wisdom,

holiness, and justice; and those which involve imperfection, as,

for example, all which belong to bodies, extension, form, etc. The

former, which are also called perfections _simpliciter_, are in God

_formaliter_; that is to say, just as they are, because their nature

involves no kind of imperfection, and, therefore, in God, they do not

diminish nor tarnish his infinite perfection. Those of the second

class, which are called perfections _secundum quid_, are in God not

_formaliter_; for the imperfection which they involve is repugnant to

his infinite perfection, but _virtualiter_ or _eminenter_; that is to

say, that all the perfection, all the being which they contain is in

God, who is infinite perfection, infinite being; and God can produce

them exteriorly by his creative omnipotence. But inasmuch as they

pre-exist in an infinite being, they are freed from all limitation and

imperfection, and identified with the infinite essence, and have a mode

of being far superior to what they are in reality. This is expressed by

the term _eminenter_.

Among these perfections _secundum quid_, extension has always been

numbered.

73. If the illustrious Archbishop of Cambrai had held to this sense, we

should have nothing to say in relation to his doctrine, but the words

which follow seem to show that he inclined to the opinion of those who

maintain that space is the immensity of God.

"Whence, then," he adds, "is it that I do not call him extended and

corporeal? It is because there is an extreme difference, as I have

already remarked, between attributing to God all that is positive in

extension, and attributing to him extension with a limit or negation.

_He that places extension without limits changes extension into

immensity_; he who places extension with limits, makes a corporeal

nature." From these words it might be believed that Fenelon did not

distinguish the two modes of being of extension as theologians do; but

he gives to God all that is positive in extension, though he gives

it to him without limit. From this it would seem to follow that God

is really extended, although his extension is infinite. With all the

respect due to the illustrious shade of one of the greatest ornaments

of the Catholic Church, and one of the greatest men of modern times, I

must say that such an opinion does not seem to me to be sustainable. A

God really extended though with an infinite extension is not God. That

which is extended is essentially composite; God is essentially simple.

Therefore, God and extension are contradictory.

74. But let us hear the illustrious prelate continue the explanation

and defence of his opinion. He says: "From the moment that you place

no limit to extension, you take from it figure, divisibility, motion,

and impenetrability;--figure, because this is only a mode of limiting

by surfaces;--divisibility, because, as we have seen, that which

is infinite cannot be diminished, therefore, it cannot be divided,

and consequently, it is not _composite_ and divisible;--motion,

because, if you suppose a whole, which has no parts nor limits,

it cannot move beyond its place, because there can be no place

beyond the true infinite; neither can it change the arrangement and

situation of _its parts_, because it has _no parts_ of which it is

composed;--impenetrability, in fine, because impenetrability can only

be conceived by conceiving two limited bodies, one of which is not the

other, and cannot occupy the same space as the other. There are no two

such bodies in infinite and indivisible extension; therefore there is

no impenetrability in this extension. These principles established,

it follows that all that is positive in extension is in God, although

God has no figure, is not movable, divisible, or impenetrable, and

consequently is not palpable, nor measurable."

From this passage it is very evident that Fenelon was far from

imagining a composite God, a God with parts. He expressly denies it

more than once in these few lines. Not less was to be looked for from

his deep penetration and the purity of his doctrines; but, although

this saves the rectitude of his intention, it does not satisfy

philosophical exactness. For my part, I honestly confess that if

extension is to be taken in its true sense, I cannot conceive how

taking away its limits destroys its parts. On the contrary, I should

rather say that an infinite extension would have infinite parts. If it

is infinite it will have no figure; because figure involves a limit;

but if it be true extension, it is a sort of immense field on which all

imaginable figures may be traced. It will have no essential figure of

its own, but it will be the recipient of all figures, the inexhaustible

sea from which they all arise. That which is traced in it, will be in

it; the points which terminate the figures must be in it. Is not this

to have parts, composition? Infinite extension could have no figure,

not because it has no parts, or is simple, but because it has infinite

parts, because its composition is infinite.

I agree that an infinite extension would not be divisible, if by

dividing, is meant separating; because in that immense fulness

everything would be in its position with infinite firmness. So also

we imagine space, the place of all motion, with its parts immovable,

the field of all separation, with its parts inseparable; but we are

treating of division, not of separation. If there is true extension, it

is divisible; we conceive space with its parts inseparable, but still

divisible; for we measure them, count them, and it is by relation to

them that we form an idea of the size, distance, and motion of bodies.

74. Such clear and conclusive reflections could not fail to present

themselves to the mind of the illustrious philosopher; but he seems

to have preferred inconsequence or obscurity of language to the fatal

corollaries of his first proposition. He said plainly and without any

restriction, that all that is positive in extension, except the limit,

is in God. He had asserted that extension with limits is corporeal, and

that to change extension into immensity it was only necessary to take

away its limits. He consequently attributed to God a true, although

infinite, extension, and then wishing to explain and strengthen

his doctrine he tells us that this extension has no parts. What is

extension without parts? Who can conceive it? Does not extension

necessarily imply an order of things of which some are outside of

others. It has been always so understood. To speak of an extension

without parts is to speak of an extension improperly so called. When

speaking of such extension it is not enough to say it has no limits,

it should be added that it is of an entirely different nature, that

the word extension is used in another sense. Fenelon seemed to know

this, when, notwithstanding the obscurity of his former expressions,

elevated on the wings of his religion and his genius, he says: "God is

in no place, as in no time; for his absolute and infinite being _has

no relation to place or time_, which are but limits and restrictions

of being. To ask if he is beyond the universe, if he exceeds its

extremities in length, breadth, and depth, is as absurd a question as

to ask if he was before the world, and if he will still be when the

world is no more. As there is neither past nor future in God, so there

is neither hither nor thither. As his absolute permanence excludes all

measure of succession, so also his immensity excludes all measure of

extension. He has not been, he will not be, but _he is_. In the same

manner, to speak properly, he is not here, he is not there, he is not

beyond such a limit, but he is, absolutely. All expressions which

place him in relation to any term, or fix him in a certain place, are

improper and unbecoming. Where then is he? He is. He is in such a

manner that we must not ask where. That which only half is, or with

limits, is a certain thing in such a way that it is nothing else. But

God is not any particular and restricted thing. He is all; he is being;

or better and more simply, _he is_. For the fewer words we use, the

more we say. _He is._ Beware of adding any thing to this."

