the question, and is, besides, an entirely gratuitous supposition.
To take the extension of space as a term by relation to which we may
explain the extension of bodies, is to suppose that to be found which
we are looking for.
We run into the same error if we try to explain the words inside and
outside, by referring them to distinct points in space, we should
define a thing by itself; for, we have the same difficulty with respect
to space to determine the meaning of inside and outside, joined and
separated, and contiguous and distant. If we presuppose the extension
of space as something absolute, and try to explain other extensions by
relation to this, we only make the illusion more complete. We have to
explain extension in itself, the extension of space must be explained
as well as the rest; to presuppose it is to assume the question already
solved, not to solve it.
137. Extension in relation to its dimensions seems to be independent
of the thing extended in the same place. An extension may remain
absolutely fixed with the same dimensions, notwithstanding the change
of place of the thing extended. If we suppose a series of objects to
pass over a fixed visual field, the things extended vary incessantly,
but the extension remains the same. If we suppose a very large object
to pass before a window, it changes continually; for the part which we
see at the instant A is not the part which we see at the instant B, but
the extension has not varied in its dimensions. This regards surfaces
only, but the same doctrine may be applied to solids. A space may be
successively filled with a variety of objects, but its capacity remains
the same. There is no identity between the object and the extension
which contains it; for any number of objects of the same size may
occupy the same place; neither is the air, or any surrounding object,
identified with the extension; for these, too, may change without
affecting the extension in which the object is contained.
138. Though the dimensions remain fixed while the objects vary, it does
not follow that extension is purely subjective, even though we suppose
that the objects which vary cannot be distinguished. If the contrary
were maintained, the change of the dimensions would prove them to be
objective; and the argument might be retorted against our adversaries.
That the dimensions are fixed shows that different objects may produce
similar impressions; and therefore we can form an idea of a determinate
dimension or figure, without reference to the particular object to
which it does, or may correspond. No one will deny that we have the
representation of dimensions, without necessarily referring them to any
thing in particular; but what we wish to determine is, whether these
dimensions exist in reality, and what is their nature, independently of
their relations to us.
139. If we admit that continuity has no external object either in
pure space or in bodies, what becomes of the corporeal world? It is
indeed to a collection of beings which in one way or another, and in a
certain order, act upon our being.
The difficulties against the realization of phenomenal continuity
are not destroyed by appealing to the necessities of the corporeal
organization of sensible beings. If any one should ask how external
beings can act upon us, and affect our organs, if they have not in
them the continuity with which they are presented to us; such a one
would show that he does not understand the state of the question. For
it is evident that if we should take from the external world all real
continuity, leaving only the phenomenal, we should at the same time
take it from our own organization, which is but a part of the universe.
There is here a mutual relation and sort of parallelism of phenomena
and realities which mutually complete and explain each other. If the
universe is a collection of beings acting upon us in a certain order,
our organization is another collection of beings, receiving their
influence in the same order. Either both are inexplicable, or else the
explanation of one involves the explanation of the other. If that order
is fixed and constant, and its correspondence remains the same, nothing
is changed, no matter what hypothesis is assumed in order to explain
the phenomenon.
140. The object of our searches here, is the reality subject to the
condition of explaining the phenomenon, and not contradicting the order
of our ideas.
It might be objected to those who take from the external world the
phenomenal or apparent qualities of continuity, that they destroy
geometry, which is based on the idea of phenomenal continuity. But this
objection cannot stand; for it supposes the idea of geometry to be
phenomenal, whereas it is transcendental. We have already shown that
the idea of extension is not a sensation, but a pure idea, and that the
imaginary representations by which it is made sensible are not the
idea, but only the forms with which the idea is clothed.
141. All phenomenal extension is presented to us with a certain
magnitude; geometry abstracts all magnitude. Its theorems and problems
relate to figures in general abstracted absolutely from their size,
and when the size is taken into consideration it is only in so far
as relative. Of two triangles of equal bases that which has greater
altitude has the greater surface. Here the word _greater_ relates to
size, it is true; but to a relative, not to any absolute size; the
question is not of the magnitudes themselves, but of their _relation_.
Consequently, the theorem is equally true whether the triangles are
immense, or infinitely small. Therefore, geometry abstracts absolutely
all magnitudes considered as phenomena, and makes use of them only
in order to assist the intellectual perception by the sensible
representation.
142. This is an important truth, and I shall explain it further when
combating Condillac's system in the treatise on ideas, where I shall
show that even the ideas which we have of bodies neither are, nor can
be, a transformed sensation. According to these principles, geometry
is a science which makes its pure ideas sensible by a phenomenal
representation. This representation is necessary so long as geometry
is a human science, and man is subject to phenomena; but geometry in
itself and in all its purity has no need of such representations.
143. In order that this doctrine may seem less strange, and may be more
readily accepted, I will ask, whether pure spirits possess the science
of geometry? We must answer in the affirmative; for, otherwise we
should be forced to conclude that God, the author of the universe and
greatest of geometricians, does not know geometry. Does God, then, have
these representations, by the aid of which we imagine extension? No;
these representations are a sort of continuation of sensibility which
God has not; they are the exercise of the internal sense, which is not
found in God. St. Thomas calls them _phantasmata_, and says they are
not found in God, or in pure spirits, nor even in the soul separated
from the body. Therefore, the science of geometry is possible, and does
really exist without sensible representations, and, consequently, we
may distinguish two extensions, the one phenomenal, and the other real,
without thereby destroying either the phenomenon or the reality, so
long as we admit the correspondence between them; so long as we do not
break the thread which unites our being with those around us; so long
as the conditions of our being harmonize with those of the external
world.(32)
CHAPTER XX.
ARE THERE ABSOLUTE MAGNITUDES?
144. The preceding doctrine will seem much more probable if we reflect
that all purely intellectual perceptions of extension may be reduced
to the knowledge of order and relation. There is nothing absolute in
the eyes of science, not even of mathematical science. The absolute, in
relation to extension, is an ignorant fancy which the observation of
the phenomena is sufficient to dissipate.
In the order of appearances there are no absolute magnitudes; all are
relations. We can not even form an idea of a magnitude, unless with
reference to another which serves for a measure. The absolute is found
only in number, and never in extension; a magnitude is absolute, not
in itself, but only by being numbered. A surface two feet square,
presents two distinct ideas; the number of its parts, and the kind of
parts. The number is a fixed idea, but the kind is purely relative. I
will try to make this clearer.
145. When I speak of a surface four feet square, the number four is a
simple, fixed, and unchangeable idea; but I can explain a square foot
only by relations. If I am asked what is a square foot, I can answer
only by comparison with a square rod or a square inch; but if I am
again asked what is a square rod or a square inch, I am again forced
to recur to other measures which are greater or smaller; I can nowhere
find a fixed magnitude.
146. If there were some fixed measure it might be some dimension
of the body, my hand, or foot, or arm. But who does not see that
the dimensions of my body are not a universal measure, and that the
hands, or feet, or arms, of all men are not equal? And even in the
same individual they are subject to a thousand changes more or less
perceptible. Shall we take for our fixed measure the radius of the
earth, or of a heavenly body? But one has no claim to preference before
the other. Every one knows that astronomers take sometimes the radius
of the earth, and sometimes the radius of its orbit as the unity of
measure. If we suppose these radii to be greater or smaller, can we not
equally in either case take them as the measure? They are preferred
because they do not change.
But even astronomers regard these magnitudes as purely relative, and at
one time consider them infinitely large, at another infinitely small,
according to the point of view from which they look at them. The radius
of the earth's orbit is considered infinite in comparison with a small
inequality on the earth's surface, and infinitely small when compared
with the distance of the fixed stars.
We can form no idea of these measures except by comparison with those
in constant use. What idea should we have of the magnitude of the
radius of the earth if we did not know how many million measures it is
equal to? What idea should we have in turn of these measures if we had
nothing constant to which we could refer them?
147. There is something absolute in magnitudes, it may be objected;
for a foot is a certain length which we both see and touch, and cannot
be greater or smaller; the surface of a square yard is in like manner
something definite which we see and which we touch; and the same may
be applied to solids. There is no necessity of going farther to find
that which is so clearly presented to us in sensible intuition. This
objection supposes that there is something fixed and constant in
intuition; this is false. I appeal to experience.
It is probable that men see the same magnitudes very differently
according to the disposition of their eyes. No one is ignorant that
this happens when the objects are at a distance; for, then, one sees
clearly what another cannot even distinguish; to one it is a surface,
while to another it is not even so much as a point. We all know what a
great variety there is in the size of objects when looked at through
differently graduated glasses. From all this we conclude that there is
nothing fixed in phenomenal magnitude; but that every thing is subject
to continual changes.
