sense, the absence of all distraction, and continual attention to only
one kind of sensations, might raise the delicacy of touch to a degree
of perfection which we probably do not know; just as the habit of
connecting ideas with respect to only one order of sensations, and of
forming judgments concerning them, produces a precision, exactness,
and variety, far superior to all that we can imagine. But however far
we might extend our conjectures upon this head, it is certain that
there is a limit in the nature of the organ and of its relations to
bodies. This organ must be limited to contiguous objects, in order to
receive well determined impressions; and with respect to those that
are distant, and can act upon it, they can do this by causing on it an
impression such as the nature of both permits, heat or cold, dryness or
dampness, and if you will, a certain pressure either greater or less.
So far as a great many other objects are concerned, we cannot imagine
any action. However much the circle of this class of sensations be
enlarged, it must ever be very limited. Moreover, we must observe, that
the perfectibility of touch by means of its isolation does not belong
to it exclusively, but extends likewise to the other senses; for it is
founded on the laws of organization, and the generation of our ideas.
63. To comprehend the superiority of hearing to touch in this matter,
we have only to consider the relation of distances, the variety
of objects, the rapidity of the succession of sensations, the
simultaneousness so much greater in hearing than in touch, and their
relations to speech.
I. Relation of distances. On this point, hearing is clearly superior to
touch, for the latter generally requires contact, the former does not,
but for the due appreciation of its object even requires a distance
suited to the class of the sound. Of how many distant objects does
hearing inform us of which touch can tell us nothing? The gallop of the
horse threatening to trample us under foot, the roaring of the torrent
which may carry us away in its course, the thunder rumbling from afar,
and announcing the tempest, the roar of cannon, telling that a battle
has begun, the rattle of carriages in the streets, drums and bells,
and clamor of voices which indicate the explosion of popular fury, the
noisy music that proclaims the joy caused by happy news, the concert
dedicated to the pleasures of the saloon, the song that brings back
melancholy recollections, sentiments also of hope and love, the groan
that warns us of suffering, the plaint that afflicts us with the idea
of misery; all this hearing tells us, but touch can tell us nothing of
any of these.
II. Variety of objects. Those distant objects which we know by touch,
are of necessity little varied; and for the same reason the ideas
resulting from it will be liable to a deplorable confusion and to great
uncertainty. Hearing, on the contrary, informs us of infinite and
exceedingly different objects, and that, too, with perfect precision
and exactness.
III. Rapidity of the succession of impressions. It is evident that
hearing has here an incalculable superiority over touch. When touch
perceives by juxtaposition, it is under the necessity of successively
going over the objects and even their different parts if it would
receive varied impressions; and this, however small their number,
requires much time. If the objects do not act by juxtaposition, but by
some medium, the succession will require much more time, and there will
be much less variety. Compare this slowness to the rapidity with which
hearing perceives a whole series of sounds in musical combinations,
the infinite inflexions of the voice, the countless number of
distinct articulations, the infinity of noises of all kinds which we
uninterruptedly perceive and classify, and refer to their corresponding
objects.
IV. The simultaneousness of sensations so vast in hearing, is extremely
limited in touch; for in the latter it can only be in relation to a few
objects; but in the other it extends to many very different objects.
V. But what most triumphantly indicates the superiority of hearing
to touch, is the facility it affords us of placing ourselves
in communication, by means of speech, with the mind of our
fellow-mortals,--a facility, resulting from the rapidity of succession
already remarked. Undoubtedly, this communication of mind with mind,
may be established by touch, if we express our words by characters
sufficiently raised to be distinguished: but what an immense difference
between these impressions and those of hearing? Even if we suppose
habit and a concentration of all the sensitive forces to have produced
such a facility in passing the fingers over lines, as far to surpass
all that we see in the most dexterous players of musical instruments,
what comparison can there be instituted between this velocity and
that of hearing? How much time would be requisite only to go over
tablets whereon is written a discourse which we hear in a few minutes?
Moreover, all men have means of hearing, they need only make use of
their organs. But in order to converse by touch, it is necessary to
prepare tablets, which can only serve for one object, and cannot be at
the same time used by two persons; whereas by means of hearing, one man
alone may in brief time communicate an infinity of ideas to thousands
of listeners.
CHAPTER XII.
CAN SIGHT ALONE GIVE US THE IDEA OF A SURFACE?
64. I have, I believe, made the inferiority of touch to sight and
hearing palpable, and have, consequently, shown the extravagance of
endeavoring to make it the basis of all cognitions, to found upon it
the certainty of the judgments to which our other senses lead us, and
to make it a supreme judge to decide in the last appeal upon the doubts
that may arise.
I hold it to be manifestly untrue that we cannot make the transition
from the internal to the external world, or from the existence of
sensations to that of the objects causing them, otherwise than by means
of touch; for not only have I combated the principal, or rather the
solitary reason upon which it is pretended to found this privilege,
but I have also demonstrated the mode of making this transition
with respect to all the senses, reasoning from the very nature and
connection of internal phenomena.
I have likewise said and proved that the sensation of extension is the
only one that is representative, and that in all others there was only
a relation of causality, that is, a connection of some sensation or an
internal phenomenon with an external object, without our transferring
to this any thing resembling what we experienced in that.
65. There are two senses which inform us with certainty of extension,
sight and touch. We shall not now inquire if that be a true _sensation_
which we have of extension, or if it be an _idea_ of a very different
order, resulting from the sensation. I propose hereafter to examine
this point, but shall now confine myself to comparing sight with touch
only as tending to give us the sensation of extension, or, if you will,
to furnish us with what is necessary to form an idea of it.
We cannot but see that extension lies within the domain of touch, and
that, too, whether it be considered only as a surface, or also as a
solid. The same faculty cannot be denied to sight, so far as surfaces
are concerned; for it is impossible to see if at least a plane be not
presented to the eye. A point without extension cannot be painted
upon the retina, but the instant an object is painted, it has painted
parts. We can by no effort of our imagination, conceive colors without
extension; for what is color without a surface over which it may extend?
66. So hostile was Condillac to the sense of sight that he was
unwilling to allow it even the faculty of perceiving extension in
surfaces; but as he is of all philosophers the one who has most
contributed to the propagation and establishment of this opinion, we
will examine his doctrine and its fundamental reasons. We have only
to read the chapters in which he explains it, to see that he was
not himself very confident of its truth, but that he felt himself
contradicted by both experience and reason.
In his _Traité des Sensations_,[36] where he examines the ideas
of a man limited to the sense of sight, he says that colors are
distinguished by the sight because they seem to form a surface of which
the eyes occupy a part, and then asks: "Will our statue, judging itself
to be at one time many colors, perceive itself as a sort of colored
surface?" We must bear in mind that, according to Condillac, the statue
confined to one sense will believe itself the sensation, that is, it
will think that it is the odor, the sound, or the taste, according
as the sense of smell, hearing, or taste, is the sense in exercise;
for which reason, if a surface enter into the sensation of sight, the
statue ought to believe itself a colored surface. I shall not examine
the correctness of these observations, but shall confine myself to the
main point, which is the relation of sight to a surface.
[36] P. 1. C. xi.
67. According to Condillac, the statue will never believe itself a
colored surface, that is, although it may perceive the color, it will
not perceive the surface. Let the philosopher himself speak, for
his own words will suffice to condemn his opinion, and to show the
uncertainty with which he advanced it, or else the obscurity under
which it labors: "The idea of extension supposes the perception of many
things, _some distinct from others_. _This perception we cannot deny
to the statue_, for it feels that it is repeated outside of itself as
many times as there are colors modifying it. When it is the red, it
feels itself _outside_ of the green; when the green, it feels itself
_outside_ of the red, and so with other colors." Some may imagine
that, conformably to these principles, Condillac goes on to establish
that sight gives us the idea of extension, since it makes us perceive
things, some _outside_ of others, in which, according to him, the idea
of extension exactly consists. But he does not; far from following
the true road, he miserably loses his way; he not only violates the
principle he has just laid down, but notably changes the state of the
question. He continues: "But in order to have a distinct and precise
idea of magnitude, it is necessary to see how the things perceived,
some outside of others, are connected, how they mutually terminate,
and how they are all enclosed in the limits which bound them." This, I
repeat, is to change the state of the question; we are not now treating
of a distinct and precise idea, but simply of an idea. How far the idea
of extension given by sight is perfect, is another question; although
it is manifest that if sight can give us an idea of extension, it will
come by continual exercise to render this idea more perfect.
68. The statue, in Condillac's opinion, could not perceive itself to
be circumscribed by any limit, because it could know nothing beyond
itself; but did he not just now tell us that the statue would believe
itself different colors; that some of these were outside of others;
and that when it would be one, it would perceive itself outside of the
others? Does this not imply not only one but many limits?
This difficulty did not altogether escape Condillac; for after having
asked if the _me_ of the statue, when modified by a blue surface,
bordered with white, would not believe itself a limited blue color,
he says: "At first sight we were inclined to believe that it would;
but the contrary opinion is much more probable." But why? "The statue
cannot perceive itself extended by this surface, save inasmuch as
each part modifies it in the same way; each part should produce
the sensation of blue color; but if it is alike modified by a foot
of this surface and by an inch, it cannot perceive itself, in this
modification, to be one magnitude rather than another. Therefore it
does not perceive itself as magnitude; therefore the sensation of
color does not involve the idea of extension." It is easy to see that
Condillac either supposes what is in debate, or else says nothing to
the point. According to him, the statue is alike modified by a foot
of colored surface and by an inch. If by this he means that the two
modifications are identical under all aspects, he supposes the very
thing he ought to have proved; for this is precisely the point in
dispute, whether surfaces differing in magnitude do, or do not, produce
different sensations. If he means, as his words seem to indicate, that
the sensation as color, and solely as color, is the same in a foot of
colored surface as in an inch, he utters, indeed, an incontestable
truth, but one not at all to his purpose. Undoubtedly, the sensation
of blue, as blue, is the same in different magnitudes, and no one ever
thought of denying it. But this is not the question: it is whether, the
color remaining one and the same, the sensation of sight is modified
differently, according to the variety of magnitude of the colored
surface. Condillac denies it, but in an uncertain and hesitating way.