76. While reading these magnificent words, I am carried away by the

elevation and grandeur of his ideas of God and of his immensity, and

I forget the objections to the first proposition, which, if not false

or inexact, is not, to say the least, expressed with all the clearness

that could be desired. Still, I do not hesitate to maintain that his

opinion coincides with Clarke's; although the illustrious writer,

Christian, and poet, seem to merit a pardon for the philosopher.

CHAPTER XII.

WHAT SPACE CONSISTS IN.

77. Descartes' opinion wholly confounds space and bodies, making the

essence of bodies consist in extension, and asserting that wherever

there is space, there is body. This opinion we have seen to be void of

all reasonable foundation. Perhaps he would come nearer the truth who

should say, that in reality space is nothing more than the extension

of bodies, without reference to the question whether extension does or

does not constitute the essence of bodies, and denying its infinity.

78. Let us examine this last opinion. Analyzing the origin of the idea

of space, we find that it is merely the idea of extension taken in

the abstract. If I hold before my eyes an orange, I may, by means of

abstractions, arrive at the idea of a pure extension, equal to that

of the orange. In order to do this, I begin by abstracting its color,

taste, smell, and all its qualities which affect the senses. I then

have left only an extended being, and if I take from it its mobility,

it is reduced to a part of space equal to the size of the orange.

It is plain that the same abstraction is possible in relation to the

universe, and the result will be the idea of all the space which the

universe occupies.

79. Here I shall answer an objection which might be made to this

explanation of the idea of space, and thereby take advantage of

this opportunity to throw some light upon the origin of the idea of

infinite, or imaginary space.

The difficulty is this. If we form the idea of space by the mere

abstraction of the qualities which accompany extension, we can only

conceive a space equal to the size of the body from which we have

abstracted all its sensible qualities. The abstraction made upon an

orange can only give a space equal to the size of the orange, and that

made upon the universe can only give a space equal to what we conceive

in the universe. Consequently, we can never, by this means, obtain the

idea of a space without limits which always presents itself to our mind

when we think of space considered in itself.

The solution of this difficulty is in the truth that abstraction

rises from the particular to the general. From the idea of gold, by

abstracting those properties which constitute gold, and attending

only to those which it possesses as metal, I arrive at the much more

general idea of _metal_, which belongs not only to gold, but to all

other metals. By this abstraction I pass the limit which separates

gold from other metals, and form an idea which extends to all, neither

specifying, nor excluding any. If from the idea of metal I abstract all

that constitutes metal, and attend only to what constitutes _mineral_,

I pass another limit, and arrive at a still more general idea. Thus

passing successively the idea of inorganic, of body, and of substance,

until I come to the idea of being, I thus form the most general idea

possible, and which includes every thing.[46]

[46] I take no notice in this place of the different manner in which

the idea of being is applicable to God and to creatures.

Thus passing over the limits which distinguish and, as it were,

separate objects, abstraction rises to the most general. If we apply

this doctrine to the abstractions made upon bodies, we shall discover

the reason of the illimitability of the idea of space.

When after the abstractions made upon the orange, I have left only the

idea of _its_ extension, the abstraction has not reached the highest

point possible; for my conception is not that of extension in itself,

but only of the extension of the orange; I conceive _its_ extension,

not _extension_ itself. But if I abstract all that makes this extension

the extension of the orange, and attend only to extension in itself,

then the idea of figure disappears, the extension expands indefinitely,

it is impossible for me to assign any term to it, for any limit would

make it a determinate, a particular extension, not extension in itself.

Then the frontiers of the universe, so to speak, disappear; for

however great the universe may be, it is limited, and can give only a

particular extension, not extension itself. This is the manner in which

the idea of imaginary space seems to be formed.

80. An observation of the phenomena of the imagination will confirm

what we have explained by the mere order of intelligence. When I

_imagine_ the extension of an orange, I imagine it with a limit, with

this or that color, and with these or those qualities; since it is

not possible for me to imagine a figure without lines which terminate

it. This limit in the imagination is distinct both from the extension

which it encloses, and from the extension which it excludes. If it

were not so distinguished, we could not imagine it as limit, and it

would not answer its object, which is to enable us to distinguish that

which it encloses. Therefore, the abstraction is not complete. In the

imagination there is always something determinate, which is the limit

or the lines which constitute the limit. Destroy these limits, and the

imagination expands, until it becomes lost in a sort of dark, unbounded

abyss, such as we imagine beyond the universe.

A very simple example will make this explanation clearer. Our

imagination may be compared to a black board on which a figure is

marked with chalk. When we see the white line on the board which forms

the figure, we see the figure also; but if we rub out the line, there

remains only the uniform figure of the board. If we suppose the lines

which terminate the black board to be indefinitely withdrawn, we shall

look in vain for a figure; we see only a black surface indefinitely

extended. There is a sufficient parity between this and the manner in

which the imagination pictures to itself an endless space.

81. The idea of an abstract extension which is limited, is a

contradiction. Limit takes from extension generality; and generality

destroys the limit. There can, therefore, be no abstract idea of

limited extension; but when we form an idea of extension in the

abstract, we conceive it as unlimited, and the imagination attempting

to follow the understanding, pictures to itself an indefinite space.

82. Summing up this doctrine, and deducing its inevitable consequences,

we may say:

I. That space is nothing else than the extension of bodies.

II. That the idea of space is the idea of extension.

III. That the different parts conceived in space are the ideas of

particular extensions, from which we have not taken their limits.

IV. That the idea of infinite space is the idea of extension in

general, abstracted from all limit.

V. That indefinite space arises necessarily from the imagination,

which destroys the limit in attempting to follow the generalizing march

of the understanding.

VI. That where there is no body there is no space.

VII. That what is called distance is only the interposition of a body.

VIII. That if every intermediate body be taken away, distance ceases;

there is then contiguity, and, consequently, absolute contact.

IX. That if there were only two bodies in existence, it would be

metaphysically impossible for them to be distant from each other.

X. That all vacuum, of whatever kind, or however obtained, is

absolutely impossible.

83. These are the consequences which follow from the principle

explained in this chapter.