When we look through a microscope objects which were before invisible,
take large dimensions; and as the microscope may be infinitely
perfected, it is not absurd to suppose that there are animals to whom
what is invisible to us appears larger than the whole earth. The
construction of the eye may also be considered in an inverse sense, and
as infinite perfection is also possible in this case, it is possible
that magnitudes which to us are immense may be invisible to other
beings. To this eye of colossal vision the terrestrial globe would
perhaps be an imperceptible atom. This is no more than what happens by
the interposition of distance; immense masses in the firmament seem to
us to be only small specks of light.
148. It must now be very evident that there is nothing absolute in
magnitudes of sight; but that all is relative, and that objects
appear to us greater or less, according to habit, the construction
of our organs, and other circumstances. The variety of appearances
is in accordance with philosophy; since no necessary relation can
be discovered between the size of the organ and the object. What
connection is there between a narrow surface like the retina of our eye
and the immense surfaces which are painted on it?
149. From sight we may pass to touch, but we find no reason of the
fixity of phenomenal magnitude. The sense of touch gives us the ideas
of magnitudes by relation to the time it takes to pass over them, and
to the velocity of our motion. The ideas of time and velocity are
also relative; they refer to the space passed over. When we measure
velocity we say that it is the space divided by the time; in measuring
time we say that it is the space divided by the velocity; and we
measure space by multiplying the velocity by the time. All these ideas
are correlative, and are measured by each other, and by their mutual
relations. This shows that these ideas have nothing absolute; their
whole character is that of a relation which is incomplete, or rather
does not exist, if one of the terms is wanting.
150. We shall find it equally impossible to determine these measures
by the impressions which the motion causes in us. If for example we
propose to measure the degree of velocity, by the agitation which
we feel in our body, we shall find that the measure varies with the
agitation, but this agitation depends on the degree of force exerted,
and still more on the strength of the subject. Thus a little child is
obliged to run till he is almost out of breath, to keep up with his
father who is walking fast.
The impossibility of any fixed measure by means of impressions will
be still more apparent if we compare the motion of a horse with the
motion of a microscopic animal. The distance which a horse would pass
over almost without any sensible motion, would require the microscopic
animal to display its whole activity, and run perhaps a whole day.
The horse would scarce believe he had changed his place, whereas the
poor animalcule would at night be overcome by fatigue like one who has
travelled a long journey. Compare now the motion of the horse with the
motion of those fabulous giants who piled up mountains to scale the
heavens; a single step of one of those giants would be a long distance
for the horse to travel.
151. Art seems to be in accordance with science on this point. In art,
size is nothing, the only thing which is regarded is the proportion
or relation. A skilful miniature represents a person as clearly as a
painting the size of life. The same principle is applied to all the
objects embraced by art, the artistic thought never refers directly to
the size; proportion, the _relative_ is all that is attended to; the
absolute counts for nothing. We see the system of relations transferred
to the order of appearances, inasmuch as they affect the faculties
susceptible of pleasure; reason is thus admirably harmonized with
sentiment, in the same manner as we have found intellect harmonized
with the senses.
CHAPTER XXI.
PURE INTELLIGIBILITY OF THE EXTENDED WORLD.
152. Objects in themselves do not change their nature, by the
variety of appearances which they produce in us. A polygon turning
with rapidity has the appearance of a circle; the stars appear like
small points; and considering the various classes of objects, we
may observe that there is a great variety of appearances depending
on circumstances. The nature of a being does not consist in what it
appears, but in what it is. Suppose there were no sensitive being
in the world, the present order of sensibility would disappear; for
without sensitive beings there would be no representations. What would
the world be in that case? This is a great problem of metaphysics.
153. A pure spirit,--the existence of which we must always suppose;
for, though all finite beings were annihilated, there would still
remain the infinite being which is God,--a pure spirit would know
the extended world _just as it is in itself_, and would not have
the sensible representations either external or internal, which we
have. This is certain, unless we mean to attribute imagination and
sensibility to pure spirits, and even to God himself.
On this supposition I ask, what would a pure spirit know of the
external world? or, to speak more properly, since the existence of
such a spirit is certain and its intelligence infinite, what does this
spirit know of the external world?
154. That which this spirit knows of the world is the world, because
he cannot be deceived. But this spirit does not know the world under
any sensible form. Therefore the world may be known without any of the
forms of sensibility, and consequently may be the object of a pure
intelligence.
There is no difficulty on this point in what regards sensations. It is
only necessary that we should say that the pure spirit knows perfectly
the principle of causality which resides in the object, and produces
the impressions which we experience. There is no need of attributing to
the intelligent spirit any sensation of the thing understood.
This question is more difficult when we come to explain what relates
to extension. For, if we say that the spirit only knows the principle
of causality of the subjective representation of the extended, it
follows that there is no true extension in the objects, because the
spirit sees all that there is, and if the spirit does not see it, it
is because it is not. We fall into Berkeley's idealism; an external
world without extension is not the world of common sense, but the
world of the idealists. If, on the other hand, we say that this pure
spirit does know extension, we seem to attribute to the spirit sensible
representation; because the extension represented seems to involve
sensible representation. What is an extension with lines, surfaces, and
figures? And these objects, as we understand them, are sensible; if,
however, they be taken in another sense, the extension of the world
will be of another nature, it will be something of which we have no
idea; and here again we fall into idealism.
155. To solve this difficulty, which is really a serious one, it is
necessary to recollect the distinction on which I insisted so earnestly
between extension as sensation and extension as idea. The former can
become subjective only in a sensible being; the second may be, and
is, subjective in a purely intellectual being. Extension as sensation
is something subjective, it is an appearance; its object exists in
reality, but without including in its essence any thing more than
is necessary in order to produce the sensation. Extension as idea is
also subjective; but it has a real object which corresponds to it, and
satisfies all the conditions of the idea.
156. Does not this theory seem to establish two geometries? We must
distinguish. The scientific and the pure ideal geometry will remain the
same, save the difference of the intelligences which possess it. But
notwithstanding this difference, what is true in one is true in the
other. Empirical geometry as the representative part of geometry will
be different: we have the idea only of our own.
157. In fact we observe two parts in geometry even in ourselves; the
one purely scientific, the other of sensible representation. The
former includes the connection of ideas; the latter the images and
particular cases by means of which we make the ideas sensible: the
first is the ground; the second is the form. But although the two
are different, we cannot separate them entirely: we cannot have the
geometrical idea without the sensible representation, we understand
it only _per conversionem ad phantasmata_, as say the scholastics.
Thus the two orders of geometry, the sensible and the intellectual,
though different, are always joined in us; whether because the pure
geometrical idea arises from the sensible, or is excited by it, or
because this is perhaps a necessary primitive condition imposed on our
mind by its union with the body.
158. This shows how the pure geometry may be separated from the
sensible, and how it may exist in pure intellectual beings, without any
of the forms which represent the geometrical idea in sensible beings.
159. But what becomes of extension in itself and stripped of all
sensible form? When we speak of extension stripped of all sensible
form, we do not mean to deprive it of its capacity to be perceived
by the senses, we merely abstract the relations of this capacity to
sensible beings. Extension is then reduced, not to an imaginary space,
nor to an eternal and infinite being, but to an order of beings, to
the sum of their constant relations subject to necessary laws. What
then are these relations? I know not. But I know that they exist and
that these necessary laws exist. That they exist in reality I know by
experience, which gives testimony of their existence; that they are
possible, I know on the authority of my ideas, the connection of which
forces my assent to their intrinsical evidence.
160. That this evidence touches but one aspect of the object, is true;
that there are many things in the object which we do not know, is
likewise true; but this only proves that our science is incomplete, not
that it is illusory or false.
161. It is difficult for us to conceive the pure intelligibility of
the sensible world, both because our ideas are always accompanied by
representations of the imagination, and because we try to explain it by
simple addition and subtraction of parts, as though all the problems
of the universe could be reduced to expressions of lines, surfaces,
and solids. Geometry plays an important part in all that regards the
appreciation of the phenomena of nature; but when we want to penetrate
to the essence of things, we must lay aside geometry and take up
metaphysics.
There is no more seductive philosophy than that which reduces the
world to motions and figures, but at the same time there is none
more superficial. A slight reflection on the reality of things shows
the insufficiency of such a system. For, though the imagination be
satisfied with it, the understanding is not, and it takes a noble
revenge on its unfaithful companion, when, forcing the imagination to
fix itself upon objects, the understanding sinks it in an ocean of
darkness and contradiction. Those who laugh at the forms, the acts, the
forces, and other such expressions used with more or less exactness
in different schools, ought to reflect that even in the physical
world there is something more than is perceived by the senses; and
that even sensible phenomena cannot be explained by mere sensible
representations. Physical science is not complete until it calls to its
aid metaphysics.