We believe his negation to be so groundless that the direct contrary
may be proved.
69. I would ask Condillac if he can have color without surface; if an
object without extension can be painted upon the retina; if we can even
conceive a color without extension. No one of these is possible, sight
is therefore necessarily accompanied by extension.
70. Condillac places the idea of extension in some things being
presented to us outside of others. This, as he him self confesses, is
verified in the sensation of color; therefore the sight of what is
colored must produce the idea of extension. Condillac's subterfuge
here is an exceedingly weak one. He pretends that it is necessary, in
order to have the idea of extension, to have that of its limits. But
first of all, we have shown from his own doctrine that these limits
are perceived by the senses; besides it is a very strange pretension
to attribute to sight the faculty of giving us the idea of unlimited
extension, and to deny to it that of producing the idea of limitation;
as if there did not by the very fact of our seeing what is extended,
rise within us the idea of limitation, if from no other cause, from
the very limitation of our organ; or as if an unlimited were not more
inconceivable than a limited sensation.
But suppose the limits not be perceived by the senses, does unlimited
extension therefore cease to be extension? Is it not rather extension
of the highest order? Does the idea of space without end, because
unlimited, cease to be an idea of extension?
71. Two colored circles, one an inch, and the other a yard in diameter,
are placed before our eyes; will the effect produced upon the retina
be the same in both, abstraction made from all sensation of touch?
Evidently not; experience shows the contrary, and the reason is founded
on the laws of the reflection of light, and on mathematical principles.
If the impressions are different, the difference will be perceived;
therefore the difference of magnitude can be appreciated.
We will now suppose some one in spite of reason and experience to
persist in maintaining that the sensation of the two circles will be
the same in order to make the extravagance, even the ridiculousness
of this opinion palpable. Let us imagine the two circles to be of a
red color, and terminated by a blue line; and now placing the less
upon the greater circle so as to bring their centres together, we ask,
will not the eye cast upon the figure see the less within the greater
circle? Will not the blue line that terminates the circle of an inch in
diameter be sure to be contained within the blue line that terminates
the other circle of a yard in diameter? But what else is the perception
of extension than the perception of some parts beyond others? Is it
not to perceive the difference of magnitude, to perceive some greater
than others, and containing them? Evidently it is. The sight therefore
perceives magnitude; therefore it perceives extension.
72. We may still further confirm this truth. Experience teaches, and
did it not exist, reason would still teach that there must be a limit
to the field of sight, according to our distance from the object. Thus,
when we fix our sight upon a wall of great extent we do not see it all,
but only a part. Now suppose an object of given magnitude to be within
the range of sight, but not so great as to cover the surface embraced
by the eye. According to Condillac's system, there can be no difference
in the perception, provided the color be the same; whence, it will
follow, that the sensation will be just the same, whether the object
occupy the whole, or only an exceedingly minute part, of the visual
field. It will likewise follow, that, if this visual field be, for
example, a great white curtain a hundred yards square, and the object a
piece of blue cloth a yard square, the sensation will be just the same
whether the blue cloth be one inch or ninety yards square.
73. These arguments, which must have occurred at least confusedly
to Condillac, made him hesitate in his expressions, and even use
contradictory language. We may have already observed this in
the passages cited, but we shall see it yet more clearly in the
following:--"We have no term to express with exactness the sentiment
that the statue modified by many colors at one time has of itself; but
in fine, it knows that it exists in many ways, and perceives itself in
a certain mode _as a colored point beyond which_ are others, in which
it turns to find itself; and under this point of view, it may be said,
that it _perceives itself extended_." He had before said, that color
did not seem extended to the statue, until, sight being instructed by
touch, the eye became accustomed to refer the one simple sensation to
all the points of the surface: and in the very next line, as we have
just seen, he asserts the contrary; the statue now perceives itself
to be extended, and the ideologist discovers no way of avoiding the
contradiction, but to warn us that the sentiment of extension will
be vague because it wants limits. This is a contradiction which we
have already made evident. But whence this want of limits? If various
figures of different colors, green, red, etc., be supposed to be upon
a visual field of a hundred yards square of white surface, the sight
will, as is evident, perceive the limits of these figures; where, then,
did Condillac discover that illimitation of which he talks?
74. Although it is very true that even if the sensation of color were
to involve that of extension, it would not therefore follow that it
would produce it in us, because we do not take from sensations all the
ideas they contain, but those only which we know. This does not at all
affect the present question. We do not treat of what we can take from
the sensation, but of what is in it. If Condillac maintains that we may
take the idea of extension from the sensation of touch, by what right
does he deny the same faculty with respect to sight, supposing the idea
of extension to be contained in both sensations?
If I mistake not, this is a tacit confession of the falseness of his
opinion. The idea of extension is in the sensation of sight, but we
cannot take it thence. Why not? Because it is vague. But then what
is to prevent exercise, involving comparison and reflection, from
rendering it distinct? The difficulty consists in acquiring it in one
way or another; to perfect it is the work of time.
Undoubtedly the first sensations of sight will not have that exactness
which they have after much exercise; but the same is true of the sense
of touch. This sense is perfected like the others; it like them needs
to be educated, so to speak; and those born blind, who, by force of
concentration and labor, come to possess it to an astonishing degree of
delicacy, offer us a manifest proof of this truth.
CHAPTER XIII.
CHESELDEN'S BLIND MAN.
75. Cheselden's blind man, of whom Condillac spoke, in confirmation
of his opinions, presents no phenomenon upon which they can rest.
This blind person was a youth of thirteen or fourteen years of age,
upon whom Cheselden, a distinguished London surgeon, performed the
operation of removing cataracts, first from one eye, then from the
other. He could before the operation tell day and night, and in a very
strong light distinguish, white, black, and red. This is an important
circumstance, and merits attention. The phenomena the most remarkable,
and having the most relation to the question now before us, were the
following:
I. When he began to see, he believed that objects touched the external
surface of his eye. This would seem to show that sight alone cannot
enable us to judge of distances; but, after close examination,
we shall clearly see that the argument is not conclusive. No one
will pretend that sight, in the first moment of its exercise, can
communicate equally clear and distinct ideas to us, as when experience
has accustomed us to compare its different impressions. This is the
same with touch as with sight. A blind person, from his frequent
custom of guiding himself, in many of his movements by sensations of
touch alone, comes to know the position and distances of objects with
wonderful precision. If we suppose a man deprived of the sense of
touch suddenly to acquire it, neither will he at first judge with the
same certainty the objects of this sense as after having exercised
it. Experience teaches that the sense of touch is capable of a high
degree of perfection. We see it in blind persons at its highest point;
and probably the lowest point of its perfection, in the first moments
of its exercise, would greatly resemble that of sight at the instant
of being freed from the cataracts; objects would be presented to it
likewise in confusion; and the subject experiencing them could not
well appreciate their differences until practice had taught him how to
distinguish and classify.
With respect to distance, it is to be observed, that this blind person
of Cheselden, so far from having the habit of appreciating it, had
false ideas upon it. As he was not totally blind, the light, which he
perceived through the cataracts, was sufficient to even enable him to
distinguish between white, black, and red, which seemed to him to touch
his eye. We may form some idea of this by observing what happens to
us if we close our eyes in a very strong light. Hence he ought, when
he gained his sight, to have imagined that the new sight was the same
as the old, and, consequently, that nothing had happened but a simple
change of object. A person totally blind would have better shown the
power of sight to appreciate distances; for he would have had no habit
either favorable or unfavorable to their knowledge.
II. It cost him much trouble to conceive that there were other objects
beyond those he saw; he could not distinguish limits; every thing
seemed to him immense. Although he knew by experience that his chamber
was smaller than the whole house, he could not conceive how he could
see this.
From these facts Condillac draws a confirmation of his system. We are
astonished that he should pretend to found an entire philosophy upon
such data. We submit the following considerations to the reader:
76. The subject is here a youth of thirteen or fourteen years, and
consequently without any habit of observation. He would naturally
express very confusedly the impressions he received in so new and
strange a situation.
The organ of sight must, when exercised for the first time, be
exceedingly weak, and consequently perform its sensitive functions
only in a very imperfect way. We ourselves repeatedly experience that
we cannot, if we suddenly pass from darkness to light, especially if
it be a very strong light, distinguish objects, but we see every thing
in great confusion; what then would happen to a poor child, when at
the age of thirteen years, he for the first time opens his eyes to the
light?
According to Cheselden's own account, objects were presented to him in
such confusion that he could not distinguish them, no matter what their
size or shape. This confirms what we have just said, that the partial,
if not the sole cause of the confusion, was that the organ did not
produce impressions well, because if these had been properly produced,
he would have been able to distinguish the limits of the different
colors; for, in simple sensation, to see is to distinguish.
We are also told that he could not recognize by sight the objects
which he knew by touch. But this only proves that not having been
able to compare the two orders of sensations, he could not know what
corresponded in one to the impressions of the other. By touch he would
have known a spherical body; but as he was still ignorant of the
impression which a globe makes on the eye, it is clear that if any one
should show him a ball which he had handled a thousand times, he would
not even have suspected that the object seen was the same which he had
touched. This leads me to another observation which I consider very
important.
77. The child on whom these experiments were made was obliged to
express his sensations in the visual order, in a language which he did
not understand. For any one who is deprived of one of the senses must
be absolutely ignorant of all the ideas which have their origin in
that sensation. Hence it follows that he knows nothing of the language
relating to that sense, and the ideas which he joins to the words
are entirely different from what those who possess that sense mean
to express. The blind man will speak of colors and the impressions
produced by sight, because he hears others speak of these things; but
for him the word to see does not mean to see, light is not light, nor
color color, as we understand them, but they express different ideas
which he has formed according to the circumstances, in conformity with
the explanations he has heard. What importance then should we attach to
what a child may say who, besides the thoughtlessness natural to his
age, is placed in a situation new to him, and required to express his
ideas in a language which he does not know? He is asked, for example,
if he can distinguish a greater object from another which is smaller,
without considering that the words greater and smaller as he understood
them, inasmuch as they expressed abstract ideas, or were referred to
the sensations of touch, were altogether new to him when applied to
objects seen, since he had no means of knowing what was meant when
referred to a sensation which he experienced for the first time. If
within a circle, a number of smaller circles of a different color were
described, he would see the smaller circles within the circumference of
the greater; but if asked if one appeared greater than the rest, or if
he could distinguish the limits which, separated the smaller circles
from each other, he could not but give very absurd answers, which the
observers might perhaps take as the expression of curious phenomena.