If the reader ask me what I think of them and of the principle on which

they are based, I frankly confess that, although the principle seems

true and the conclusions legitimate, still the strangeness of some of

them, and yet more so with regard to others which I shall point out as

we come to them, makes me suspect that there is some error concealed in

the principle, or else the reasoning which deduces these consequences

contains some defect which is not easy to discover. I do not put

forth a settled opinion, so much as a series of conjectures, with the

arguments in their favor. The reader may see by this what sense I

attach to the word _demonstration_, when in the sequel he sees it often

employed in treating of the deduction of certain consequences which

are exceedingly strange, although, in my opinion, deserving a careful

attention. I say this not only to explain what is passing in my own

mind, but also to warn the reader against too great confidence on these

points, whatever may be the opinion which he adopts. Before commencing

these investigations on space, I remarked that the arguments on both

sides seemed equally conclusive; which shows that the human reason

has reached its bounds, and makes us suspect that this investigation

is beyond the sphere to which the mind is restricted by a primary

condition of its nature.

However this may be, let us continue to conjecture; and although we

cannot pass beyond certain limits, let us exercise the understanding

by examining them in their full extent. Thus, if we were placed on

a very elevated ground with deep precipices on all sides, we should

take pleasure in walking around the circumference, and gazing upon the

immense depth under our feet.

I shall now proceed to deduce other results, and to solve as far as

possible the difficulties which arise, making some applications, the

immense importance of which produces uncertainty and causes fear.

CHAPTER XIII.

NEW DIFFICULTIES.

84. If space is the extension of bodies, it follows that extension has

no recipient, that is to say, no place in which it can be situated.

This seems to be in direct contradiction to our most common ideas; for

when we conceive any thing to be extended, we conceive the necessity of

a place equal to it in which it can be contained and situated.

This difficulty, which seems so serious at first, immediately vanishes

if we deny that every extended thing needs a place in which it may be

situated. What is this place? It is an extension in which the thing

may be contained. Does this extension also require another extension

in which it may be placed, or does it not? If it does, then the same

question may be asked of this new place in which the other place is

contained, and so on _ad infinitum_. This is evidently impossible, and

therefore we must admit that it is false that all extension requires

another extension in which it may be placed. Just as the extension of

space does not require another extension, so the extension of bodies

does not require space. There is no disparity between the two cases.

Therefore the necessity of a place for every extension is merely

imaginary, and is opposed to reason. Extension, therefore, may exist in

itself, and there is no reason why the extension of bodies may not also

exist in this manner.

85. What in this case would be the meaning of changing place? It would

simply mean that bodies change their respective position. This is the

explanation of motion.

Suppose three bodies, A, B, and C, to be situated in space. Their

respective distances are the bodies which are interposed between them.

The change which a new position causes, is motion.

86. Therefore, if there were only one body there could be no motion.

For motion is necessarily the passing over a distance, and, there is no

distance when there is only one body.

This seems at first absurd, because it is opposed to our way of

thinking and imagining; but if we carefully examine this way of

thinking and imagining, we shall see that the phenomena of our mind are

in accordance with this theory.

Motion has no meaning for us, we do not feel or perceive it, when we

cannot refer it to the position of different bodies among themselves.

If we sail down a river, shut up in the cabin of the vessel which bears

us on, we really move, though we have no perception of this motion.

We know that we move when watching the objects on the shore, we see

that they are continually changing. Even then, the motion seems to be

in the objects around us, not in ourselves, and the phenomena would

be absolutely the same with respect to us, if, instead of the objects

being at rest, and the vessel in motion, the vessel should be at rest

and the objects in motion, supposing the motion of the objects to be

properly combined.[47]

[47] See Book II., Chap. xv.

Therefore, take away the agitation, which is all that informs us of

our own motion, and we are unable to distinguish whether the motion is

in us or in the objects; and we are naturally more inclined to refer

the motion to them than to ourselves. When the vessel that carries us

leaves the port, we know very well that it is not the port which moves,

and yet the illusion is complete, the port seems to retire from us.

Hence motion for us is only the change of the respective position of

bodies. If we had not experienced this change, we should have no idea

of motion. Thus no one denies that the phenomena of diurnal motion are

the same, whether the heavens revolve around us from east to west, or

the earth turns on its axis from west to east.

Therefore, the motion of only one body is a pure illusion; and there is

no proof of the argument founded on it which is brought to oppose our

doctrine of space.

Hence, also, the whole universe considered as only one body, is

immovable, motion takes place only in its interior.

87. But one of the strangest results of this theory is the _a

priori_ demonstration that the universe can only be terminated in a

certain manner, to the exclusion of a multitude of figures which are

essentially repugnant to it.

According to the doctrine which we have put forth, if we suppose only

one body to exist, it cannot have any part of its surface so disposed

that the shortest line from any one point to another shall pass outside

of the body. For, as we suppose only one body, _outside_ of it is pure

nothing; and can, therefore, contain no distances which can be measured

by lines. This excludes a multitude of irregular figures, and thus we

find geometrical regularity growing out of a metaphysical idea.

Hence if only one body were in existence, it would be impossible for

it to have any angles entering into it. For, its figure requires that

the point A, the vertex of the angle, should be at the distance A D

from the point D, the vertex of another angle. This distance cannot

exist, for there is no distance where there is no body. Therefore,

the distance would exist and not exist at the same time, which is

contradictory. It would also be an absurdity, because the capacities

marked by the angles would not be filled.

The observation of nature confirms the former result, inasmuch as its

tendency is always to terminate every thing with curved lines and

surfaces. The orbits of the stars are curves, and the stars themselves

terminate in curve surfaces. The great irregularities which are

observed in their surfaces might seem to destroy this conclusion,

but it must be remembered the limit of the figure is not in these

irregularities, but in the atmosphere which surrounds them, and which,

being a fluid, can have no irregularities of surface.

88. Another consequence, as strange as the former, is, that we are

obliged to admit the existence of a perfect geometrical surface, and

this _a priori_.

If, where there is no body, distance is metaphysically impossible,

this must be just as true in small as in great things, and even in

infinitesimals. This is also a reason of the impossibility of vacuum.

It is evident that a surface is not perfect when some of its points go

farther out than others, so that the less they go out from the surface

the more perfect it becomes. As there are no such points in the last

surface of the universe, this surface is the realization of geometrical

perfection.