The best proof of this will be found in the next chapter, where we
shall see the imagination entangled in its own representations.
CHAPTER XXII.
INFINITE DIVISIBILITY.
162. The divisibility of matter is a question that torments
philosophers. Matter is divisible because it is extended, and there is
no extension without parts. These parts are extended or are not: if
they are, they are again divisible; if they are not, they are simple,
and in the division of matter we must come to unextended points.
This last consequence can be avoided only by recourse to the infinite
divisibility of matter, and even this is a means of escaping the
difficulty rather than a true solution. I intimated elsewhere[52] that
infinite divisibility seems to suppose the very thing which it denies.
Division does not make the parts, it supposes them; that which is
simple cannot be divided; therefore, the parts which may be divided
pre-exist in the infinitely divisible composition.
[52] Chap. v.
Let us imagine God to exert his infinite power in dividing, will he
exhaust divisibility? If you say no, you seem to place limits to his
omnipotence; if you say yes, we shall have arrived at simple points,
as otherwise the divisibility would not be exhausted.
Even supposing that God does not make this division, his infinite
intelligence certainly sees all the parts into which the composite
is divisible; these parts must be simple, or else the infinite
intelligence would not see the limit of divisibility. If you answer
that this limit does not exist, and therefore cannot be seen, I reply
that we must then admit an infinite number of parts in each portion
of matter; there would, in this case, be no limit of divisibility,
because the number of parts would be inexhaustible; but this infinite
number would be seen by the infinite intelligence, as it is, and all
these parts would be known as they are. The difficulty still remains;
these parts are simple or composite; if simple, the opinion which we
are opposing does, at least, admit unextended points; if composite,
the same argument may be repeated; they are again divisible. We shall
then have a new infinite number in each one of the parts of the first
infinite number; but as this series of infinities must be always known
to the infinite intelligence, we must come to simple points, or else
say that the infinite intelligence does not know all that there is in
matter.
It does not mend the matter to say that the parts are not actual but
only possible. In the first place, possible parts are existing parts,
because, if the parts are not real, there must be real simplicity, and
consequently, indivisibility. Secondly, if they are possible, they may
be made to exist by the intervention of an infinite power; and then
what are these parts? they are either extended or unextended, and the
matter returns to where it was before.
163. Some say that a mathematical quantity, or a body mathematically
considered, is infinitely divisible, but that natural bodies are not,
because their natural form requires a determinate quantity. This is the
explanation which was given in the schools; but it is very clear that
there is no ground for affirming that these natural bodies require a
certain quantity, beyond which division is impossible. This cannot be
proved either _a priori_ nor _a posteriori_: not _a priori_, because we
do not know the essence of bodies, and cannot say that there is a point
where the natural form requires the limit of divisibility; neither can
it be proved _a posteriori_, because the means of observation at our
disposal are so coarse, that it is impossible for us to reach the last
limit of division and discover a part which cannot be divided. Besides,
when we reach this quantity beyond which division cannot go, we have a
true quantity, by the supposition; if it is quantity it is extended; if
it is extended it has parts; if it has parts it is divisible. Therefore
there is no reason for saying that there is any natural form which
limits division.
164. The distinction between a natural and a mathematical body is
not admissible in what relates to division. This is a result of the
nature of extension, which is real in natural bodies, and ideal in
mathematical. That the parts in natural bodies are not actual but
possible, may be understood in two ways; it may mean that they are
not actually separated; or, that they are not distinct. That they are
not separated has no bearing on the question; for division may be
conceived without separating the parts. But, if they are not distinct,
the division is impossible; for it cannot even be conceived where the
things are not distinct.
165. This distinction seems to have originated in the attempt to avoid
the necessity of admitting infinite divisibility in natural bodies.
But the difficulty still remaining with regard to mathematical bodies,
the philosophical mystery still subsists. It consists in this, that
no limit can be assigned to division so long as there is any thing
extended; and, on the other hand, if, in order to assign this limit,
we come to simple points, then it is impossible to reconstitute
extension. The difficulty arises from the very nature of extended
things, whether realized or only conceived; the real order escapes
none of the difficulties of the ideal. If ideal extension cannot be
constituted out of unextended points, neither can real extension; if
ideal extension has no limit to its divisibility until we come to
simple points, the same is also true of real extension; for in both it
is a result of the essence of extension, and inseparable from it.
CHAPTER XXIII.
UNEXTENDED POINTS.
166. There are two strong arguments against the existence of unextended
points: the first is, that we must suppose them infinite in number, for
otherwise it does not seem possible to arrive at the simple, starting
from the extended: the second is, that even supposing them infinite in
number they are incapable of producing extension. These arguments are
so powerful as to excuse all the aberrations of the contrary opinion,
which, however strange they may seem, are not more strange than the
simple forming extension, and the smallest portion of matter containing
an infinite number of parts.
167. It does not seem possible to arrive at unextended points unless by
an infinite division. The unextended is zero in the order of extension,
and in order to arrive at zero by a decreasing geometrical progression
it must be continued _ad infinitum_. Mathematical calculation presents
a sensible image of this. When two parts are united they must have a
side where they touch, and another where they are not in contact.
If we separate the interior side from the exterior we have two new
sides, one which touches and another which does not. Continuing the
division the same thing happens again; we must, therefore, pass
through an infinite series in order to arrive at the unextended,
which is equivalent to saying that we shall never arrive there. To
continue the division _ad infinitum_ we must suppose infinite parts,
and consequently the existence of an actual infinite number. From the
moment that we suppose this infinite number to exist it seems to become
finite, since we already see a limit to the division, and also other
numbers greater than it. Let us suppose that this infinite number of
parts is found in a cubic inch; there are numbers which are greater
than this which we suppose infinite; a cubic foot, for example, will
contain 1,728 times the infinite number of parts contained in the cubic
inch.
Thus the opinion of unextended points seeking to avoid infinite
division, runs into it; just as its adversaries trying to escape from
unextended points are forced to acknowledge their existence. The
imagination loses itself and the understanding is confused.
168. The other objection is not less unanswerable. Suppose we have
arrived at unextended points, how shall we reconstitute extension? The
unextended has no dimensions; therefore, no matter how many unextended
points we may take, we can never form extension with them. Let us
imagine two points to be united, as neither of them alone occupies
any place, neither will they both together. We cannot say that they
penetrate each other; for penetration cannot exist without extension.
We must admit that these parts being zero in the order of extension,
their sum can never give extension, no matter how many of them we may
add together.
169. It is certain that a sum of zeros can give only zero for the
result, but mathematicians admit that there are certain expressions
equal to zero, which multiplied by an infinite quantity will give a
finite quantity for the product. 0 + 0 + 0 + 0 + N × 0 = 0; but if we
take 0/M = 0, and multiply it by the expression M/0 = 0, we shall have
(0/M) × (M/0) = (0 × M)/(M × 0) = 0/0 which is equal to any finite
quantity, which we may express by A. This is shown by the principles of
elementary algebra only; if we pass to the transcendental we have dz/dx
= o/o = B; B expressing the differential coefficient which may be equal
to a finite value. Can these mathematical doctrines serve to explain
the generation of the extended from unextended points? I think not.
It is evident that, multiplication being only addition shortened, if
an infinite addition of zeros can give only zero; multiplication can
give no other result, although the other factor be infinite. Why then
do mathematical results say the contrary? This contradiction is not
true, but only apparent. In the multiplication of the infinitesimal by
the infinite we may obtain a finite quantity for product, because the
infinitesimal is not regarded as a true zero, but as a quantity less
than all imaginable quantities, but still it is something. If this
condition were wanting, all the operations would be absurd, because
they would turn upon a pure nothing. Shall we therefore say that the
equation, dz/dx = o/o, is only approximate? No; for it expresses the
relation of the limit of the decrement, which is equal to B only
when the differentials are equal to zero. But as geometricians only
consider the limit in itself, they pass over all the intervals of the
decrement, and place themselves at once at the point of true exactness.
Why then operate on these quantities? Because the operations are a
sort of algebraic language, and mark the course that has been followed
in the calculations, and recall the connection of the limit with the
quantity to which it refers.