They speak to him of figures, lines, extremities, size, position, and
distances in relation to sight, and as he is ignorant of this language,
yet knows not that he is ignorant of it, he must necessarily talk in a
very strange manner. A more attentive and profound observer would have
perceived the same misunderstanding as when a deaf man disputes without
hearing what was said.
These remarks are further confirmed by the contradiction in the account
of Cheselden. The oculist tells us that the child could not distinguish
the objects, even those which differed most in form and size: but that
he found those most agreeable which were the most regular. He must
then have distinguished them; for otherwise, the sensation could not
have been more or less pleasing. And here in choosing an alternative
in this contradiction, we must hold that he distinguished the objects,
since there is a strong argument in its favor. When two objects,
the one regular, the other irregular, were presented to him, and he
was questioned as to their resemblance and difference, he must have
answered so absurdly as to create the suspicion that he could not
distinguish them. The reason of this is, that besides the confusion of
sensations, to which he was always more or less subject, he was also
ignorant of the language, and although he distinguished the objects
plainly, still he could not understand what he was asked, nor express
what he felt. But when examined as to the nature of the impression
and whether it was pleasing or otherwise, he found himself on a field
common to all sensations, the ideas of pleasure and displeasure were
not new to him, and he could say without confusion, this pleases me;
that is displeasing to me.
To sum up what I have said, I believe that the phenomena of Cheselden's
blind man, only prove that sight, like all the other senses, needs a
certain education, that its first impressions are necessarily confused,
that the organ acquires the proper strength and precision only after
long practice, and finally, that the judgments formed in consequence,
must be very incorrect until comparison, joined with reflection, has
taught how to rectify inaccuracies.[37]
[37] See Book 1, § 56.
CHAPTER XIV.
CAN SIGHT GIVE US THE IDEA OF A SOLID?
78. It has been asserted that sight can not give us the idea of size or
of a solid, but that this can be obtained only by the help of touch. I
believe the contrary may be proved with convincing certainty.
What is a solid? It is the union of three dimensions. If sight can
give us the idea of surfaces which consist of two, why not also of
solids which consist of three dimensions? This one reflection is enough
to show that it has been denied without reason; but I shall not stop
with this, but shall prove, by the most rigorous observation, and the
analysis of its phenomena, that sight can give us the idea of a solid.
79. I willingly agree, that if we suppose a man deprived of all the
other senses, to have his eyes immovably fixed on an immovable object,
he would never be able to distinguish between what is solid and what
is merely perspective in the object; or, in other words, that all the
objects permanently painted on the retina will appear to be projected
on a plane. The reason of this is founded on the very laws of the
organ of this sense, and of the transmission of its impressions to the
brain.
The soul refers the sensation to the extremity of the visual ray;
and since in the present instance it has been unable to make any
comparisons, it can have no motive for placing these extremities at
unequal distances, which constitutes the third dimension.
In order to understand this better, let us suppose the object to be
a cube placed so that three of its sides are seen. It is evident
that although the three surfaces are equal, they will not appear so
to the eye, because their respective positions do not permit them to
send their rays equally to it. But as the soul has not had occasion
to compare this sensation with any other, it can not calculate the
difference produced by the different positions and distances, but must
refer all the points to the same plane, regarding the sides of the cube
as unequal; though, in reality, they are not so.
Sight, in this case, presents the whole object on a perspective plane;
and as it could have no means of calculating the distance of the object
from the eye, it would probably believe it joined to the eye, or,
more strictly speaking, the sensation would represent only a simple
phenomenon, the relations and cause of which we could not explain.
80. It is likewise probable, that if, while the eye remained fixed, we
could open and shut the lids, we might form the idea that the object
seen was outside of us; so that by this motion alone, we should obtain
a point of comparison, by the succession of the alternate disappearance
and reproduction of the sensation of the object by the interposition
or non-interposition of an obstacle. Then the idea of a greater or
less distance would arise, and as this would be in the direction
perpendicular to the plane of the object, we should already have the
idea of a solid.
Fortunately, nature has been more beneficent to us, and we are not
obliged to limit ourselves to a supposition which thus curtails our
means of acquiring ideas. Still it will not be useless to have examined
the phenomenon on this supposition; for, from this examination, we
shall gain light to understand what I propose to demonstrate.
81. In order that sight may originate the idea of a solid, it requires
motion. This motion is an indispensable condition, though it may be
either in the object or in the eye itself.
Let us suppose an immovable eye, and see how by the motion of the
objects, the sensation of sight may present or produce the idea of
a solid. The only difficulty is to show how it can add to the two
dimensions which constitute the plane, the third which forms the solid.
Let a fixed eye be directed to a point where there is a right
rectangular parallelopipedon B, so placed that its two bases are wholly
concealed, and let the right line drawn from the centre of the eye to
the edge of the parallelopipedon divide the plane angle into two equal
parts. Let us also suppose the sides of the parallelopipedon to be of
different colors,--white, green, red, and black. In this case, the
eye sees the two planes as one, and the edge appears as a right line
separating the two parts of the same plane which differ only in color.
It is impossible for it to conceive the inclination of the two planes,
because as it refers the object to the extremity of the visual ray, and
has not been able to compare the varieties which result from difference
of position and distance, and from the manner in which the object
receives the light, it can only distinguish the different parts of the
same plane.
It is well known that perspective can perfectly imitate a solid. For,
if instead of the solid B, we suppose two planes exactly representing
the two sides seen, the sensation will be the same, the illusion
complete. Therefore, there are two distinct ways of producing the
same sensation; and consequently, unless there has been a previous
comparison, there is no means of distinguishing them apart; but the
idea which would naturally result would be the most simple; that is,
the idea of a plane.
82. If we suppose the parallelopipedon B to revolve on a vertical axis,
it will present the four planes successively to the eye, and they will
appear greater or less according to their inclination to the visual
ray, the surface of the plane reaching its maximum when perpendicular
to the ray, and its minimum when parallel to it.
The succession and variety of the sensations will immediately produce
the idea of motion; for the same planes of the parallelopipedon are
seen in different positions. The uniform manner in which these planes
succeed one another, will also suggest the idea that the green which
appears a few moments after the black, is the same which was seen a few
moments before; and so of the other colors. Also, as one is constantly
hiding behind the other, this naturally gives rise to the idea of
extension in the direction, or continuation of the visual ray; and this
is sufficient to produce the idea of size or of a solid. When we see a
plane we have the two dimensions which constitute a surface; to form
the idea of a solid, we need only the idea of one dimension more; this
can not be found in the same plane, but is produced by the motion of
the parallelopipedon.
83. This motion which we have supposed to be around a vertical axis, we
may equally suppose to take place around a horizontal axis. We shall
then see in succession the two opposite sides, and the bases of the
parallelopipedon with different appearances, according to their various
positions; or, in other words, according to the angle formed by the
planes and the visual ray. These appearances will help more and more
to form the idea of the third dimension, which is not to be found in
the primitive plane, and consequently to supply what was wanted to
constitute the idea of a solid.
84. Just as we have supposed the eye fixed and the object movable, we
may suppose the eye in motion and the object immovable. The result
is the same; for, it is evident that if the eye should move around
the parallelopipedon, now vertically, and now horizontally, it
would experience the same sensations as when it was quiet, and the
parallelopipedon moved. Thus, although we suppose the subject wholly
deprived of the sense of touch, so as to be unable to perceive its own
motion, it can still form the idea of solid by the impressions of sight
alone. True, it could distinguish which moved, the eye or the object,
but this does not interfere with the formation of the idea composed of
the three dimensions.
CHAPTER XV.
SIGHT AND MOTION.
85. I said that the observer could not distinguish between his own
motion and that of the object; sight alone can not give us a true idea
of motion. Thus in a boat, although we are certain that we are moving,
the motion seems to us to be in the objects along the shore. Also if
the motion of the object and that of the observer are simultaneous,
in the same direction, and with the same velocity, all appearance of
motion is lost. But if there are two objects, one of which moves in the
same direction as ourselves, and the other in the opposite direction,
we perceive only the latter. Thus in a canal boat, the horse which
walks on the bank in the same direction which the boat follows, seems
to move without advancing. Of the two motions of the horse, we perceive
only the vertical, the horizontal escapes us.
The reason of this is clear, we can judge the object only by our
impressions. When the impression varies, we have the idea of motion;
but not otherwise. When the object or the eye is in motion, there is
a succession of impressions on the retina, from which the idea of
motion arises. But if the motion of the eye accompanies the motion of
the object, one cancels the other, the impression on the retina is
constant, and the object does not seem to move.
86. In the same manner if the motion of the object and that of the
eye are simultaneous, but of unequal velocity, we perceive only the
difference; that is to say, if the motion of the eye be represented by
3 and that of the object by 5, the motion of the object will appear as
2, or the difference between 5 and 3. If our motion is more rapid than
the motion of the object, although in the same direction, the object
will appear to move in the opposite direction, as when we sail down a
river faster than the current, the water seems to flow backwards. An
immovable object at the same time seems to move in a direction opposite
to our own with greater velocity than the current; for, here also, of
the two motions we perceive only the difference. The motion of the
boat, which is equal to 5, seems transferred to the fixed object, which
appears to move in the opposite direction with the velocity represented
by 5; and if we suppose the velocity of the current to be equal to 3,
it will have the appearance of moving backwards with a velocity of 5-3,
or 2.
87. From these considerations it would seem to follow that although
sight is sufficient to give us the idea of motion, it is not
sufficient to enable us to distinguish our own motion from that of the
object, but for this we have need of touch. But this is not so; for by
sight alone, we can distinguish the motion of the eye from that of the
object, and if in some cases this is impossible, the same is true of
touch.
We must observe that in the above examples touch is of much less use
than sight in order to preserve us from illusions. How by the aid of
touch alone could we perceive the motion of a boat gliding smoothly
down a river? Sometimes by the help of sight we observe this motion,
especially if we regard the objects along the bank which we pass; but
touch is essentially limited to what affects the body immediately, and
therefore cannot discover motion when the body is not affected by it.