We have demonstrated that it is impossible for the surface to have any

angles entering into it; it is equally impossible for it to have any,

even the least, prominence. The difference is only in greater or less,

which does not affect the metaphysical impossibility. It is, therefore,

demonstrated that in the ultimate surface of the universe there is no

irregularity, but that its surface is geometrically perfect.

CHAPTER XIV.

ANOTHER IMPORTANT CONSEQUENCE.

89. I now proceed to deduce the last consequence of the principle

explained above. It is of the greatest importance, and seems to deserve

the careful attention of all those who unite their metaphysical and

physical studies.

The existence of universal gravitation may be demonstrated _a priori_.

Universal gravitation is a law of nature by which some bodies are

directed to others. [We abstract here the manner.] This direction is

metaphysically necessary, if we suppose that there is no distance

where there is no body. For, if this be so, two bodies cannot exist

separated. The law of contiguity is a metaphysical necessity, and

therefore the incessant approaching of some bodies to others is a

continual obedience to this necessity.

The velocity with which they approach must be in the ratio of the

velocity with which the medium departs. The limit of the velocity of

this motion is the relation of space with an indivisible instant, such

as we might suppose if God should suddenly annihilate the intervening

body.

As the solid masses which revolve above our heads would in this case

be submerged in a fluid, supposing this fluid to be of such nature as

easily to change its place, it follows that the stars must be subject

to the law of approximation, because the medium which separates them is

continually retiring in various directions. If we suppose this fluid to

be immovable, the metaphysical necessity of this approximation ceases.

90. This theory seems to lead to the explanation of the mechanism of

the universe, by simple geometrical laws, and destroys what some have

called occult properties, and others forces.

Although it is easy to explain by metaphysical and geometrical ideas,

the fact of gravitation, or the mere tendency of bodies mutually to

approach, it is still very difficult to determine by this order of

ideas the conditions which govern gravitation.

91. If the motion of approximation depended only on the intervening

body, inequality of these bodies would produce unequal motions. It is

impossible to calculate the degree of this inequality in bodies which

are not subject to our observation.

92. Besides this difficulty there is another still greater, which is,

that bodies which move in a medium have no fixed direction, but vary

their motions with the variations of the medium.

If the gravitation of the body A towards the body B, depends only on

the motion of the retiring medium, the gravitation will not be in the

right line AB, but will follow the undulations described by the medium.

This is contrary to experience.

93. From these considerations, it follows that even though the

gravitation naturally arises from the position of the bodies, still

this necessity would not produce the order which exists, if its results

were not subject to certain laws. And, therefore, the phenomena of

nature, although founded on a necessity, would still, admitting the

existence and position of bodies, be contingent in all that relates to

the application of this necessity.

94. Going still deeper into this matter, we find that the tendency to

approximation, although necessary, is not sufficient either to produce

motion or to preserve it.

Whenever one body moves, it is always necessary that another should

follow it, in order to preserve the contiguity; but, there being no

vacuum, there is no reason why any body should move, and consequently,

no cause of motion.

Therefore, geometrical ideas are not sufficient to explain the origin

of motion, but we must look for its cause elsewhere. Contiguity being

a metaphysical necessity, if the body A moves in any direction, the

contiguous bodies B and C must also move; but if the contiguity already

existed, there is no reason why the body A should begin to move, nor,

consequently, why the bodies B and C should follow its motion.

At any instant whatever, if we suppose motion, we must suppose

contiguity; for the state of the question supposes this condition

always present, as being metaphysically necessary. There is then

no reason why the motion should at any time be prolonged; for the

bodies being at every instant contiguous there is no reason for its

continuation. The motion of the body A draws with it the body B; B

draws C, and so on. Now, if the motion of the body B has no other

origin than its contiguity to A, the motion of C has no other origin

than its contiguity to B. The cause of the motion is only not to

interrupt the contiguity; this contiguity always existing as is

absolutely necessary, there is no reason why the motion should begin,

or after it has begun, why it should continue.

95. The laws of nature cannot then be explained by geometrical and

metaphysical ideas, although we suppose approximation to be an

intrinsical necessity of bodies. Under any supposition it is necessary

to seek out of matter a superior cause which impresses, regulates, and

continues motion.

CHAPTER XV.

ILLUSION OF FIXED POINTS IN SPACE.

96. Since space is only the extension of bodies, and there is no

space where there are no bodies, it follows that the extension which

we conceive distinct from bodies, with fixed points and dimensions,

immovable in itself, and the receptacle of all that is movable, is a

pure illusion, and there is nothing in reality corresponding to it.

In order to explain this doctrine and at the same time to solve certain

objections which may be made, it will not be out of place to analyze

the idea which we form of fixedness in relation to space. Because

there are certain immovable points in the world in relation to which

we conceive directions, we form the idea that these points are fixed,

and in relation to them and because of them we imagine fixedness,

immobility, as one of the properties which distinguish this ideal

receptacle which we call space. The four cardinal points, East, West,

North, and South, have had a great influence in producing this idea.

Still it is easy to show that there is no such thing and that it is a

pure illusion.

97. We shall first destroy the fixedness of East and West. Supposing

the earth to have a diurnal motion of rotation on its axis, as

astronomers now hold, the points of East and West, so far from being

fixed, are continually changing their position. Thus, supposing an

observer at the point A of the earth, East to him will be the point B,

and West the point C. If the earth revolves on its axis, the East and

West of the observer will be successively at the points M, N, P, Q,

etc. of the heavenly arch. Although we suppose this arch fixed, East

and West have no fixed meaning.

If we deny the rotation of the earth, the appearances will be the same

as though this rotation existed; and the most that we can say is that

this fixedness is an appearance. Besides, if we suppose the earth to be

at rest, and the heavens to move round it, it is still more impossible

to determine the fixed points of East and West; for, in this case, the

points in the heavens to which we refer them are in continual motion.

We repeat that all this is a mere appearance. If a man who knows not

that the earth is spherical, but imagines it to be a plane surface,

walks from West to East, he will believe that these two points are

immovable, although they are continually changing. He would still

imagine that he was going farther from the place where he started,

although, after passing over the whole circumference of the earth, he

would find himself where he was at first.

98. North and South seem to present greater difficulty, by reason of

their fixedness in relation to us; still it is easy to show that this

is not absolute, but only apparent. Let N and S represent the north

and south poles. If we imagine the earth and the heavens to turn at

the same time from south to north, it is evident that the fixedness

of the points N and S would not exist, and yet the observer A would

believe that every thing was immovable, because the appearances would

be absolutely the same.