170. Unity which is not number produces number; why then cannot points
without extension produce extension? There is a great disparity between
the two cases. The unextended, as such, involves only the negative
idea of extension; but in unity, although number is denied, this
negation does not constitute its nature. No one ever defined unity
to be the negation of number, yet we always define the unextended to
be that which has no extension. Unity is any being taken in general,
without considering its divisibility; number is a collection of
unities; therefore the idea of number involves the idea of unity, of
an _undivided_ being, number being nothing more than the repetition
of this unity. It belongs to the essence of all number that it can be
resolved into unity; it contains unity in a determinate manner. But the
extended can not be resolved into the unextended, unless by proceeding
_ad infinitum_, or else by some process of decomposition which we know
nothing of.
CHAPTER XXIV.
A CONJECTURE ON THE TRANSCENDENTAL NOTION OF EXTENSION.
171. The arguments for or against unextended points, for or against
the infinite divisibility of matter seem equally conclusive.
The understanding is afraid that it has met with contradictory
demonstrations; it thinks it discovers absurdities in infinite
divisibility, and absurdities in limiting it; absurdities in denying
unextended points, and absurdities in admitting them. It is invincible
attacking an opinion, but its strength is turned into weakness as
soon as it attempts to establish or defend any thing of its own. Yet
reason can never contradict itself; two contradictory demonstrations
would be the contradiction of reason, and would produce its ruin;
the contradiction can, therefore, only be apparent. But who shall
flatter himself that he can untie the knot? Excessive confidence on
this point is a sure proof that one has not understood the true state
of the question, and such vanity would be punished by the conviction
of ignorance. With all these reserves I now proceed to make a few
observations on this mysterious subject.
172. I am inclined to believe that in all investigations on the
first elements of matter, there is an error which renders any result
impossible. You wish to know whether extension may be produced from
unextended points, and the method which you employ consists in
imagining them already approached, and then trying to see if any part
of space can be filled by them. This seems to me like trying to make a
denial correspond to an affirmation. The unextended point represents
nothing determinate to us except the denial of extension; when,
therefore, we ask if this point joined with others like it can occupy
space, we ask if the unextended can be extended. Our imagination makes
us presuppose extension in the very act in which we wish to examine
its primitive generation. Space, such as we conceive it, is a true
extension; and, as has been shown, is the idea of extension in general;
to imagine, therefore, that the unextended can fill space, is to change
non-extension into extension. It is true that this is precisely what is
required, and in this consists the whole difficulty; but the error is
in attempting to solve it by a juxtaposition which makes these points
both unextended and extended, an evident contradiction.
173. In order to know how extension is generated, it would be necessary
to free ourselves from all sensible representations, and from all
ideas which are in the least degree affected by the phenomenon, and to
contemplate it with an eye as simple, a look as penetrating, as that
of a pure spirit. It would be necessary to take from all geometrical
ideas all phenomenal forms, all representations of the imagination,
and present them to the imagination purified from all mixture with the
sensible order. It would be necessary to know how far extension, real
continuity, agrees with the phenomenal. It would, in fine, be necessary
to eliminate from the object perceived, all that relates to the subject
which perceives it.
174. In extension, as we have already seen, there are two things to
be considered; multiplicity, and continuity. As to the first, there
is no objection to supposing that it may be the result of unextended
points, since number results from various units whether they are
simple or composite. But the difficulty is with regard to continuity,
which sensible intuition clearly presents to us as the basis of the
representations of the imagination, but the nature of which is a
puzzle to the understanding. It may perhaps be said that continuity,
abstracted from the sensible representation, and considered only in
the transcendental order, is, in its reality and as it appears to a
pure spirit, nothing more than the constant relation of many beings,
which are of a nature to produce in a sensitive being the phenomenon of
representation, and to be perceived in the intuition which we call the
representation of space.
According to this hypothesis extension in the external world is real,
not only as a principle of causality of our impressions, but also as
an object subject to the necessary relations which we conceive.
175. But, then, it will be asked, is the external world such as
we imagine it? To this we must answer, in accordance with what we
have said when treating of sensations, that it is necessary to take
from sensations all that is subjective, and which by an innocent
illustration we look upon as objective; we may then say that extension
really exists outside of us and independent of our sensations;
considered in itself, it exists free from all sensible representation,
and in the same manner in which a pure spirit may perceive it.
176. We see no objection which can reasonably be made to this theory
which affirms the reality of the corporeal world, at the same time that
it settles the difficulties of idealism. To give my opinion in a few
words, I say: That extension in itself, exists such as God knows it,
and in the cognition of God there is no mixture of any of the sensible
representations which always accompany man's perception. That which is
positive in extension is multiplicity, together with a certain constant
order; continuity is nothing more than this constant order, in so far
as sensibly represented in us, it is a purely subjective phenomenon
which does not at all affect the reality.
177. We may even assign a reason why sensible intuition has been given
to us. Our soul is united to an organized body,--that is to say, a
collection of beings bound together by constant relation to each other
and to the other bodies of the universe. In order that the harmony
might not be interrupted, and that the soul which presides over this
organization might rightly exercise its functions, there was need of
a continued representation of this collection of the relations of our
own and other bodies. This representation must be simultaneous and
independent of intellectual combinations; for otherwise the animal
faculties could not be exercised with the promptness and perseverance
which the satisfaction of the necessities of life demands. Therefore
it is that all sensible beings, even those which have not reason, have
been endowed with this intuition of extension or space: which is like
an unlimited field on which the different parts of the universe are
represented.
CHAPTER XXV.
HARMONY OF THE REAL, PHENOMENAL, AND IDEAL ORDERS.
178. We may consider two natures in the external world, the one real,
the other phenomenal; the first is particular and absolute, the second
is relative to the being which perceives the phenomenon; by the first
the world is, by the second it _appears_. A pure intellectual being
knows the world as it _is_; a sensitive being experiences it as it
_appears_. We can discover this duality in ourselves; in so far as we
are sensitive beings, we experience the phenomenon, but in so far as
intelligent, although we do not know the reality, we attempt to reach
it by reasoning and conjecture.
179. The external world in its real nature, abstracted from the
phenomenal, is not an illusion. Its existence is known to us not by
phenomena only, but by principles of pure intelligence which are
superior to all that is individual and contingent. These principles,
based on the data of experience,--that is, on sensations the existence
of which we know from consciousness, assure us that the objectiveness
of sensations, or the reality of the external world, is a truth.
180. This distinction between the essential and the accidental, and
between the absolute and the relative, was admitted in the schools.
Extension was considered not as the essence, but as an accident
of bodies; the relations of bodies to our senses are not founded
immediately on their essence, but on their accidents. Matter and
substantial form united constitute the essence of bodies; the matter
receiving the form, and the form actuating the matter. Neither the
matter nor the substantial form can be immediately perceived by the
senses, because this perception requires the determination of figure
and other accidents distinct from the essence of body.
Therefore the scholastics distinguished sensible objects into three
classes; particular, common, and accidental, _proprium, commune, et
per accidens_. The particular is that which appears immediately to
the senses, and is only perceived by one of them, as color, sound,
taste, and smell. The common is that which is perceived by more than
one sense, as figure, which is the object of sight and of touch. The
accidental is that which is not directly perceived by any of the
senses, but is hidden under sensible qualities, by means of which
it is discovered, as are substances. The sensible _per accidens_ is
connected with sensible qualities; but they do not present it to the
understanding as an image presents the original, but as a sign the
signified. Hence they did not consider the sensible _per accidens_ as
proceeding from the _species_ and reducing the sensitive faculty to
act: it was intelligible rather than sensible.
181. In the corporeal universe considered _in its essence_, there
is no necessity of supposing any thing resembling the sensible
representation, but we must suppose the object to correspond to the
idea; for otherwise we should have to admit that geometrical truths may
be contradicted by experience.
182. Although extension is an order of beings of which we cannot form
a perfect conception, because we cannot purify our ideas from all
sensible form, still this order must correspond to our ideas, and even
to our sensible representations, so far as is necessary to prove the
truth of the ideas.
It is evident that although the phenomenal order is distinct from the
real, it depends on it, and is connected with it by constant laws.
If we suppose that there is no parallel between the reality and the
phenomenon, and that the reality has not all the conditions necessary
to satisfy the demands of the phenomenon, there can be no reason why
the phenomena should be subject to constant laws, and why experience
should not suffer continual confusion. Without a fixed and constant
correspondence between the reality and the appearance, the world
becomes a chaos to us, and all regular and constant experience becomes
impossible.
183. Let us examine this at greater length. One of the elementary
propositions of geometry says: "When two straight lines intersect each
other, the opposite or vertical angles, which they form, are equal."