It is also well to observe that we do not refer the motion perceived by
touch to the objects around us until after we have acquired this habit
by means of repeated comparisons. When for the first time the hand is
passed over an object, we are unable to tell whether the hand moves
over the body, or the body under the hand.
The reason of this is that the sensation of motion is essentially
a successive sensation, and this succession exists equally whether
the hand moves or the object. Let us suppose the hand to pass along
an object of a varied surface, we shall experience the variety of
sensations corresponding to the surface; suppose now that the hand
remains motionless, and the object passes under it with the same
velocity, pressure, and friction, the sensations will be the same as
before. Every one must have observed that when leaning on a slippery
object, it is often difficult to tell whether it is the object which
moves, or ourselves. Therefore touch also confirms what we have
advanced, that the distinction between the motion of the member and
that of the object does not arise from simple sensation.
88. In this respect, therefore, touch does not help sight; let us see
if sight alone can enable us to distinguish between the motion of the
eye and that of the object. We have already observed that a single
sensation with respect to one object only is insufficient, but there
is no difficulty in proving that this result may be obtained by the
comparison of different sensations.
Let us suppose the eye at a point A, looking at an object B; the object
will appear at the extremity of the range of the sight as if projected
on a plane. To be more definite we will imagine the object B to be
a column in the middle of a large hall, and the point A a corner of
the same hall. The column will appear to the eye to be a part of the
opposite wall. If the eye changes its position, the column will appear
in another part of the wall; so that if the eye should pass around the
column, it would appear successively on every part of the wall. The
same succession of phenomena would be observed if the eye should remain
fixed and the column should move around it; for it is evident that if
the observer is placed in the centre of the room, and the column moves
around him, the column will appear on all the parts of the opposite
wall. From this we infer that only one sensation of sight, with only
one object, is not enough to determine whether the eye moves or the
object.
But if instead of one object we suppose several moving simultaneously,
it is easy to see how the distinction of motions arises. Let us suppose
that at the same time that the eye sees the column, it also sees
other objects, such as chandeliers, statues, or other columns, placed
between the eye and the opposite wall. If the eye moves every time the
column changes its position on the opposite wall, the other columns,
the chandeliers, statues, everything in the room seems to change its
position; whereas, if the column moves and the eye remains fixed,
the column alone changes its position, while everything else remains
motionless. Therefore sight alone gives us two distinct orders of
phenomena of motion:
I. The first, in which all the objects change their position.
II. The second, in which one object only changes its position.
These two orders of phenomena cannot remain unperceived; for by the
help of reflection excited and enlightened by the repetition of the
phenomena, we must come to the conclusion that when there is an entire
and constant change of all the objects, it is not they that move, but
the eye; and that when only one or a part of the objects change their
position, the rest remaining fixed, it is not the eye that moves, but
the objects which change their position. When everything around us
changes we infer that it is the eye that moves; when one or two change
their position we conclude that they move and not the eye. This is not
merely a supposition, it is the reality. The ideas derived from touch
are essentially limited, and it is therefore impossible that they
should proceed from distant objects which cannot be touched.
89. I believe I have demonstrated that the pretended superiority of
touch is without foundation, and that the opinion which makes this
the basis of our knowledge of external objects, the touch-stone of
the certainty of the sensations transmitted by the other senses, is
an error. Without it we can acquire the certainty of the existence
of bodies; without it we can form the idea of surfaces and solids;
without it we discover motion, and distinguish the motion of the object
from that of the organ which receives the impression. The theory of
sensation here explained, and the results which are deduced from the
relations of the dependence or independence of the phenomena among
themselves, and with our will, may all be applied to the sight as well
as to the touch.
90. Summing up all we have said, we have the following results:
I. We distinguish sleep from waking, even abstracting the objectiveness
of the sensations.
II. We distinguish two orders of phenomena of sensation;--the one
internal, the other external, here also abstracting their objectiveness.
III. The senses give us certainty of the existence of bodies.
IV. Sensations have no type in the external object of what they
represent, except _extension_ and motion.
V. Touch is not the basis or touch-stone of certainty.
VI. All that we know by means of the senses may be reduced to this;
that there are external beings, that is to say, beings placed outside
of ourselves, which are extended, subject to necessary laws, and which
produce in us the effects which we call sensations.
CHAPTER XVI.
POSSIBILITY OF OTHER SENSES.
91. Lamennais writes: "Who can say that a sixth sense would not disturb
the harmony of the others by a contrary impression? On what foundation
could he deny it? If we suppose other senses different from those which
nature gave us, might not our sensations and our ideas be different?
Perhaps a slight modification in our organs would be sufficient to ruin
our whole science. Perhaps there are beings so organized that their
sensations are wholly opposed to ours, and what is true for us is false
for them, and reciprocally. For, if we examine the matter closely, what
necessary connection is there between our sensations and the reality?
And if there were such a connection, how could the senses make it known
to us?"[38]
[38] Essai sur l'Indifference, Tome II., Part III., Ch. I.
The questions which these words raise are of the highest importance and
merit a serious examination.
92. Is there any intrinsical impossibility of an organization different
from ours, and an order of sensations different from those which we
experience? It seems not; and if this impossibility exists, it is
unknown to man.
Whatever opinion we adopt as to the manner in which external objects
act upon the soul by means of the organs of the body, there is no
necessary relation, nor even analogy, between the object and the effect
which it produces in us.
A body receives upon its surface rays of the fluid which we call
_light_, these rays are reflected upon the retina, which is another
surface in communication with the brain. So far all is well, and
easily understood. There is a fluid which moves, goes from one surface
to another, and may cause this or that purely physical effect on the
cerebral matter; but what connection is there between this and the
impression of a distinct order which we call _seeing_, an impression
which is neither the fluid nor the motion, but an affection of which
the living and thinking being, the _me_ is intimately conscious?
If, instead of the luminous fluid and its mechanism, we suppose
another, as, for example, the air which vibrates upon the tympanum,
what _essential_ reason is there why this should not produce a
sensation similar to that of sight? It must be confessed that it is
impossible to assign an _essential_ reason. To one who has no idea of
our present organization, both phenomena are equally incomprehensible.
93. What has been said of sight and hearing may be applied to the other
senses. In all there is a bodily organ affected by a body; we see the
surfaces placed one before or under the other, we see motions of one
kind or another; but how can we pass over the immense distance which
separates these physical phenomena from the phenomenon of sensation?
For my part, I see no way to do it; this point is a barrier to the
human intellect; all appearances indicate that there is no connection
between these two orders of phenomena except what the will of the
Creator has _freely_ established; if there is any necessary connection,
this necessity is a secret to man. Examine the textures which receive
the impression of the objects, the material substance which composes
the nervous system which is the organ of sensations, and say what
relation you can find between the physical phenomena of this matter and
the wonderful harmony of sensible phenomena.
94. Still greater will be the difficulty if you consider that, although
protected from any injury, the organs cease to produce sensations from
the moment they are deprived of communication with the substance of
the brain. The phenomena of light are produced in the cavity of the
skull amid the most profound darkness; and all the wonderful magic
of sensations by which the magnificent spectacle of the universe
is presented to our mind, which plunges the soul into raptures at
the sound of music, and which produces such varied and delightful
sensations of taste and odors, all arises in the brain, a whitish,
rude, and unformed substance, from the appearance of which no one could
imagine it destined to such noble functions.
95. Why is it that when the nerve A, in communication with the brain is
affected, we experience the sensation which we call _seeing_, or if the
nerve B is affected, the sensation which we call _hearing_, and so of
the other senses? There may be a reason, but, at least, we do not know
it; and it is probably no other than the free will of the Creator.
Here, it is true, philosophy confesses its weakness, but, at the same
time, it shows its power; for it sees the immense distance which
separates these phenomena, between which there can be no point of
communication but what is established by the Almighty. When there are
second causes, it is the merit of philosophy to discover them; but when
there are none, its merit is in rising to the first cause. A confession
of its ignorance is sometimes a more sublime act of reason than the
impotent effort of an unbounded pride. If the perception of profound
truths exalts the intellect, is not the intellect exalted in perceiving
its own ignorance, which is sometimes a profound truth?
96. The existence of another sense is, then, possible; at least, we see
no impossibility of it. If the deaf man who has no idea of sound, and
the blind man who knows not what color is, would be foolish to deny
the possibility of those sensations of which they are deprived, can
we, with any more show of reason, assert the impossibility of an order
of sensations different from what we possess? If we examine the system
of sensations by the light of reason, we can discover no essential
dependence between the sensations and their respective organs, nor
between the organs and the objects and circumstances by which they are
affected. Why does the impression of the light upon my eyes cause in me
a particular sensation, which cannot result from the same impression
on a different part of my body? Why may not the brain receive the same
impression in various forms? Why must this fluid which we call _light_,
and no other, produce the impression? Why may not this same sensation
of _seeing_ proceed equally from other affections of the brain? A
violent blow on the head produces the sensation of many luminous
points, whence the common expression of "seeing stars by daylight."
We must confess that philosophy knows nothing of these secrets, that
as yet it has not been able to penetrate them, and it can give no
answer to these questions. It sees an order of facts, but no necessary
connection between them, or rather, judging from its ideas of mind and
body, every thing induces it to believe that these phenomena in our
life depend solely on the will of our Creator.
97. If an entirely new order of sensations is possible, there may be
beings with six or seven senses. The imagination cannot conceive their
nature; but reason sees in them no impossibility.
CHAPTER XVII.
EXISTENCE OF NEW SENSES.
98. Is it certain that we have only five ways of sensation? I have
some doubts on this point. In order to present them with the greatest
clearness, and solve the questions which they raise, it is well to
settle the meaning of the terms.