To an observer travelling from the equator toward either pole, the pole

would rise over the horizon, while to another who remains in the same

place, the pole would be at rest.

Even in relation to the same position on the earth the altitude of the

pole changes, by the variation of the angle formed by the plane of the

ecliptic with the plane of the equator, which variation is according

to some calculations 8″ in a century, according to others 0″.521 in a

year, or 52′.1″ in a century.

99. It follows from these reflections that the position of bodies

is not absolute, but relative; that one body might exist alone, but

then it would have no position, as this is entirely a relative idea,

and there is no relation in this case, because there is no point of

comparison; and that absolutely speaking there is no such thing as

_above_ or _below_; for although we imagine these to be fixed points,

this imagination is only a comparison which we make between two points:

below being that point toward which we gravitate, and above the

opposite. Thus in the antipodes above is what we call below, and below

what we call above.

100. Direction is impossible without points to which it can be

referred. Therefore, without the existence of bodies, directions are

purely ideal, and if only one body existed, it could have no directions

out of its own extension.

101. Here arises a difficulty apparently serious, but in reality of

little weight. If only one body existed, could God give it motion? To

deny it seems to limit the omnipotence of God; and to concede it is to

destroy all that has been said against space distinct from bodies.

This objection derives its seeming importance from a confusion of

ideas, which is caused by not understanding the true state of the

question. Is this motion _intrinsically impossible_, or is it not? If

it is impossible, there is no reason why we should be afraid to say

that God cannot produce it: for omnipotence does not extend to things

which are contradictory. If the possibility of this motion is admitted,

then we must return to the questions on the nature of space, and

examine whether the reasons on which this impossibility is founded are,

or are not, valid.

The questions relating to omnipotence are out of place here, and this

difficulty can be solved without them. If the impossibility of the

motion is demonstrated, it is no limitation of the omnipotence of

God to say that he cannot produce it, no more than it is when we say

that he cannot make a triangle a circle. If the impossibility is not

demonstrated, then the question of omnipotence does not come in at all.

102. Neither does the argument founded on the existence of vacuum

destroy the doctrine which we have established. Natural philosophers

generally admit vacuum, and suppose it necessary for the explanation of

motion, condensation, rarefaction, and other phenomena of nature. But

to this I reply as follows:

I. The opinions of Descartes and Leibnitz are of weight in what relates

to nature, whether experimental or transcendental, and neither of them

admitted a vacuum.

II. No observation can prove its existence, because disseminated vacuum

would occupy such small spaces that no instrument could reach them, and

also because observation can only be made on those objects which affect

our senses, and we know not but what there may be bodies which, on

account of their excessive tenuity, are not perceptible by the senses.

III. We can determine nothing certain concerning the internal

modifications of matter in motion, condensation, and rarefaction, until

we know the elements of which it is composed.

IV. It is not strange that we are unable to comprehend the phenomena

which seem incompatible with the denial of matter: for we can neither

understand infinite divisibility, nor how extension can be composed of

unextended points.

V. The existence of vacuum is a metaphysical question which does not

belong to the regions of experience, and is not affected by the system

of the sciences of observation.

103. By making the idea of space consist in abstract or generalized

extension we reconcile all that is necessary, absolute, and infinite

in it with its objective reality. This reality is the extension of

bodies, while necessity and infinity are not found in the bodies

themselves, but in the abstract idea. Objects themselves are confined

to the sphere of reality, and are, therefore, limited and contingent.

The objectiveness of the abstract idea includes both the existent and

the possible, and has, therefore, no limits, and is not subject to any

contingency.

CHAPTER XVI.

OBSERVATIONS ON KANT'S OPINION.

104. We have already shown that extension considered in us, is

something more than a mere sensation, that it is a true idea, the basis

of some sensations, and at the same time a pure idea. As far as it

relates to sensations, it is the foundation of our sensitive faculties;

and in so far as it is an idea, it is the root of geometry. This is an

important distinction, and we shall find it useful to enable us rightly

to appreciate the value of Kant's opinion of space.

105. All our sensations are, either more or less, connected with

extension; although if we consider sensation _a priori_ by itself,

and independently of all habit, it would seem as though only the

sensations of sight and touch were necessarily connected with an

extended object. It does not seem to me that the loss of these two

senses would necessarily involve the privation of the impressions of

hearing or smelling, or, perhaps, even of taste; for although it is

true that the sensations of touch, such as hardness or softness, etc.,

are always united with the sensations of the palate; it is equally

certain that those sensations are wholly distinct from the sensation

of taste, and we have no reason for asserting that they cannot be

separated from it.

106. Extension, considered in us or in its intuition, may be regarded

as a necessary condition of our sensitive faculties. Kant saw this,

but he exaggerated it when he denied the objective reality of space,

asserting that space is only a subjective condition _a priori_ without

which we cannot receive impressions, the form of phenomena, that is, of

appearances, but nothing in reality. I have already said that space,

as distinguished from bodies, is nothing, but the object of the idea

of space is the extension of bodies; or, rather, this extension is

the foundation from which we deduce the general idea of space, and is

contained in this idea.

107. To say, as Kant does, that space is the form under which the

phenomena are presented to us, and that it is a necessary subjective

condition of their perception, is equivalent to saying that the

phenomena which are presented as extended, require that the mind should

be capable of perceiving extension. This is very true, but it throws

no light on the nature of the idea of space, either in itself or in

its object. "Space," says Kant, "is no empirical conception which is

derived from external experience. For in order that certain sensations

may be referred to something out of me, that is, to something in

another part of space than that in which I am, and in order that I may

conceive them as outside of and near one another, and, consequently,

not only as separated, but also as occupying separate places, the

conception of space must be placed as the foundation. Therefore, the

conception of space cannot be obtained by experience from the relations

of the external phenomenon, but this external experience itself is

possible only by this conception."[48]

[48] Kant, _Transc. Æstœœh._ I. Absch. § 2, 1.