In order to demonstrate this, I must have the internal intuition of
two lines intersecting each other. But the geometrical proposition is
not confined to any particular intuition, but embraces all that can be
imagined, without any limit to their number, or any determination as to
the measure of the angles, the length of the lines, or their position
in space.
Here the pure idea extends to an infinity of cases, whereas the
sensible intuition represents them only one at a time, and isolated
if represented successively. The understanding is not limited to the
affirmation of this relation between the ideas, but applies it to the
reality, and says: Whenever the conditions of this ideal order are
realized, that which I see in my ideas is true in reality, and the
relation expressed will be more or less exact in proportion to the
exactness of the realization of the conditions; the more delicate
the real lines are, that is, the more they approach the condition of
right lines, the nearer will the relation of the two angles approach
to perfect equality. This conviction is founded on the principle of
contradiction, which would be false if the proposition were not true;
and it is confirmed by experience, so far as it touches the conditions
of the ideal order.
184. What is there in reality which corresponds to this proposition? An
existing or real line is an order of beings; two lines which intersect
each other are two orders of beings with a determinate relation; the
angle is the result of this relation, or, rather, it is the relation
itself; the equality of the opposite angle is the correspondence of
these relations in the ratio of equality by the continuation of the
same order in another sense. These relations between the orders and the
beings, and the correspondence of these orders to each other, is what
corresponds in reality to the pure geometrical idea, or to the idea
separated from all sensible representation. Since the relations of the
idea have their corresponding objects in the relations of the reality,
geometry exists not only in the ideal order, but also in the real.
Since the phenomenon or sensible representation is subject to the same
conditions as the idea, because the order of phenomena presents certain
relations of the same nature as the relations of the idea and the fact;
the idea, the phenomenon, and the reality agree, and it is explained
why the intellectual order is confirmed by experience, and experience
receives with confidence the direction it gives.
185. This harmony must have a cause; we must look for a principle which
is the sufficient reason of this wonderful agreement between things so
distinct. Here new problems arise which overwhelm the understanding,
but at the same time expand and invigorate it by the grandeur of the
spectacle presented to its view, and the immensity of the field opened
to its investigations.
CHAPTER XXVI.
CHARACTER OF THE RELATIONS OF THE REAL ORDER TO THE PHENOMENAL.
186. Is the agreement of the idea, the phenomenon, and the reality
necessary, is it founded on the essence of things, or has it been
freely established by the will of the Creator?
If the world had no other reality than that expressed by the sensible
representation, if the appearances were an exact copy of the essence
of things, we should have to say that this agreement is unalterable,
that things are what they appear, and that if we suppose them to exist,
it is absolutely necessary that they should be just what they appear;
for nothing can be in contradiction with its constitutive notion. That
which now is extended, would be necessarily extended, and could not but
be extended in the _same manner_ in which it appears to us, and under
the _same conditions_; the relation of bodies to each other would be
necessarily subject to the same phenomenal laws, and all which does not
come under this order would be a contradiction, and beyond the limit of
omnipotence.
187. Bodies are presented to us in the sensible intuition with a
determinate magnitude, and in a certain fixed relation which we
calculate by comparison with an immovable extension, such as we imagine
space. By magnitude, bodies occupy a certain space, determinate,
though changeable by motion; by the relation of magnitudes they occupy
a greater or smaller place, and mutually exclude each other; this
exclusion is called impenetrability. The question to be examined here
is, whether the determination of magnitudes, and their relation in
respect to the occupation of place, are things absolutely necessary, so
that their alteration involves a contradiction, or not. I answer that
they are not.
188. Relation to place considered as a portion of pure space,
means nothing; for I have already shown that this space is only
an abstraction of our understanding, and that in itself it has no
reality,--it is nothing. Therefore the relation to it must be nothing
also, because the relation is destroyed if one of the terms is nothing.
Therefore, the relations of bodies to place can only be the relations
of bodies to one another.
189. This is the principal thing to be noticed in this question.
The understanding gets confused when it begins by supposing space
an absolute nature with necessary relation to all bodies. We must
remember the doctrine of the chapters,[53] where we explained how the
idea of space is generated in us, what object corresponds to this idea
in reality, and how; and we shall easily perceive that the absolute
and essential relations which we think we discover between bodies
and a _vacant and real_ capacity, are illusions of our imagination,
in consequence of our not sufficiently purifying the ideal order by
separating from it all sensible impressions. We cannot understand so
much as the meaning of these questions, if we do not make an attempt at
this separation as far as is possible to our nature. If this is done,
then the questions proposed in the following chapters will appear very
philosophical, and their solution will seem probable, if not true; but
they must seem absurd, if we confound the pure intellectual order with
the sensible. We cannot admit the idealism which destroys the real
world; but the empiricism which annihilates the ideal order, is equally
objectionable. If we cannot rise above the sensible representations,
let us renounce philosophy, give up thinking, and confine ourselves to
sensation.
[53] XII., XIII., XIV., and XV.
CHAPTER XXVII.
WHETHER EVERY THING MUST BE IN SOME PLACE.
190. Is it necessary that whatever exists should be in some place?
This question may seem strange, but it is profoundly philosophical.
_To be_ is not the same as _to be in a place_. To be, whether taken
substantively as signifying to exist, or copulatively, as expressing
the relation of the predicate to the subject, does not involve the
idea of being in a place. The relation of an object to place is not
necessary to it; for it is not contained in the notion of object. It is
something added to the object, whether it is given to the object with
more or less foundation by ourselves, or the object has it in reality
by communication from some other.
The imagination can represent nothing which does not occupy a place,
but the understanding may conceive things that are not situated in
any place. When we reflect on the essence of objects, what position
does our mind give them? The intellectual act is always accompanied
by sensible representations, which sometimes assist it, and sometimes
embarrass and confuse it; but in either case the act of the
understanding is always distinct from these representations.
191. There is no reason for saying that every thing must occupy a
place. The imagination cannot see how any thing can exist otherwise,
but the understanding finds no absurdity in it, and it is in accordance
with the principles of philosophy. If place considered in itself is
only a part of space terminated by a surface, and space abstracted from
bodies is nothing, the relation to place or to points in space must be
nothing. We must have bodies in order to have a term of the relation;
therefore, if we suppose a being which has no relation to bodies, it is
not necessary that it should be in any place.
192. The relation of a being to bodies may be of three kinds: that of
commensuration, as is the relation of lines, surfaces, and solids to
each other; that of generation, as we conceive the line generated by
the point; and that of action in general, as we conceive the relation
of pure spirits to matter. The first cannot exist if the object has
no dimensions; for then it cannot be measured; the second can exist
only in unextended or infinitesimal points, from which extension is
generated; therefore these two relations can only exist between bodies,
or their generative elements. Therefore, nothing which is not a body or
an element of body, can occupy _place_ under either of these aspects.
As to the third relation, that of action of a cause upon a body, it
may be found in all agents capable of acting upon matter; but it is
evident that the position which results from this, is something very
different from that which we conceive in bodies or their elements; it
is something of a wholly distinct order, and belongs rather to the pure
idea of causality than to the intuition of space.
193. We can conceive a being which is not a body, nor an element of
body, and which does not exercise any action on bodies; in this case,
this being has none of the three relations of which we have spoken,
consequently it is not in any place, and to say that it is here, or
that it is there, that it is near or distant, would be using words
without meaning.
194. Viewed from the point of this doctrine, the following questions
are easy to answer:
Where must a pure spirit be which has no relation of causality nor
influence of any kind upon the corporeal world? Nowhere. The answer
will not seem strange to one who understands that the question is
absurd. In the case supposed, there is no _where_, for this involves a
relation and there are no relations here.
Where would the pure spirits be if the world did not exist? Nowhere,
unless we have a mind to say they would be in themselves. But, the word
_to be_ does not mean the position of which we are speaking here, but
only the existence of the spirit, or its identity with itself.
Where was God before the world was created? _He was_, but he was not in
_any place_; for he has no parts.
195. I wish here to expose an error of Kant. This philosopher believed
that space was conceived by us as a condition of all existence in
general, and on this he founded one of his arguments that space was a
purely subjective form. In the second edition of his _Critic of pure
Reason_, explaining the subjectiveness of space, he seems to hold,
that we do not even conceive things in the pure intellectual order,
without referring them to space. He observes that in natural theology,
when treating of things which cannot be the object of intuition either
for us or for themselves, we are very careful not to attribute to
this intuition or manner of perception time and space, which are the
conditions of human intuition. "But," he adds, "by what right do we
proceed thus, when time and space have already been established as
the forms of things in themselves, and conditions of their existence
_a priori_, subsisting still after all else has been annihilated by
thought? As conditions of all existence in general, they must be the
conditions of the existence of God. If we do not make space and time
the objective forms of _all_ things, it _only remains_ for us to make
them the subjective forms of our mode of intuition, as well internal
as external." Kant is right in saying that space and time ought not
to be considered as real forms, not susceptible of annihilation, and
therefore necessary and eternal; but I do not see the necessity of the
disjunctive by which he asserts that if we do not make space and time
the objective forms of _all_ things, we must make them the subjective
forms, and that, otherwise, we should make space and time conditions of
the existence of God.