What is sensation? In the ordinary acceptation of the word, it is the
perception of the impression transmitted to us by one of the organs of
the five senses. Thus understood it is clearly limited to the action
of the organs, but if considered as expressing a certain class of
animal phenomena, it is the experiencing of any affection produced by
an impression of the organism. Even in common use the word sensation
in its broadest signification is not restricted to the impressions
of the five senses, and although we make a great difference between
_sentiment_ and _sensation_; still we are often forced to confound
them, and to use the word _sensation_ to express things which have
nothing whatever to do with the five senses. Thus we say: "The news
made a great sensation;" "I cannot resist the force of such strong
sensations," etc., in which cases it is evident that there is no
reference to seeing, hearing, smelling, tasting, or touching, but to a
different order of affections of the soul.
99. I said we were forced to use the word in the broader meaning;
it is the truth which forces us. For, to the eyes of philosophy,
the phenomenon of sensation consists in the production in the soul
of a particular affection determined by an impression on an organ;
and of whatever order this affection may be, and whatever organ may
be affected, the animal phenomenon is substantially the same. The
difference is in the class of affections and of the organ which is
their medium, the essence of the phenomenon does not change. And if by
sensations we understand such distinct orders of affections as those of
sight and of touch, why may we not include other impressions caused by
any other organ, whatever that organ may be?
100. Whatever use we may make of the word sensation, it is certain that
we experience many affections caused by organic impressions, besides
those of the five senses. What are passions but affections of the soul,
springing from organic impressions? Does not the mere presence of an
object often excite love, anger, pity, joy, grief, and many other
sentiments of the soul?
You may say there is an essential difference between the impressions of
the senses and those of the passions, that the former are independent
of all previous idea and reflection, which the latter more or less
presuppose. Thus, when an object is present to our open eyes, we
cannot but see it and always in the same manner; and yet this object
will excite in us at one time one passion, at another time another, and
sometimes none; and almost always with great difference in the degree
of its intensity. Moreover it is not only the mere presence of the
object which causes an affection, but certain conditions are necessary,
for example; the remembrance of a benefit or of an injury, etc., from
which it is easy to see that there is an essential difference between
the two classes of impressions.
101. If we reflect well upon this objection we shall find that though
it is specious and under many aspects true, it contradicts nothing
which I have asserted. I did not deny that the new impressions were
subject to very different conditions from those that govern the five
senses; but on the contrary I have all along supposed a difference
not only in the class of impressions and the diversity of the organ,
but also in the manner in which the organ is affected, and the
circumstances in which the sensation is produced in the soul. I only
contended that the animal phenomenon was substantially the same, that
we find in it the three things which constitute its nature; a corporeal
object; an organ affected by this object; and an impression produced in
the soul. Because this impression cannot exist without the aid of this
or that idea, this or that recollection, it does not follow that the
phenomenon does not exist, or that it is not the same; it is merely to
impose a new condition, and nothing more.
102. But there is no necessity of admitting that some previous idea
or reflection is requisite in order that the sight of the object may
produce certain impressions in the soul;--daily experience proves
the contrary. How is it that the presence of an object charms in an
instant a tender and perhaps innocent heart? Whence then arises that
sudden fascination which is preceded by no idea, accompanied by no
affection, and is scarce voluntary? Not from the thought of gross
enjoyments; for perhaps he of whom I speak knows not their existence
until he experiences this emotion; he feels for the first time in his
breast a trouble unknown before. We must therefore recur to an organic
affection similar to that which we find in the other senses. Certain
conditions of age and temperament may be requisite, one object may have
been necessary, among a thousand, in particular circumstances, of which
the soul can give no account to itself though affected by them; yet it
is still true that there is an external object, an affection of the
organism, and an impression in the soul, all connected together by a
mysterious, but undeniable bond.
It is easy to discover a series of strong impressions in the phenomena
relating to reproduction; but although they presuppose the action of
some one of the five senses, they nevertheless belong to a different
order. No physiological studies are necessary to prove that these
affections depend on the organization, and that they are greatly
influenced by age, health, temperament, food, climate, and the seasons.
103. There is a difference between sentiments and sensations which,
though it does not change the fact physiologically and psychologically
considered, still greatly modifies it in its intellectual and moral
relations. The passions are commonly excited by an animate and sensible
object, whence it would seem that there is more communication between
mind and mind, between soul and soul, than there is between one body
and another. The sad and mournful appearance not only of a man, but
even of an animal, immediately excites in our breast the sentiment of
compassion, because it expresses the suffering of a living being. This
only proves that nature has mysterious ways by which it transmits to us
the knowledge of hidden things; but this transmission is made by the
medium of a body which affects in some way our organic constitution.
There is here, if you please, a more admirable, more penetrating,
and more spiritual a magic than that of the senses alone; but the
difference is in the degree, not in the nature of the phenomena.
It is certain that living beings, and those of the same species in
particular, are in a constant communication which mutually excites
their affections, and that these affections frequently suppose a
mysterious correspondence with unknown agencies. Physical nature
is full of fluids whose qualities are daily becoming known through
scientific observation. The phenomena of electricity and galvanism have
revealed secrets of which we had no suspicion before. Who can tell
by what means the functions of this vast and complicated system of
animal life, spread over the universe, are performed? It is probable
that there are profound secrets in the correspondence and relation of
organisms and in the way in which they influence one another yet to
be discovered; perhaps they will remain forever veiled to the eyes of
mortality.
104. Is it true that sensible beings can alone excite the passions?
or have not inanimate causes repeatedly affected our organs? Why are
we sometimes joyful and sometimes sad, at some times peaceful and at
others irritable, when we have had no communication with any living
being? It is clear that this depends on the affections of our organism,
and has no relation to the state of other sensible beings.
105. Therefore, besides the impressions caused by the five senses,
there are others which proceed from purely corporeal and inanimate
objects. Besides the phenomena of ordinary sensations, there are others
which differ from them only in the kind of impression and the organ
affected; and there is no more difference between these sensations
and the former than there is between the impressions of one and those
of another of the five senses. Therefore it is not correct to say that
there are only five kinds of sensation.
CHAPTER XVIII.
SOLUTION OF LAMENNAIS' OBJECTION.
106. From the preceding observations we shall now deduce an important
consequence,--the solution of the difficulty presented by Lamennais.
The existence of new senses would involve new sensations, it is true;
but they would not disturb the harmony of those we already have. We
have shown that bodies affect our organs in a different manner, and
produce impressions different from those of the five senses; but this
does not disturb the agreement of our sensations, nor change our ideas.
Consequently, the supposition of Lamennais would not involve the
disorder which he suspects.
107. Sensations in themselves are mere affections of the soul, and have
no external object which corresponds to them except the existence and
extension of bodies. Therefore a new order of sensations would only be
a new order of affections, which would in nowise alter our ideas.
From what we have hitherto said, it is easy to see that the supposition
of Lamennais is already realized; for there are sensations different
from those of the five senses; therefore this supposition does not
contradict the nature and order of our ideas, nor the certainty of our
knowledge.
A musical instrument beautifully fashioned has charms for the ear, the
eye, and the touch, none of these impressions destroys the other; if we
suppose it placed in new relations with our organs, so as to produce in
the soul new impressions, why is it impossible that they should accord?
Does the melody of its sound cease because our soul experiences new
affections whose nature has no connection with it? Certainly not. Why
then fear the overthrow of our knowledge by the introduction of a new
order of sensations? Why give such importance to a supposition, the
effects of which we can very well calculate, and which, if we examine
the phenomena of our present sensations, we find already realized?
108. It is true that we know of no other means of placing ourselves
in contact with external objects than the five senses; but it is
equally true, that this contact existing, the impressions in the soul
correspond mysteriously to the external objects; so that, while we
observe the sensations by which the communication is established, it is
still impossible for us to explain them.
Let us examine the magical effects of music. They are of two orders;
the purely auditive, and the intellectual or moral. The first stop
at the ear, the second pass to the brain and to the heart; and one
may be admirably organized for the former, yet unable to appreciate
the latter. Two persons listen to a sonata, both hear the _material_
music, but the intellectual and moral effects are not the same on both.
Both perceive the least defect in the time or in the instrument, both
admire the art of the composer, both are charmed; but while the heart
of one is unmoved, the brain and the heart of the other are bounding
with delight, the power of his fancy is multiplied, thoughts and images
crowd upon his mind, as though he had caught inspiration from the
magic notes of the music. His heart is transported with tenderness,
melancholy, hatred, love, anger, generosity, and courage. He is
under a magical influence which, moves him in spite of himself; the
vibrations of a chord have raised in his heart a mysterious tempest
which the might of reason can hardly quiet.
109. From this we must conclude, that besides the ordinary relations
between objects and the organs of the senses, there are other relations
still more intimate and more delicate between these objects and our
organic system, and that these latter are as certain as the former.
In them there is greater variety of individuals, and the conditions
necessary to produce determinate results are less known, but there
can be no doubt of their existence, and this in the eyes of sound
philosophy is sufficient to dissipate those absurd suppositions which
would pretend to undermine the edifice of our knowledge.
110. Thus, then, the objection is answered, which says: "If we had
another sense, what would it tell us?" Nothing which would destroy the
certainty of our knowledge, or the nature and order of our ideas. The
only new result would be _one more_ added to the many ways in which
objects now affect us. The same thing would happen to us as to a man
who after being deprived of the sense of smell, should suddenly regain
it: he would have one sensation more; the same thing would happen to
us as to a man who experiences a new sentiment which he had not known
before: he has one affection more. New impressions have their own rank,
neither interfering with, nor changing those which previously existed.
BOOK THIRD.
EXTENSION AND SPACE.
CHAPTER I.
EXTENSION INSEPARABLE FROM THE IDEA OF BODY.
1. Having seen that among the objects of our sensations, extension
alone has any external existence for us as any thing more than a
principle of causality, let us now try to understand what extension is.
The idea of extension seems to be inseparable from that of body; at
least, I am unable to conceive a body without extension. Take away
extension, and the parts disappear, and with them all that has relation
with our senses; there is no longer an object, or, if the object
remains, it is something altogether different from what is contained
in the idea of body. Imagine an apple, for instance, from which you
suddenly take away extension. What will remain of it?
I am not now going to examine whether Descartes is right when he says,
that the essence of body consists in extension; all that I here assert
is that a body cannot be conceived without extension. I do not affirm
the identity of two things, but only the inseparability of two ideas in
our mind. It is not an opinion, but a fact asserted by consciousness,
which is now under discussion.