There is a great confusion of ideas here. What are the conditions which

are necessary to the phenomenon of the sensation of the extended? We

are not here treating of the appreciation of dimensions, but merely of

extension as represented or conceived. I do not see how this phenomenon

requires any thing _a priori_, except the sensitive faculty which,

in fact, exists _a priori_, that is to say, is a primitive fact of

our soul in its relations to the organization of the body which is

united to it, and of the other bodies which surround it. Under certain

conditions of our organization, and of the bodies which affect it, the

soul receives the impressions of sight or touch, and with them the

impression of extension. This extension is not presented to the mind in

the abstract, or as separated from the other sensation which accompany

it, but as united with them. The mind does not reflect, then, upon the

position of the objects, but it has an intuition of the arrangement

of the parts. So long as the fact is confined to mere sensation, it

is common to the learned and the unlearned, to the old and the young,

and even to all animals. This requires nothing _a priori_ except

the sensitive faculty, which simply means that a being, in order to

perceive, must have the faculty of perceiving, and should hardly

deserve to be announced as a discovery of philosophy.

109. There is no such discovery in Kant's doctrine of space, for on the

one side he asserts a well known fact, that the intuition of space is

a necessary subjective condition, without which it is impossible for us

to perceive things, one _outside_ of another; and on the other side he

falls into idealism, inasmuch as he denies this extension all reality,

and regards things and their position in space as pure _phenomena_,

or mere appearances. The fact which he asserts is true at bottom;

for it is, in fact, impossible to perceive things as distinct among

themselves, and as outside of us, without the intuition of space; but,

at the same time, it is not accurately expressed, for the intuition

of space is this perception itself; and, consequently, he ought to

have said that they are identical, not that one is an indispensable

condition of the other.

110. Prior to the impressions, there is no such intuition, and if

we regard it as a pure intuition and separated from intellectual

conception, we can only conceive it as accompanied by some

representation of one of the five senses. Let us imagine a pure space

without any of these representations, without even that mysterious

vagueness which we imagine in the most distant regions of the universe.

The imagination finds no object; the intuition ceases; there remains

only the purely intellectual conceptions which we form of extension,

the ideas of an order of possible beings, and the assertion or denial

of this order, according to our opinion of the reality or non-reality

of space.

111. It is evident that a series of pure sensations cannot produce a

general idea. Science requires some other foundation. The phenomena

leave traces of the sensible object in the memory, and are so connected

with each other, that the representation of one cannot be repeated

without exciting the representation of the other, but they produce no

general result which could serve as the basis of geometry. A dog sees

a man stoop, and make a certain motion, and is immediately struck with

a stone, which causes in him a sensation of pain; when the dog sees

another man perform the motion, he runs away; because the sensations of

the motions are connected in his memory with the sensation of pain, and

his natural instinct of avoiding pain inspires him to fly.

112. When these sensations are produced in an intelligent being, they

excite other internal phenomena, distinct from the mere sensitive

intuition. Whether general ideas already exist in our mind, or are

formed by the aid of sensation, it is certain that they are developed

in the presence of sensation. Thus, in the present case we not only

have the sensitive intuition of extension, but we also perceive

something which is common to all extended objects. Extension ceases

to be a particular object, and becomes a general form applicable

to all extended things. There is then a perception of extension in

itself, although there is no intuition of the extended; we then begin

to reflect upon the idea and analyze it, and deduce from it those

principles, which are the fruitful germs from the infinite development

of which is produced the tree of science called geometry.

113. This transition from the sensation to the idea, from the

contingent to the necessary, from the particular fact to the general

science, presents important considerations on the origin and nature of

ideas, and the high character of the human mind.

Kant seems to have confounded the imagination of space with the idea

of space, and notwithstanding his attempts at analysis, he is not so

profound as he thinks, when he considers space as the receptacle of

phenomena. This a very common idea, and all that Kant has done is to

destroy its objectiveness, making space a purely subjective condition.

According to this philosopher, the world is the sum of the appearances

which are presented to our mind; and just as we imagine in the

external world an unlimited receptacle which contains every thing, but

is distinct from what it contains, so he has placed space within us as

a preliminary condition, as a form of the phenomena, as a capacity in

which we may distribute and classify them.

114. In this he confounds, I say, the vague imagination with the idea.

The limit between the two is strongly marked. When we see an object we

have the sensation and intuition of extension. The space perceived or

sensed is, in this case, the extension itself perceived. We imagine a

multitude of extended objects, and a capacity which contains them all.

We imagine this capacity as the immensity of the ethereal regions, a

boundless abyss, a dark region beyond the limits of creation. So far

there is no idea, there is only an imagination arising from the fact

that when we begin to see bodies we do not see the air which surrounds

them, and the transparency of the air permits us to see distant

objects, and thus from our infancy we are accustomed to imagine an

empty capacity in which all bodies are placed, but which is distinct

from them.

But this is not the idea of space; it is only an imagination of it, a

sort of rude, sensible idea, probably common to man and the beasts. The

true idea, and the only one deserving the name, is that which our mind

possesses when it conceives extension in itself, without any mixture of

sensation, and which is, as it were, the seed of the whole science of

geometry.

115. It should be observed that the word representation as applied to

purely intellectual ideas must be taken in a purely metaphorical sense,

unless we eliminate from its meaning all that relates to the sensible

order. We know objects by ideas, but they are not represented to us.

Representation, properly speaking, occurs only in the imagination

which necessarily relates to sensible things. If I demonstrate the

properties of a triangle, it is clear that I must know the triangle,

that I must have an idea of it; but this idea is not the natural

representation which is presented to me like a figure in a painting.

All the world, even irrational animals have this representation, yet we

cannot say that brutes have the idea of a triangle. This representation

has no degrees of perfection, but is equally perfect in all. Any

one who imagines three lines with an area enclosed, possesses the

representation of a triangle with as much perfection as Archimedes; but

the same cannot be said of the idea of a triangle, which is evidently

susceptible of various degrees of perfection.

116. The representation of a triangle is always limited to a certain

size and figure. When we imagine a triangle, it is always with such

or such extension and with greater or smaller angles. The imagination

representing an obtuse angled triangle sees something very different

from an acute or right angled triangle. But the idea of the triangle

in itself is not subject to any particular size or figure; it

extends to all triangular figures of every size. The general idea of

triangle abstracts necessarily all species of triangles, whilst the

representation of a triangle is necessarily the representation of a

triangle of a determinate species. Therefore the representation and the

idea are very different, even in relation to sensible objects.