196. We regard space as an actual condition of things, which occupy
place, but not of all things. We conceive existence in pure spirits
without the necessity of any relation to place, and, consequently,
independent of all position in space.
On this point, as on all relating to the pure intellectual order, we
find in the theologians doctrines which are highly important, and
deserve to be consulted by all who wish to go deeply into philosophical
questions. The author of the _Critic of Pure Reason_ would have found
there some observations which would have cleared up the difficulties
which embarrassed him. He would have found how incorrect it is to
say that space is a condition of the existence of all things, in the
beautiful as well as profound theory by which many of the scholastics
explain the presence of God in the corporeal world, and the presence of
the angels in different places, their motion from one point to another
without passing through the intermediate points, and the manner in
which the soul is wholly in the whole body and in every part of the
body. In these works, unfortunately so little consulted, the German
philosopher would have learned that the presence of a spirit in a
place is something different from the presence of a body, and has no
relation to the intuition of space, whether regarded as the basis of
sensible representations or as a geometrical idea.
197. St. Thomas[54] asks if God is in all things, and answers that he
is. In proving this assertion he does not consider the necessity of
every thing being in some place, but on the contrary seems rather to
forget the idea of space, and regards only causality.
[54] _Sum. Theol._ P. I., Q. viii., Art. 1.
"As God," he says, "is being itself by his essence, created being must
be his effect, as to burn is the effect of fire. But God causes this
effect in things not only when they begin to be, but as long as they
are preserved in being; thus the light is caused in the air by the sun
as long as air remains illuminated. As long therefore as things retain
their being, God is necessarily present to them, according to the
manner in which they have their being. But being is that which is most
internal, and most closely inherent in every thing because it is the
form of all that is in it, God therefore is in all things internally."
To be situated in space is to be contained in it; so, at least, we
conceive whatever we consider situated in space. St. Thomas rejects
this meaning as applied to spiritual beings, and says, that although
corporeal beings are contained in things, spiritual beings on the
contrary contain the things in which they are.
In the second article he asks whether God is in all places (_ubique_);
and, he says, that as God is in all things, giving them being and
the power of acting, so he is in all places giving them being and
capacity (_virtutem locativam_). He states as an objection that
incorporeal things are not in any place, and answers in the following
philosophical words: "Incorporeal things are not in place by the
contact of measurable quantity, like bodies; but by the contact of
activity (_virtutis_)." Then explaining how the indivisible can be in
different places, he says: "The indivisible is of two kinds; first,
it is the limit of the continued, as a point in permanent things, and
a moment in successive things. The indivisible in permanent things,
cannot be in different parts of place or in different places, because
it has a determinate position; and in the same manner the indivisible
in action or in motion cannot be in different parts of time, because
it has a determinate order in action or motion. But there is another
indivisible which is _beyond all kind of continuation_, and in this
sense incorporeal substances, as God, the angels, and the soul, are
called indivisible. The indivisible in this manner, is not applied to
the continued as _any thing which belongs to it_, but only as reaching
it by its activity; therefore as its activity may extend to one or
many, to the small or to the great, it may be in one place or in many
places, in a small place or in a great place."
What can be clearer, relatively to the intuition of space, than that
when any thing is in a place it cannot be out of that place? But the
holy Doctor, rising above sensible representations, boldly maintains
that God may be whole in the whole, and in every part of the whole,
as the soul is whole in every part of the body. And why? Because
what is called totality in corporeal things relates to quantity, but
the totality of incorporeal things relates to essence, and cannot be
measured by quantity, and is not confined to any place.
In the _Treatise on the Angels_,[55] he says that the expression to be
in place is used equivocally (_œquivoce_),[56] when applied to angels
and bodies. Bodies are in place by the contact of measurable quantity,
but angels by virtual quantity, that is to say, by the action which
they may exercise upon a body. We cannot, therefore, say that an angel
has a position in the continued (_quod habeat situm in continuo_). In
the _Treatise on the Soul_[57] he maintains that the soul is whole
in every part of the body. He distinguishes the totality of essence
from the totality of quantity, and makes use of an argument similar
to that which he used with respect to the angels. The more we reflect
on this doctrine the more profound it appears; those who have made
light of it, have shown that they never penetrated beyond the surface
in all that concerns the relations of spiritual to corporeal things.
It is generally dangerous to laugh at opinions held by great men;
for if they are not certain, they have, at least, powerful arguments
in their favor. Nothing is more contrary to sensible representations
than the possibility of any thing being in different places at the
same time, but we shall find nothing more in conformity with the
principles of sound philosophy than this possibility, after we have
profoundly analyzed the relations of extension with unextended things,
and discovered the difference between the position of quantity and the
position of causality.
[55] _Sum. Theol._ Q. LII., Art. I.
[56] Dialecticians understand by an _equivocal_ term one which in
different things has an entirely different meaning. They give as an
example the term LION which is applied _equivocally_ to an animal, or
a constellation. Æquivoca sunt quorum nomen commune est, et ratio per
nomen significata, simpliciter diversa, is the scholastic definition.
[57] _Sum. Theol._ Q. lxxvi., Art. 8.
198. From these doctrines it may be concluded, that to be in space
is not a general condition of all existences, even according to the
manner of existences; for we can conceive existences without relation
to any place. Many have confounded imagination with understanding
on this point, and believed that what is impossible for the former
is equally so for the latter. It is certain that we can _imagine_
nothing without referring it to points of space, and even in purely
intellectual objects there is always a sensible representation, but
the understanding regards these representations as false and does
not conform to them. As imagination is a sort of continuation of
sensibility, or an internal sense, and the basis of sensations is
extension; it is impossible for us to exercise this internal sense,
without the presence of space, which, as we have shown, is only the
idea of extension in general. Position in space is consequently a
general condition of all things, as perceived by the senses, but not as
perceived by the intellect.
CHAPTER XXVIII.
CONTINGENCY OF CORPOREAL RELATIONS.
199. Position in place is the relation of a body to other bodies.
Is this relation necessary? I distinguish: conditionally, yes;
essentially, no. God has established this relation, and therefore it is
necessary; but God might have ordered it otherwise, and can even now
change it, without varying the essence of things.
If we admit, as we must, a correspondence between the subjective and
the objective, or between the appearance and the reality, we cannot
deny that the relations of bodies are constant, and this constancy must
proceed from some necessity. But that the existing order is subject
to fixed laws, does not prove that these laws have their root in the
essence of things, in such a manner that, supposing the existence of
objects, their relations could not have been very different from what
they actually are.
200. In order to assert that the existing order of the universe is
intrinsically necessary, we must know the essence of things; but this
is not possible for us, because objects are not immediately present to
our understanding, and we see them only under one aspect, that which
places them in relation with our sensitive faculties. The best proof of
our ignorance of the essence of bodies is the great division of opinion
on this subject. Some maintain that the essence of bodies is extension
or dimensions; and others that extension is merely an accident, not
only distinct, but even separable from corporeal substance.
The great obscurity in which the investigation of the constitutive
elements of bodies is involved, proves that their essence is unknown
to us, and that we know nothing of them except their relation to our
sensibility.
201. It is not necessary that the aspect under which being is presented
to us should contain its whole nature. To say that bodies contain
nothing besides what we perceive in them, is to make our faculties
the type of things in themselves, a ridiculous pretension in a being
which finds its activity limited at every step and is almost always
passive in its relations to bodies, and which, in order to exercise
its faculties externally, is forced to submit to the laws of the
external world, or else to encounter obstacles which are absolutely
insurmountable.
If we are ignorant of the essence of bodies we can have no certain
knowledge of what is intrinsically necessary in them; with the
exception of composition, which even the sensible order presents to
us, and which we cannot take from bodies without seeming to run into
a contradiction. Simplicity and composition in the same object are
incompatible and contradictory.
202. Hence, in all that pertains to the relations of bodies we must
abstain from judging absolutely, and speak only conditionally. We may
say: "This happens now; this must happen according to the order now
established;" but we cannot say: "This happens, and it is absolutely
necessary that it should happen." The transition from the first
proposition to the second, implies the knowledge of what no man can
know, that the aspect under which the external world is presented to us
is the image of its essence.