Abstracting extension, I can conceive, it is true, a substance, or, to
speak more generally, a being; but, then, there is no idea of body,
unless we confound this idea with, that of substance or of being, in
general.
2. All our notions of bodies are obtained through the senses, but
without extension no sensation is possible; for without it there can
be no color, no sound, no touch, no smell, and no taste; therefore,
without extension there remains only something of which we have no
idea, a vague notion which cannot enable us to distinguish one object
from another, a pure abstraction, and nothing more.
3. To solve the difficulties which attend the separation of the two
ideas of extension and of body, it is necessary to determine the
essence of body. When we can distinguish the essence of a body from its
extension, the difficulty will be overcome, but not until then.
4. In order to understand the reason of this inseparability, it
is necessary to remember what was said before, that extension is
the basis of all other sensations; it is the _substratum_ which is
confounded with none, depends on none of them in particular, yet is an
indispensable condition of them all.
I look at an apple, and examine the mutual relations of the sensations
which it produces.
It is evident that though I abstract the smell, I do not thereby
destroy any of the other sensations which it causes. Though it lose its
odor, it is still extended, colored, it has a taste, and may produce
a sound. I may also, in like manner, abstract its taste, its color,
and all that relates to the sight, but I have still an object which is
tangible, and consequently extended, figured, and possessed of all its
other properties which affect the touch.
If instead of abstracting what relates to the sight, I abstract what
belongs immediately to the touch, I may do this without destroying the
other sensations; for I can still see the apple, its extension, form,
and color.
I may even go farther, and strip the apple of all its sensible
qualities, of its taste, smell, color, hardness, and whatever the
senses can perceive, still there remains extension, not indeed
sensible, but conceivable. Extension exists abstracted from its
visibility, since it exists for the blind man: abstracted from its
tangibility, since it exists for the sight; abstracted from odor,
taste, and sound, since it exists for those who are deprived of these
sensations, so long as they have sight or touch.
5. Here a difficulty arises. There seems to be a mistake in what
we have said of the existence of extension abstracted from other
sensations; for, although in making this abstraction we conceive
ourselves to be deprived of these sensations, still we retain the
_imagination_ of them; thus, when I strip the apple of all light and
color, it is still extended; but that is because I still imagine a
color, or, if I make a strong effort to destroy the color, it appears
to me like a black object, on a ground of greater or less darkness,
distinct from the apple. Does not this prove that there is an illusion
in such abstractions, and that there is no complete abstraction, since
the reality which we abstract is succeeded by the imagination of the
same qualities, or of others which supply their place, so as to make
the extension perceptible?
This objection is specious, and it would be difficult to give a
satisfactory answer if the existence of men deprived of sight did not
instantly dissipate it. No such imagination is possible in the case
of a blind man, for him there is no color, no shade, no light, no
darkness, nor anything which relates to sight, and still he conceives
extension.
6. But at least, some one will answer, it must be confessed that the
idea of extension is necessarily dependent on the sensations of touch;
blind men also possess this sense, and by it they acquire the idea of
extension. Therefore the idea of extension is inseparable from the
sensations of touch. This argument is no better than the other; for,
although we may acquire the idea of extension by the sense of touch,
and this sense is all that is required to produce it, it is not true
that this idea can only be acquired by touch. I have already proved
that sight is sufficient of itself alone to produce the idea of the
three dimensions which constitute a solid or extension in its full
complement. But here I do not need the idea of a solid, that of a
surface is sufficient; the extension of a surface is inseparable from
sight. There is no sight without color, or light of some kind or other,
and this cannot even be imagined without a surface.
I have another argument. Geometricians, doubtless, conceive extension,
and yet they abstract all its relations to sight or touch; therefore,
there is no necessary connection between them.
In any object submitted to the sight, what quality relating to the
touch is necessary in order to produce the idea of extension? If we
examine it closely, we shall find that there is none. Let us take a
liquid; is its fluidity the necessary quality? No; for when congealed
extension remains. Is it heat or cold? No; for without destroying
its extension we may change its temperature as much as we please,
no alteration is perceptible. Whatever quality relative to touch we
may take, we shall find that it may be varied, modified, or entirely
destroyed, without visibly affecting the extension.
It often happens that we have a clear and definite idea of the
extension of an object without knowing any thing of its qualities in
relation to touch. I see an object at a distance, I distinguish its
color and its form, but I know not of what material it is, whether
it is of marble, or wood, or wax, nor whether this material is hard
or soft, moist or dry, warm or cold. I do not even know if it is
tangible, as in the case of figures formed by vapors which are
imperceptible to the touch.
7. Without extension there can be neither sight, nor touch, nor any
other sensation. As to taste, it is clear that it requires touch, and
cannot exist without it. Our assertion is less clear with regard to
sound and smell; for, although we cannot separate these sensations from
the idea of extension as they always involve this idea in one way or
another, we do not know how it would be with a man who was deprived of
all the other senses, and retained only those of smelling and hearing.
But without speculating on this hypothesis, it is enough to know:
I. That nothing which is not extended can act upon our organs, unless
by means wholly unknown to us, and which would give no idea of what we
understand by body.
II. That even supposing the sensations of smelling and hearing to be
possible without the idea of extension, they would in that case be only
simple phenomena of our being, and would not place us in communication
with the external world, as we now perceive it; because, if we should
not know that they proceeded from another cause, we could have no more
consciousness of them than that which we have of the _me_; and if
we should know it, this cause would be represented to us only as an
agent influencing us, and not by any means as a being having any thing
similar to what we understand by body.
III. That in such a case we should have no idea of our own
organization, nor of the universe; for it is clear that every thing
being reduced to mere internal phenomena, and their relation to the
agents producing them, and the idea of extension wanting, neither the
universe nor our own body would be to us what they now are. What would
the universe,--what would our body be without extension?
IV. That for the present we limit ourselves to the demonstration of
the dependence which in the present system, of things, all sensations
have in relation to extension; and this demonstration holds good, even
though we suppose the man who possesses only the sense of smelling or
that of hearing not to form any idea of extension, and not to need it
in order to experience its sensations.
V. That even on this supposition, the proposition before established,
that the idea of extension is independent of the other sensations,
still remains unassailed.
VI. That the truth which we are principally endeavoring to demonstrate,
that for us the idea of extension is inseparable from that of body,
also stands firm.
8. This inseparability is so certain, that theologians explaining the
august mystery of the Eucharist, distinguish in the extension of bodies
the relations of the parts to each other, and their relation to place,
_in ordine ad se, et in ordine ad locum_; and they say that the sacred
body of our Lord Jesus Christ is in this august Sacrament, by extension
_in ordine ad se_, though not by extension _in ordine ad locum_. This
proves that the theologians saw that it is not possible for man to
lose all idea of extension, without at the same time losing all idea
of body; and thus they invented this ingenious distinction, of which I
shall speak at greater length in another place.
CHAPTER II.
EXTENSION NOT PERCEPTIBLE AS THE DIRECT AND IMMEDIATE OBJECT OF
SENSATIONS.
9. Extension has the remarkable peculiarity of being perceived by
different senses. As regards sight and touch this is evident; it is
also true as far as concerns the other senses. We perceive taste in
different parts of the palate, and we refer sound and smell to distinct
points in space, and this involves the idea of extension.
But what is more strange is, that although extension is the
indispensable basis of all sensations and therefore perceived by all
the senses, it is, in itself, and separated from every other quality,
imperceptible to them all. The eye perceives only light, and the ear
sound, the palate taste, the smell odor, and the object of touch is
that which is warm or cold, moist or dry, solid or liquid, etc. None
of these objects is extension, none _in particular_ is necessary for
the perception of extension; for we constantly find it separated from
each of these qualities, and yet it is still perceptible. No one _in
particular_ is necessary for the perceptibility of extension, but some
one is indispensable; for, unless accompanied by some one of them, it
is imperceptible to the senses.
Hence, extension is a necessary condition of our sensations, but is
not itself perceived by the senses. Still it is not therefore unknown,
and this brings me to some other reflections which take us out of the
phenomenal into the transcendental order, and give rise to very serious
and difficult questions, which have hitherto been insolvable, and it is
to be feared must ever remain so.
10. We have seen that extension in itself is not the direct object of
sensation. What, then, is it? What is its nature?
There are two things which may be considered in the idea of extension:
that which it is in us, and that which it represents to us; or, in
other words, its relation to the subject, and its relation to the
object. The first being subject to immediate observation, inasmuch as
it exists within us, is difficult but not impossible to explain. The
second is more difficult, and almost impossible to explain, because it
is a very abstract and transcendental idea, and also requires a series
of arguments, the thread of which may be broken without the one who
reasons perceiving it.
11. Extension in us is not a sensation, but an idea. Sometimes we
imagine it under a sensible form, confounding it with a determinate
object; at other times we picture it to ourselves as a vague
obscurity in which bodies are placed; but these are only fictions of
the imagination. A man born blind can have none of these internal
representations, and yet he forms a very good conception of extension.
We ourselves in thinking of extension abstract all these forms under
which we imagine it.
Two different sensations, those of sight and touch, produce the same
idea of extension. This is conclusive proof that extension is rather
intelligible than sensible.
Whatever may be the relation of extension to sensation, we cannot
deny that it is an idea if we reflect that it is the foundation of
the whole science of geometry. Thus, although we form various images
of extension, they are only the particular forms with which the mind
clothes the idea, if we may use the expression, according to the
circumstances of the case. That which is fundamental and essential in
the idea, is of a different and higher order, and has nothing in common
with the applications which the mind makes in order to explain and
apply it. This idea includes dimensions, but not determined or applied;
they are mere conceptions which represent nothing in particular.
12. The idea of extension is a primitive fact of our mind. It is not
produced by sensations, but precedes them, if not in time, at least
in the order of being. There is no ground for asserting that the idea
of extension exists in the mind prior to the first impression of the
senses, but unless extension serves as their basis these impressions
are inconceivable. Whether this idea is innate or developed, or
produced in the mind by the impressions, there can be no doubt that it
is distinct from them, necessary to them, and independent of any one of
them in particular.
It may be that when these impressions are first received extension
may not be known as a separate idea; but it is certain that it
is afterwards separated and stripped of the corporeal form, and
spiritualized, and that this phenomenon may be occasioned but not
caused by the sensation.