117. It is the same with space. Its representation is not its idea. The

representation is always presented to us as something determinate, with

a clearness like that of the air illuminated by the sun, or a blackness

like the darkness of night. There is nothing of this sort in the idea,

or when we reason upon extension and distances.

The idea of space is one; its representations are many. The idea is

common to the blind man and to him who sees. For both it is equally the

basis of geometry, but the representation is very different in these

two. The latter represents space as a confused reproduction of the

sensations of sight; the blind man can only represent it as a confused

repetition of the sensations of touch.

The representation of space is only indefinite, and even this

progressively. The imagination runs over one space after another, but

it cannot at once represent a space without limits; it can no more do

this than the sight can take in an endless object. The imagination is

a sort of interior sight, it reaches a certain point, but there it

finds a limit. It can, it is true, pass beyond this limit, and expand

still farther, but only successively, and always with the condition of

encountering a new limit. Space is not represented as infinite, but as

indefinite, that is to say, that after a given limit there is always

more space, but we can never advance so far as to imagine an infinite

totality. It is the contrary with the idea; we conceive instantaneously

what is meant by infinite space, we dispute on its possibility or

impossibility, we distinguish it perfectly from indefinite space, we

ask if it has in reality limits or not, calling it in the first case

finite, in the latter infinite. We see in the word indefinite the

impossibility of finding limits, but at the same time we distinguish

between the existence of these limits, and finding them. All this shows

that the idea is very different from the representation.

To regard space as a mere condition of sensibility is to confound the

two aspects under which extension should be considered, as the basis of

sensations, and as idea; as the field of all sensible representations,

and as the origin of geometry. I have often insisted on this

distinction, and shall never weary of repeating it; because it is the

line which divides the sensible from the purely intellectual order, and

sensations from ideas.

CHAPTER XVII.

INABILITY OF KANT'S DOCTRINE TO SOLVE THE PROBLEM OF THE POSSIBILITY OF

EXPERIENCE.

118. I think that Kant's _Transcendental Æsthetics_, or theory of

sensibility, is not sufficiently transcendental. It is too much

confined to the empirical part, and does not rise to the height which

we should expect from the title. The problem of the possibility of

experience which Kant proposed to solve, either is not at all touched

by his doctrine, or else it is solved in a strictly idealist sense.

It leaves the problem untouched, if we consider only what relates to

observation; for he only repeats what we already knew in establishing

the fact of the _exteriority_ of things; it solves the problem in a

strictly idealist sense, inasmuch as these things are only considered

as phenomena or appearances.

119. A purely subjective space either does not explain the problems

of the external world, or it denies them in denying all reality. What

progress has philosophy made by affirming that space is a purely

subjective condition? Before Kant, did we, perchance, not know that we

had perception of external phenomena? The difficulty was not in the

existence of this perception attested by consciousness; but in its

value to prove the existence of an external world, in relation with it.

The difficulty was in the objective, not the subjective part of the

perception.

120. To say that the perception is nothing more than a condition of

the subject, is to cut the knot instead of untying it. It does not

explain the manner of the possibility of experience, but denies this

possibility.

What is experience if there is only the subject? There will be the

_phenomenon_ or _appearance_ of objectiveness, but nature is then only

a mere appearance, and there is nothing in reality which corresponds

to our experimental perceptions. We then have experience reduced to

the perception of appearances; and as even this purely phenomenal

experience is only possible by virtue of a purely subjective condition,

the intuition of space; all experience remains purely subjective, and

we find ourselves holding the system of Fichte, admitting the _me_ as

the primitive fact, the development of which constitutes the universe.

Thus the system of Fichte follows from Kant's doctrine; the former has

only carried out the principles of his master.

121. In order to make the connection between the two doctrines still

clearer, we shall make some further reflections on Kant's system. If

space is something purely subjective, a condition of the sensibility

and of the possibility of experience, it follows that the mind instead

of receiving any thing from the object, creates whatever is in the

object, or rather, whatever we consider as in it. Things in themselves

are not extended; extension is only a form with which the mind clothes

them. In the same manner, they are not colored, sonorous, tasteful,

or odorous, except inasmuch as we transfer to them that which is

in ourselves alone. Every thing being reduced to mere appearances,

there is in the external world not even the principle of causality of

subjective extension; the mind gives it to objects, does not receive

it from them. These objects are pure phenomena; and, consequently, the

soul only sees what it contains in itself, it knows no other world than

that which is its own creation. Thus, we see the real world spring from

the _me_; or, rather, the real world is only the ideal creation of the

mind. On this supposition, the laws of nature are only the laws of our

own mind, and instead of seeking for the types of our ideas in nature,

we ought to regard our ideas as the generative principle of all that

exists, or seems to exist; and the laws of the universe are merely the

subjective condition of the _me_ applied to phenomena.

122. Some of the disciples of Kant show no fear of his idealist

tendencies; in fact they accept them without any hesitation, as may be

seen by the comparisons which they use in explaining his doctrine. If

a seal be applied to a piece of soft wax, it will leave its impression

on the wax; if we suppose the seal to be capable of perception, it

would see its mark on the wax, and attribute to the object what it had

itself given it. If a vase full of water were capable of perception,

it would attribute to the water the form, which in reality is only the

form of the vase itself, and is communicated from it to the water. In

a similar manner the mind constructs the external world, giving to it

its impression and form, and then believing it has received from the

external world what it has itself communicated to it.

123. Still we must confess that Kant, in the second edition of his

_Critic of Pure Reason_, rejects these conclusions, and expressly

combats idealism. There is no necessity of examining how far the second

edition contradicts the first: it is sufficient for me to inform the

reader that this contradiction exists, and that in the first edition

there are expressions which so plainly lead to idealism, that it is

impossible not to be surprised on finding the same author in the second

edition of his work strongly opposing the idealist system. I have

pointed out the consequences of the doctrine; if the author understood

it in a different sense from that which his words expressed, this is

merely a personal, not a philosophical question.(31)

CHAPTER XVIII.

THE PROBLEM OF SENSIBLE EXPERIENCE.

124. The great problem of philosophy does not consist in the

explanation of the possibility of experience; but in establishing the

reason of the consciousness of experience, as experience. Experience in

itself is a fact of our soul attested by consciousness, but _to know_

that this fact is a fact of experience, is something very different

from mere experience; for, by knowing this, we pass from the subjective

to the objective, referring to the external world what we experience

within us.