203. One of the greatest errors of Descartes was, that he did not make
sufficient account of this difference: he placed the essence of bodies
in dimensions, which is to confound the real world with the phenomenal,
and to take one aspect of things for their nature. It is true that
whatever affects us has extension, and that extension is the basis of
the relations of our sensibility with the external world; but it does
not follow that the essence of this world is nothing more than what
is presented to us in its dimensions. We might as well say that the
essence of man is the lines which mark his form.
204. The different aspects under which the external world is presented
to our senses, ought to prevent us from confounding what is absolute
in it with what is relative. A man deprived of one sense would not
reason well if he should conclude that the world has no other aspects
than those which he perceives. What do we know of the manner in which
objects are presented to pure spirits, or of the many other phases
which they might offer to our sensibility?
Let us then leave nature its secrets; and let us not limit omnipotence
by saying, that the order of the world is so intrinsically necessary
that its present relations cannot be changed without contradiction.
When we examine the possibility of a new order of relations between
the beings which we call bodies, let us not settle the question too
quickly, taking for our only type of the possible the vain impotence
of our faculties. What should we think of a blind man who should laugh
at those who see, if he heard them speak of the relations of objects
as seen? Yet we present the same spectacle to a pure spirit when we
talk of the impossibility of an order different from what our senses
perceive.
205. The principles of physical science are in great part conditional;
for they are true only on the supposition of the reality of the data
furnished by experience. If position and relation to place are not
essential to bodies, distance and motion are conditional facts true
only under certain suppositions. All the natural sciences, as we have
seen, are reduced to the calculation of extension and motion; they
do not reach the essence of things, but are limited to one aspect,
that presented by experience. In these sciences there is consequently
nothing strictly absolute; in this respect, they are far below
metaphysics, which knows things that are absolutely necessary. A
further explanation of this doctrine is required, and will be given in
the following chapters.
CHAPTER XXIX.
SOLUTION OF TWO DIFFICULTIES.
206. Must not the theory which supposes the relations of bodies to be
variable, put an end to all the natural sciences? Can there be science
without a necessary object? and can there be a necessity which is
compatible with variability?
The natural sciences have two parts: one physical, and the other
geometrical. The first supposes the data furnished by experience;
the second forms its calculations relative to these data. Change the
relations of external beings, and the data will be different, you will
have a new experience producing a new physical science: the calculation
will be the same, only new results will be obtained from the new data.
The difficulty thus disappears. All the physical sciences are based on
observation, all their combinations are made from data furnished by
experience; therefore the physical sciences are not wholly absolute,
but they have a part which is conditional. The theory of universal
gravitation is developed as a body of geometrical science, but it
starts from the data furnished by experience. Destroy these data and
from a body of physical science it becomes a body of pure geometry. In
mechanics, the problems of the composition and decomposition of forces
have a physical signification, inasmuch as they presuppose the data of
experience; suppress these data and there remains only a composition of
lines which mean nothing when we call them forces. Therefore mechanics
is only a system of geometrical applications.
207. Here another difficulty arises which is apparently more serious
than the other. If the relations of bodies are not essential, but are
subject to variation; if our calculations upon them are not founded
upon data which are intrinsically necessary, it seems that geometry
is destroyed, or limited in such a way to the ideal order, that it
cannot be sure that on descending to the field of experience it will
not find that false which it regarded as true, and that true which it
reputed false. For example, the distances of bodies are calculated by
considerations of geometry: if the relation of distance is variable,
and a body may be in many places at the same time, geometry turns out
false. Such a supposition is no more than the application of the
foregoing theory; for, if the relations are variable, this variation
may affect distance, which is only a relation. I said this difficulty
was more serious than the other, because it leaves the field of
experience, and attacks the order of our ideas, an order which we
must hold to be indestructible, unless we wish to give up our reason.
What would become of our reason if geometry were contradicted by the
reality? what would become of an order of ideas in contradiction
to facts? Still I repeat that the force of this difficulty is only
apparent, and if analyzed will be found of no more weight than the
objection which we have already answered.
A body which is a hundred yards distant from another, cannot be only
one yard distant; geometry would be opposed to it. But if the relations
of bodies are variable this proposition can mean nothing with respect
to the reality. Therefore geometry is false. I admit the consequence;
but the principle on which it is based involves a supposition contrary
to my theory. If you alter or destroy the relations of bodies, you
destroy distance, which is a relation, consequently you cannot have
a distance of one hundred yards, nor of one yard, nor any distance
at all, and if there is no distance there is no contradiction. If,
then, you ask how great is the distance between them, your question is
absurd; for it supposes a distance, whereas there is no distance at all.
208. This solution rests on a fundamental principle which we ought
never to lose sight of. Geometrical truth is true in reality when the
conditions of geometry exist in reality; if these conditions do not
exist, there is no real geometry. There is nothing strange in this:
in fact, the same occurs in the purely ideal order; even there,
geometry rests on certain postulates, without which it is impossible.
Two triangles with the same base and altitude are equivalent to each
other. This is a true proposition, but only on the supposition that
there are those orders of points which are called lines, and that the
lines form angles, and are united at three points. If these relations
are not presupposed, the geometrical theorem has no meaning.
209. Geometry in itself, or in the purely ideal order, is founded
on the principle of contradiction. The truth of this principle
being absolutely necessary, that of geometry is equally so. But the
principle of contradiction, like all purely ideal principles, abstracts
existence, and is applied to nothing in practice, unless we suppose
some fact to support it. Yes and no at the same time are impossible;
but the principle determines nothing for or against either of the
extremes. It only affirms that one excludes the other; if we suppose
_yes_, it excludes _no_, and if we suppose _no_, it excludes _yes_;
that is to say, it always needs a condition, a datum which only
experience can furnish.
It is the same with geometry. All its theorems and problems refer to
the ideal field within us, where there are certain conditions which
lead to certain results, by virtue of the principle of contradiction:
whenever the conditions exist, the results are true; but if the former
fail the latter are false. Ideal sciences consider the _connection_ of
conclusions with principles in the order of possibility, but take no
note of facts. If the connection is admitted the science is true.
CHAPTER XXX.
PASSIVE SENSIBILITY.
210. Active sensibility, or the faculty of perceiving by the senses,
has been a subject of great dispute among philosophers. Passive
sensibility, or the capacity of an object to be perceived, is a
question of not less interest.
Can every thing which exists be perceived by the senses?
Before answering this question, let us remember that to be perceived by
the senses may be understood in two ways: First, it may mean, to cause
an impression in a sensitive being; and secondly, to be the immediate
object of sensible intuition. The first is true of every being capable
of producing the impression; the second is true only of those beings
which unite the conditions which the intuition supposes.
211. To produce an impression is simply _to cause_; and causality is
not repugnant to simple beings. There is, therefore, no absurdity in
supposing that pure spirits can produce sensible impressions: were it
otherwise God could not act upon our soul, causing an impression in
it, without the mediation of bodies. This causality cannot be called
passive sensibility; the being which has it is not perceived by the
senses. The relation of the sensation to the being which produces it
would be only that of an effect to its cause.
212. To be the immediate object of sensible intuition, is to be
presented to this intuition as an original to the copy. Under this
view, only the extended can be perceived by the senses; that is to
say, multiplicity combined with continuity is an absolutely necessary
condition of our sensitive faculties in relation to external objects.
213. In this manner, it is a manifest contradiction to say that the
simple can be sensible. Instinct and reason force us to suppose a real
object of sensible intuition. This intuition is referred to the object
as to something essentially composite, belonging to the order which
we call continuity. If we make this object simple, it ceases to be
sensible; and we both affirm and deny its sensible objectiveness. It is
a contradiction to suppose a faculty in act, and at the same time to
deprive it of the conditions to which its action is necessarily subject.
214. It may be said, that there is no necessity of transferring to the
object the conditions of the subject, and therefore a simple object may
be presented to the senses. But this is to elude the question at issue.
For, either the sensible intuition is referred to the object, or it is
not; if it is, the object cannot be simple; if it is not, we fall into
idealism, which we have so often combated in the course of this work.
215. If you answer, that our soul, which is simple, has the
representation of the composite, I reply, that the objective
representation is not the same thing as the subjective perception of
the composite; nor the presentation of the object as multiple the
same thing as the perception of the multiple. Our soul perceives the
multiple, and for this reason must itself be one, or it could not
perceive that which is multiple. So much for the subjective; as to the
objective, we must remark, that our sensible representations do not
always proceed from real objects; but they always refer to objects
which are at least possible; that is to say, the intuition is never
entirely void; and when it has no object in reality, it finds one in
possibility.