In sight, abstracting extension, there is color, but we cannot discover
in it any thing from which we can produce so fruitful an idea as
that of extension. Even at first we see that the color itself is not
perceptible without extension, and so far from extension being produced
by color, it is on the contrary an indispensable condition without
which color cannot be perceived.
Colors as the objects of sensation are only individual phenomena,
which have no connection with one another nor with the general idea of
extension. What has been said of them will equally apply to all the
impressions of touch.
CHAPTER III.
SCIENTIFIC FRUITFULNESS OF THE IDEA OF EXTENSION.
13. In order to understand the superiority of the idea of extension
over mere sensations; or rather, in order to understand that there is
a true idea of extension considered in itself, and that there is no
such idea of the direct and immediate objects of sensation, I wish to
call attention to the fact that among all the objects of the senses,
_extension alone gives origin to a science_.
This is a very important fact;--to explain it as it deserves, I shall
establish the following propositions:
FIRST PROPOSITION.
Extension is the basis of geometry.
SECOND PROPOSITION.
Not only is extension the basis of geometry, but all that we know
of the nature of bodies may be reduced to the manifestations,
applications, and modifications of extension, with the addition of the
ideas of number and time.
THIRD PROPOSITION.
Whatever we know of sensations that deserves the name of science is
included in the modifications of extension.
FOURTH PROPOSITION.
We can form no fixed idea of corporeal objects, nor make any
observation on the sensible world, unless we are guided by the rule of
extension.
These four propositions are nothing more than the enunciation
of certain facts, the mere exposition of which is a sufficient
demonstration.
14. Extension is the basis of geometry. This is evident, since geometry
treats only of dimensions, and the idea of dimension is essential to
extension.
When geometry treats of figures, it is still extension which it is
treating of; for figures are only extension with certain limitations.
The quadrilateral contains two triangles. To distinguish them, it is
only necessary to draw their limit, which is the diagonal. The idea of
figure is merely the idea of limited extension, and the figure is of
this or that kind according to the nature of its limits. Consequently,
the idea of figure is nothing new superadded to extension; but merely
its application.
Moreover, limit or termination is not a positive idea; it is a pure
negation. If I have extension and wish to form all the figures
possible, I need not conceive any thing new, but only abstract what I
have already; I do not add, but take away. Thus in the quadrilateral
I obtain the conception of the triangle by abstracting one of the two
equal parts into which it is divided by the diagonal. In the same
manner I deduce the quadrilateral from a pentagon by abstracting the
triangle formed by a line drawn from one of its angles to either of the
opposite angles. These observations apply to all geometrical figures.
The idea of extension is like an immense ground on which we have only
to _draw limits_ in order to obtain whatever we want.
It does not follow from this that the understanding cannot proceed
by addition or the synthetic method; for, just as the subtraction
of one of the parts of the quadrilateral formed a triangle, so
also the addition of two triangles with an equal side will produce
a quadrilateral. And in the same way points produce lines, lines
surfaces, and surfaces solids. In all these cases the idea of figure
is that of limited extension, since the quantities which constitute it
are merely extension with certain limitations.
15. An observation here presents itself to my mind, which I think must
throw great light upon the question which we are now discussing. If we
compare the two methods by which the idea of figure is obtained; the
synthetic, or that of composition or addition, and the analytic, or
that of subtraction or limitation, we shall find that the second is
more natural than the other; because that which the analytic method
produces is permanent in the figure and essential to it, whilst the
synthetic only seems to constitute it, and as soon as it is thus
constituted the marks of its formation are obliterated.
An example will make this clearer. In order to conceive a rectangle
I have only to limit indefinite space by four lines in a rectangular
position; that is, to _affirm_ a part, and _deny_ the rest. The lines
are nothing in themselves, and represent only the limit beyond which
the space included in the rectangle cannot pass. To abstract this
limitation or denial of all that is not contained in the surface of the
rectangle, would be to destroy the rectangle. Therefore, the denial
in which this method consists is always permanent, the manner of the
production of the idea is inseparable from the idea itself.
But if, on the other hand, I proceed to form the rectangle by addition
or by joining the hypotheneuse of two right-angle triangles, the
ideas of the two component parts are not necessary to the idea of
the rectangle after its formation. I can conceive the rectangle even
abstracting the diagonal.
Thus, then, it is demonstrated that the idea of extension is the only
basis of geometry, and that this idea is an immense field on which,
by means of limitation or abstraction, we can obtain all the figures
which form the object of geometry. Figures are only extension limited,
a positive extension accompanied by a negation, and consequently
whatever is positive in geometry is extension.
16. We cannot doubt that, whatever we know of the nature of bodies, may
be reduced to certain modifications or properties of extension, if we
observe that the entire object of the natural sciences is the knowledge
of the motion or of the different relations of things in space, which
is nothing more than the knowledge of the different kinds of extension.
Statics is occupied in determining the laws of the equilibrium of
bodies, but in what way? Does it penetrate into the nature of the
causes? No; it only determines the conditions to which the phenomenon
is subject, and the only ideas which enter into these conditions are
the _direction of the force_, that is to say, a _line_ in space, and
the velocity, which is the relation of space to time.
The idea of time is the only idea which is here joined with that of
extension. In another place I shall prove that time, separated from
things, is nothing, and consequently, although this idea is here joined
to that of extension, it does not interfere with the truth of what I
have established. In statics, all that relates to other sensations is
counted as nothing; in order to solve the problems of the composition
and decomposition of forces, we abstract all color, smell, and other
sensible qualities of bodies in motion. What has been said of statics
applies equally to dynamics, hydrostatics, hydraulics, astronomy, and
to all sciences which regard motion.
17. Here an objection may be made. That with the ideas of time and
space, we seem to combine another which is distinct from them, and
necessary, in order to complete the idea of motion, and this is the
idea of a body moved. It is not time, nor is it space, for space is
not moved, therefore it is distinct from them.
To this I reply, first, that I am speaking of extension, and not of
space alone, which it is important to remember, for what I shall
afterwards say; and secondly, that science regards the thing moved as a
point, and this is sufficient for all its purposes. Thus in the systems
of forces there is a point of application for each of the component
forces, and another for the resultant. This point is not regarded as
having any properties, but is in relation to motion what the centre
is in relation to a circle. Every thing is related to it, yet it is
nothing in itself, except inasmuch as it occupies a definite position
in space. It may change according to the quantity and direction of
the forces, it may run over or describe a line in space with greater
or less velocity, and the line may be of this or that class, and
accompanied by various conditions. If a body be impelled by two forces,
B and C, acting upon a point A, science considers in the body only the
point through which the resultant of the forces B and C passes, and
abstracts all the other points of the body which, being joined to the
point A, move with it.
18. When I say that the natural sciences go no farther than the
consideration of extension, I only mean to exclude the other
sensations, but not ideas; for it is clear that the ideas of time and
number are combined with the idea of extension. This is so true in
mechanics, in this sense at least, that all its theorems and problems
are reduced to geometrical expressions, and even the idea of time is
expressed by lines.
In every force there are three things to be considered: the direction,
point of application, and intensity. The direction is represented by a
line, and the point of application by a point in space. The intensity
is represented only in the effect which it can produce, and this
is expressed by a line, the length of which expresses the intensity
of the force. The effect of the intensity which is represented by a
line includes the time also; for the measure of a motion cannot be
determined until we know its velocity, which is merely the relation
of space to time. Therefore, although the idea of time is combined
with that of extension, the result is expressed by lines, that is, by
extension.
19. There is another circumstance still which shows the fruitfulness
of the idea of extension. It is that in the expression of the laws of
nature, it reaches cases which are beyond the idea of number. If we
suppose two equal rectangular forces, AB and AC, acting on the point A,
the resultant will be AR. Now, if we consider AR to be the hypotheneuse
of a right-angled triangle, AR^2 = AB^2 + AC^2, extracting the square
root AR = √(AB^2 + AC^2). If we suppose each of the component forces
equal to 1, AR = √(1^2 + 1^2) = √2, a value which can neither be
expressed in whole numbers nor in fractions, but which is represented
by the hypotheneuse.
20. In the physical sciences, such words as force, cause, agent, etc.,
are frequently used, but the ideas which these terms express are a part
of science only inasmuch as they are represented by effects. This is
not because true philosophy confounds the cause with the effect, but
as physical science regards only the phenomenon in all that relates to
the cause, it limits itself to the abstract idea of causality, which
presents nothing determinate, and consequently is not the object of its
scientific labors. The system of universal attraction has immortalized
the name of Newton, and he begins by confessing his ignorance of the
cause of the effect which he explains. When we go beyond the phenomena
and the calculations to which they give rise, we enter the field of
metaphysics.
21. The natural sciences consider certain qualities of bodies which
have no relation to extension, as, for example, heat and light, and
this might seem to be a refutation of what we have said of extension.
Still this objection disappears when we examine in what manner science
takes note of these qualities, and instead of overthrowing our thesis,
the result will strengthen, extend, and explain it.
Heat is not measured by the sensation which it produces in us. If we
enter a room where the temperature is very high, we experience a strong
sensation of heat, which gradually grows weaker, while the temperature
remains the same. If we reach our hand to a friend we experience a
sensation of heat or cold, in proportion as his hand is warmer or
colder than our own.
Heat and cold are measured, not in themselves, nor in relation to our
sensations, but in the effect which they produce. These effects are
included in the modification of extension; for the thermometer marks
the temperature by a greater or less elevation of the mercury in a
_line_. Its degrees are expressed by parts of a line, on which they are
marked.
I know that what is measured is distinct from extension; but, its
measurement is only possible by relation to extension, and by attending
to effects which are modifications of extension. Thus, the temperature
at which water boils is 212°, and this is discovered by the motion of
the water, and has relation to extension. So, also, the rarefaction
and condensation of bodies are modifications of extension, since these
states consist in the occupation of greater or less space, or in the
increase or diminution of their dimensions.
22. All that science teaches us of light and colors relates to the
different directions and combinations of the rays of light. Our
observation goes no farther than sensation. We know that we can combine
the rays in different manners, and direct them, so as to modify our
sensation, but this is nothing more than the scientific knowledge of
extension in the medium which we make use of, and of the sensation
experienced in consequence. All beyond this is entirely unknown.