We refer objects to different points of space, and regard them as

outside of, and distinct from, each other: to say that the instinct by

which we so regard them is a condition of the subject and of sensible

experience is to establish a sterile fact. The difficulty is in knowing

why we have this instinct; why the representation of an extension is in

our soul; and why this subjective extension in a simple being should

be presented to our perception as the image of something external and

really extended.

125. Transcendental esthetics may determine the following problems:

I. To explain what is the subjective representation of extension,

abstracted from all that is objective.

II. Why this representation is found in our soul.

III. Why a simple being contains in itself the representation of

multiplicity, and an unextended being the representation of extension.

IV. Why and how we pass from ideal to real extension.

V. To determine how far we may apply to extension what is true of the

other sensations, which are considered as phenomena of our soul,

having no external object like them, and no other correspondence with

the external world than the relation of effects to their cause.

126. What is the subjective representation of extension, abstracted

from all that is objective? It is a fact of our soul; no further

explanation is possible; he that has it, knows what it is; he that has

it not, does not, except intelligences of a higher order, which know

what this representation is, without experiencing it as we do.

127. I do not pretend that it is possible to explain why the

representation of extension is found in our soul; we might as well ask

why we are intelligent and sensible beings. The only reason _a priori_

which we can give, is that God has so created us. This representation

may be found in us, and it is so found, for we experience it; but this

internal experience is the limit of philosophy; immediate observation

can go no farther back. Reason raises us to the knowledge of a cause

which created us, but not to a phenomenon which is the source of the

phenomena of experience.

128. Why a simple being contains in itself the representation of

multiplicity, and an unextended being the representation of extension,

is the problem of intelligence, which, because it is intelligence, is

one and simple, and capable of perceiving multiplicity and composition.

129. We pass from ideal to real extension by a natural and irresistible

impulse, which is confirmed by the assent of reason. This has been

demonstrated in the first book, and also in the second when treating of

the objectiveness of sensations.

130. Of the five problems the last remains. We must determine how far

we may apply to extension what is true of the other sensations, which

are considered as phenomena of our soul, having no external object like

them, and no other correspondence with the external world than the

relation of effects to their cause.

131. The solution of this problem settles the question for or against

the idealists. If we may apply to extension what is true of the other

sensations, idealism triumphs, and the real world, if it exists, is a

being which has no resemblance to the world which we think.

I have proved in treating of sensations[49] that extension is something

real, and independent of our sensations, and I have shown[50] that it

represents multiplicity and continuity. This is sufficient to overthrow

idealism, and also to explain, to a certain extent, what extension

consists in; but as the idea of space, which is closely connected

with extension, had not then been examined, it was not possible for

us to rise above the order of phenomena and regard extension under a

transcendental aspect, examining it in itself, abstracted from all its

relations with the world of appearances. This is what I propose to do

in the following chapters.

[49] Bk. II., Chs. VII., VIII., and IX., and Bk. III., Ch. IV.

[50] Bk. II., Ch. VIII., and Bk. III., Ch. VI.

132. We come now to a more cragged path; we have to distinguish the

reality from appearance; our understanding, which is always accompanied

by sensible representations, must now depart from them, and place

itself in opposition to a condition to which it is naturally subjected

in the exercise of its functions.

CHAPTER XIX.

EXTENSION ABSTRACTED FROM PHENOMENA.

133. That which is extended is not one being only; it is a collection

of beings. Extension necessarily contains parts, some outside of, and

consequently distinct from, others. Their union is not identity; for,

the very fact that they are united, supposes them distinct, since any

thing is not united with itself.

It would seem from this that extension in itself and distinguished from

the things extended, is nothing; to imagine extension as a being whose

real nature can be investigated is to resign one's self to be the sport

of one's fancy.

Extension is not identified in particular with any one of the beings

which compose it, but it is the _result_ of their union. This is

equally true whether we consider extension composed of unextended

points, or of points that are extended but infinitely divisible.

If we suppose the points unextended, it is evident that they are

not extension, because extended and unextended are contradictory.

Neither are these points identified with extension, if we suppose

them extended; for extension implies a whole, and a whole cannot be

identified with any of its parts. If a line be four feet long, there

cannot be identity between the whole line and one of its parts a foot

long. We may suppose these parts, instead of a foot, to be only an inch

in length, and we may divide them _ad infinitum_, but we shall never

find any of these parts equal to any of its subdivisions. Therefore,

extension is not identical with any of the particular beings which

compose it.

134. The idea of multiplicity being involved in the idea of extension,

it would seem that extension ought to be considered, not as a being in

itself, but as the result of a union of many beings. This result is

what we call continuity. We have already seen[51] that multiplicity

is not sufficient to constitute extension. It enters into the idea of

number, and yet number does not represent any thing extended. We also

conceive a union of acts, faculties, activities, substances, and beings

of various classes, without conceiving extension, and yet multiplicity

is a part of all these conceptions.

[51] Bk. II. Chap. VIII.

135. Therefore continuity is necessary, in order to complete the idea

of extension. What, then, is continuity? It is the position of parts

outside of, but joined to other parts. But what is the meaning of

the terms, _outside of_, and _joined to_? Inside and outside, joined

and separated, imply extension, they presuppose that which is to be

explained; the thing to be defined enters into the definition in the

same sense in which it is to be defined. Exactly; for, to explain the

continuity of extension is the same as to show the meaning of the terms

inside and outside, joined and separated.

136. We must not forget this observation, unless we wish to accept the

explanations which are found in almost all the books on the subject.

To define extension by the words _inside_ and _outside_, is not to add

any thing, under a philosophic aspect; it is merely to express the

same thing in different words. Without doubt this language would be

the simplest, if all we wanted was to establish the phenomenon only,

but philosophy will not be satisfied with it. It is a practical, not

a speculative, explanation. The same may be said of the definition

of extension by space or places. What is extension?--the occupation

of place:--but, what is a place?--a portion of space terminated by

certain surfaces:--what is space?--the extension in which bodies

are placed, or the capacity to receive them. But even admitting the

existence of space as something absolute, what is the capacity of

bodies to fill space? Who does not see that this is to define a thing

by itself, a vicious circle? The extension of space is explained by the

capacity of _receiving_; the extension of bodies by the capacity of

_filling_. The idea of extension remains untouched; it is not defined,

it is merely expressed in different words, but which mean the same

thing.