23. We may say the same of all other sensations, that of touch
included. What is that quality of bodies which we call hardness? the
resistance which we encounter when we touch them? But abstracting
sensation, which only produces the consciousness of itself, what do we
find? Impenetrability. And what do we understand by impenetrability?
The impossibility of two bodies occupying the same space at the
same time. Here, then, we meet with extension. If, by hardness, we
mean the cohesion of molecules, in what does cohesion consist? In
the juxtaposition of parts in such manner that they cannot, without
difficulty, be separated. But, to be separated, is to be made to occupy
a place different from that which was before occupied. Here, too, we
find the idea of extension.
Of sound we know nothing scientifically, except as relates to extension
and motion. The musical scale is expressed by a series of fractional
numbers representing the vibrations of the air.
24. These examples demonstrate the third of the above propositions,
that whatever we know of sensations that deserves the name of science,
is included in the modifications of extension.
25. It is the same with the fourth proposition, that without the idea
of extension, we can have no fixed idea of any thing corporeal, no
fixed rule in relation to phenomena, but are like blind men. If, for
an instant, we abstract the idea of extension, it is impossible for us
to take a step in advance. The examples already adduced in order to
demonstrate the second proposition, render further explanation here
unnecessary.
26. Although extension is essentially composed of parts, there is in it
something fixed, unalterable, and, in some manner, simple. There may be
more or less extension, but not different kinds. One right line may be
longer or shorter than another, but its length is not of a different
species. One surface may be larger than another, a solid of a certain
kind greater than another of the same kind, but not in a different
manner.
When I say that in the idea of extension objectively considered there
is a _certain sort_ of simplicity, I do not mean that there is any
thing _entirely_ simple; for I have just said that its _object_ is
_essentially_ composite. Neither do I abstract its essential elements,
which are the three dimensions, nor any idea which it involves, as its
limitability, or capacity to be limited in various ways. All I wish to
show is that in all the different figures these fundamental notions are
sufficient, that they are never modified, but always present the same
thing to the mind.
Let us compare a right line with a curve. A right line is a direction
which is always constant; the curve a direction which is always
varied. A direction always varied is a collection of _right directions
infinitely small_. Therefore, the circumference of a circle is
considered as a polygon of an infinite number of sides. The curve is
therefore formed by the variety of directions reduced to infinitesimal
values. This theory which explains the difference of the right line and
the curve, is evidently applicable to surfaces and solids.
Let us compare a quadrilateral with a pentagon; all that the second has
which the first has not is one side more in perimeter, and in area the
space contained in the triangle formed by a line drawn from one of its
angles to either of the opposite angles. The lines are of the same
kind, the surfaces differ only in the ways in which they terminate. But
termination is the same as limitation. Therefore, all that is essential
to the idea of extension, that is, direction and limitability, remain
always the same and unchangeable.
This intrinsical constancy is indispensable to science. That which
is mutable, may be the object of perception, but not of scientific
perception.
CHAPTER IV.
REALITY OF EXTENSION.
27. We now come to more difficult questions. Is extension any thing in
itself, abstracted from the idea of it? If any thing, what is it? Is it
identified with bodies, or is it confounded with space?
I have proved[39] that extension exists outside of ourselves, that it
is not an illusion of the senses; and this solves the first question,
whether extension is any thing.
[39] Book II. Ch. ix.
Whatever may be its nature or our ignorance on this point, there is in
reality something which corresponds to our idea of extension. Whoever
denies this truth must be content to deny every thing except the
consciousness of himself, if indeed he does not experience doubts even
of this too. Whatever idealists may assert, there is not, nor ever was
a man who in his sound judgment seriously doubted the existence of an
external world. This conviction is for man a necessity against which it
is vain to contend.
This external world is for us inseparable from that which is
represented by the idea of extension. It either does not exist, or
else it is extended. If we could be persuaded that it is not extended,
it would not be difficult to convince us that it does not exist. For
my part, I find it just as difficult to imagine the world without
extension as without existence, and if I could be made to believe its
extension an illusion, I should easily believe its existence also an
illusion.
28. It is to be observed that although we confess our ignorance of the
internal nature of extension, it is still necessary to admit that we
know something of it; its dimensions, namely, and what serves as the
basis of geometry. The difficulty is not in knowing what extension
is geometrically considered, but what it is in reality. We know the
geometrical essence, but what we want to ascertain is, whether this
essence realized is something which is confounded with some other real
thing, or is only a quality which we know without knowing the being to
which it belongs. Without this distinction we should deny the basis of
geometry; for, it is evident that if we should not know the essence of
extension in the aforesaid manner, we could not be sure that we are not
building in the air when we raise upon the idea of extension the whole
science of geometry.
29. Thus then under this aspect, we are certain that extension exists
outside of us, and that there are true dimensions. This idea is a
necessary consequence of the idea of the external world, as we said
before. The dimensions in the external world must be subject to the
same principles as those which we conceive, or the very idea which we
have formed of the external world is reversed. I do not mean by this
that a real circle may be a geometrical circle, but only that what is
true of the second must be true of the first also, in proportion as
it is constructed with greater or less exactness. Beyond what can be
formed by the most perfect and exact instruments, I can conceive,
without passing from the order of reality, a circle or any other
figure, as near as I please to the geometrical idea. The sharpest
instrument can never mark an indivisible point, nor draw a line without
breadth; but this surface, on which the point is marked, on the line
drawn, being infinitely divisible, I can conceive a case in which the
reality will come infinitely near to the geometrical idea.
30. Astronomy and all the physical sciences rest on the supposition
that real extension is subject to the same principles as ideal
extension; and that experience comes closer to theory in proportion
as the conditions of the second are more exactly fulfilled in the
first. The art of constructing mathematical instruments, which has been
brought in our day to a surprising perfection, regards the ideal as the
type of the real order; and progress in the latter is the approximation
to the models of the former.
Theory directs the operations of practice, and these in their turn
confirm by the result the foresight of theory. Therefore, extension
exists not only in the ideal order, but also in the real; and it
is something, independently of our ideas; and geometry, that vast
representation of a world of lines and figures, has a real object in
nature.
How far the real corresponds with the ideal, we shall examine in the
next chapter.
CHAPTER V.
GEOMETRICAL EXACTNESS REALIZED IN NATURE.
31. The disagreement which we discover between the phenomena and the
geometrical theory makes us apt to think that reality is rough and
coarse, and that purity and exactness are found only in our ideas.
This is a mistaken opinion caused by want of reflection. The reality
is as geometrical as our ideas; the phenomenon realizes the idea in
all its purity and vigor. Be not startled by this seeming paradox; for
it will soon appear to you a very true, reasonable, and well-grounded
proposition.
We shall first prove that the ideas which are the elements of geometry
have their objects in the real world, and that these objects are
subject to precisely the same conditions as the ideas. This proved, it
clearly follows that geometry in all its strictness exists as well in
the real as in the ideal order.
32. Let us begin with a point. In the ideal order, a point is an
invisible thing, it is the limit of a line and its generating element,
and it occupies a determinate position in space. It is the limit of a
line; for when we take away its length, we have a point remaining which
we are forced to regard as the limit of the line unless we destroy it
entirely so as to have nothing left. The more the line is shortened
the nearer it approaches to a point, yet can never be identified with
it until its length is wholly suppressed. The point is the generating
element of the line; for we form the idea of lineal dimension by
considering a point in motion. The occupation of a determinate position
in space is another indispensable condition of the idea of a point, if
we wish to use it in geometrical figures. The centre of a circle is a
point in itself indivisible, it fills no space; but in order that it be
of any use as centre, we must be able to refer all the radii to it, and
this is impossible unless it occupy a determinate position equidistant
from all points of the circumference. As a general rule, geometry acts
upon dimensions, and these dimensions require points in which they
commence, points through which they pass, and points in which they
end, and by which distances, inclinations, and all that relates to
the position of lines and planes, are measured. Nothing of all this
can be conceived unless the point, although not extended, occupies a
determinate position in space.
33. Does there exist in nature anything which corresponds to the
geometrical point, and unites all its conditions with as great
exactness as science in its purest idealism can desire? I believe there
does.
Philosophers have adopted different opinions as to the divisibility
of matter. Some maintain that there are unextended points in which
the division ends, and that all composite bodies are formed of these.
Others assert that it is not possible to arrive at simple elements,
but the division may continue _ad infinitum_ continually approaching
the limit of composition, but never reaching it. The first of these
opinions is equivalent to the admission of geometrical points realized
in nature; the second, though apparently less favorable to this
realization, must come to it at last.
Unextended molecules are the realization of the geometrical point, in
all its exactness. They are the limit of dimension, because division
ends with them. They are the generative elements of dimension,
because they form extension. They occupy a determinate position in
space, because bodies with all their conditions and determinations
in space are formed of them. Therefore, from this opinion, held by
eminent philosophers like Leibnitz and Boscowich, it follows that the
geometrical point exists in nature in all the purity and exactness of
the scientific order.
The opinion which denies the existence of unextended points, admits, as
it necessarily must admit, infinite divisibility. Extension has parts,
and therefore is divisible; these parts, in their turn, are either
extended or not extended; if unextended, the supposition fails, and
the opinion of unextended points is admitted; if extended, they are
divisible, and we must either come at last to unextended points, or
continue the division _ad infinitum_.
I remarked above that, although less favorable to the real existence of
geometrical points, this opinion as well as the other does acknowledge
their realization. The parts into which the composite is divided are
not created by the division, but exist before the division, and without
them the division would be impossible. They do not exist because they
may be divided, but they may be divided because they exist. This
opinion therefore, does not expressly admit the existence of unextended
points, but it admits the possibility of eternally coming nearer to
them, and this not only in the ideal, but also in the real order;
because the divisibility is not affirmed of the ideas, but of the
matter itself.
Although our experience of division is limited, divisibility itself
is unlimited. A being endowed with greater powers than we possess,
might carry the division further than we are able to do. Our ability
to divide is limited, but God, by his infinite power, can push the
division _ad infinitum_, and His infinite intelligence sees in an
instant all the parts into which the composite may be divided.