216. The external world, as involving multiplicity, or a collection of
many beings, and as susceptible of this order which we call continuity,
may be the object of sensible intuition, as we experience in reality.
But this passive sensibility is not intrinsically necessary to it:
I mean that God could so have disposed the collection of beings
constituting the universe as not to be sensible. This is based on the
variability of the relations of bodies; for, it is evident that if
these relations did not exist, or were not subject to the conditions
required by sensible representation, this representation would be
impossible, and the world not sensible.
217. Experience confirms this conclusion which is obtained from
transcendental philosophy. We find a slight alteration continually
changing sensible bodies into insensible, and making sensible those
that were insensible. The condensation of the air makes it visible; and
its rarefaction invisible. A liquid body is tangible, but it ceases to
be so when converted into vapor. The same variety which is caused by
the alteration of the object may also proceed from a modification of
the organ. A proof of this is found in what happens to the sight when
aided by certain instruments. If, then, these transitions from sensible
to insensible are now possible, without infringement of the fundamental
laws of the relations of bodies, why could there not be a radical
change in these relations which should make bodies wholly insensible?
218. By the variation of the relations of the beings which compose
the corporeal universe, the sensible might become insensible; and, on
the other hand, there are many insensible beings which by a different
arrangement might be made sensible. To a certain extent we have
something besides idle conjectures on this matter: facts speak; in
proportion as the field of experience is expanded, new phenomena are
discovered; thus magnetic attraction, electricity, and galvanism, have
been added to experimental science.
In these phenomena there are agents at work which are not perceptible
to the senses; why may they not be disposed in such way as to be
perceived like other bodies? Where is the limit of these agents? We
know not; but reasoning from analogy we may believe that there are many
others whose existence is not known to us.
The perfection of a sensitive organ by means of instruments, is an
arrangement by which we vary the ordinary system of the relations
of our body to those around us. This perfectibility is indefinite,
and the farther we advance, the greater do we find its extension. It
is therefore probable, that in the universe there are many beings
which are imperceptible to our senses, but which a modification of
our organs, or a change of some of the laws of nature would render
sensible. What a vast field of bold conjectures and sublime meditations!
CHAPTER XXXI.
POSSIBILITY OF A GREATER SPHERE IN ACTIVE SENSIBILITY.
219. Having treated of passive sensibility in the order of possibles,
a similar question naturally arises with respect to the active
sensibility of beings subject to different conditions from those of our
soul while united to the body.
I speak only of possibility, for, limited to what experience teaches
us, we know not what may be in the sphere of beings with which we have
no communication. Whatever we know of them is by divine revelation; and
the object of revelation is not to teach us philosophy, but virtue.
220. To examine how far active sensibility is possible in an order
different from that of our experience, not only raises curious and
interesting questions, but it also gives an opportunity to explain
by new reflections, the nature of this phenomenon in its relations to
bodily organization. There is a special reason why we should seek to
investigate this question. It consists in the interest inspired by
every thing which relates to a state of existence into which we must
soon enter. Short are the moments allotted to man to dwell in this
world. We all hasten with astonishing rapidity to the final instant
when the fragile organization which envelops our mortal spirit shall
dissolve, and crumble into dust,--when the being which feels, thinks,
and wills within us, shall pass to a new state, and be separated from
the bodily organization. What will then be its faculties? This is a
question which we cannot be indifferent to; for it concerns us, and the
state of our future existence.
221. If we are asked whether a pure spirit is capable of sensible
perception, we must answer negatively; because we are treating of
active sensibility, which is not possible without the mediation of a
body. I believe that some explanation of the question may be given. But
we must first of all determine the meaning of the words. Sometimes we
understand by a pure spirit, one which is not united to a body; but,
more strictly speaking, the term is confined to a spirit which neither
is united to a body, nor destined to this union. Thus the human soul is
a spirit, but not a pure spirit; for it is either actually united to a
body or is destined to this union.
It might appear at first sight that as we are limiting ourselves to
the sphere of possibility, there is no difference between the two
acceptations of the term; for, if it is not essentially repugnant to
the soul when separated from the body, to have sensible intuition, it
will not be so to other spirits. The parity is not certain; still, for
the present, when speaking of pure spirits in general, I shall include
souls separated from bodies.
222. What do we understand by sensing? This word may mean two things.
It may mean the receiving of an impression by means of bodily organs;
or it may mean simply the experiencing of the impression, independently
of the bodily organ. For example: I see an object. Here is the
affection called _seeing_, and the mechanism by which the object
transmits light to the retina, and a certain impression to the brain.
These are two very different things; the first is a fact of my mind;
the second a modification of my body.
223. If by sensing is meant the receiving of the impression of a bodily
organ, it is clear that a spirit which has no body cannot sense; but
if by it is meant only the subjective affection abstracted from the
medium by which it is produced or communicated, then the question is
different, and the existence or non-existence of bodies cannot affect
its answer either affirmatively or negatively.
224. The question then becomes this: Can a pure spirit have the various
affections and representations which we call sensible?
Simplicity is not opposed to the sensitive faculty. Our soul senses,
and still it is simple. The body aids it in the exercise of the
sensitive faculties; but this aid is instrumental, not, however, in
such a manner that the soul senses _by the body_, as an action is
performed by means of the instrument. That which senses is the soul
itself, and the instrumental action of the body consists in providing
certain conditions from which sensation follows, by a physical or
occasional influx. Therefore, the simplicity of a pure spirit is no
argument against the sensitive faculties. Such an argument would prove
too much; consequently, it proves nothing.
225. Hence there would be no _intrinsical_ repugnance in God
communicating to a pure spirit sensitive faculties; whether
representative like those which place us in relation with the corporeal
world, or purely subjective, like those of pleasure or pain.
226. Although in the present order these functions depend on certain
conditions to which bodies are subject, considered in themselves,
inasmuch as they are a modification of the soul, they have no essential
relation to the corporeal world. It would therefore seem contrary to
the principles of sound philosophy to say, that the soul separated
from the body could not experience affections similar to those it has
in this life. If this is not repugnant to the soul in its separate
existence, why should it be so to other spirits?
The sensitive faculties are a sort of inferior order of perception.
We see them in beings united to bodies, but they are not exercised
immediately by a bodily organ. So far from contradicting simplicity,
they require it; and therefore we have seen[58] that matter is
incapable of sensation. Many grave philosophers are of opinion that the
causality of bodies with respect to sensations, is only occasional.
This opinion is founded on the difficulty of explaining how a composite
being can produce affections of any kind in a simple being. Instead
of a repugnance between simplicity and the sensitive faculties, there
is, on the contrary, a necessary connection. No composite being can be
sensitive.
[58] B. II., Ch. II.
227. Perhaps it may now be thought that there is no longer any doubt of
the possibility of sensation independently of the bodily organs; and
that to hold the contrary, it would be necessary to maintain that God
can not produce immediately that which he produces by means of second
causes. The observations which we have made may seem to have exhausted
the matter, but if we reflect on it, we shall find that we have scarce
entered on it.
It must not be forgotten that we are examining the possibility of
sensitive faculties, in relation to one attribute only, that of
simplicity. This greatly limits the question, as it leaves it to be
solved under one aspect only. Simplicity is a negative property. When
we say that any thing is simple, we deny that it has parts, but we
affirm none of its properties; we say what it is not, not what it is.
Therefore, in maintaining that sensitive faculties are not repugnant to
a pure spirit, we ought to restrict the proposition; we should express
our meaning more exactly, if instead of saying "sensitive faculties are
not repugnant to a pure spirit," we should say, "sensitive faculties
are not repugnant to the _simplicity_ of a pure spirit."
228. This last observation seems to me to present the question in its
true point of view. Any other expression of it seems only to confuse
ideas and raise problems which we have not sufficient data to solve.
In fact, how do we know but what the repugnance which does not exist
between sensibility and simplicity, may exist between sensibility and
some attribute which we know nothing about? This argument is not valid
for the human soul, because we already know that the soul is capable of
sensing; but it is valid for other spirits, whose essence is unknown to
us, and the character of whose perceptive faculties experience has not
discovered to us.
229. One of the distinctive marks of sensitive perception is the
reference to individual objects, not in what concerns their essence,
but inasmuch as they are arranged in a certain order, the variations
of which do not affect their internal nature. Extension itself, which
both instinct and reflection teach us to regard as objective, is rather
a result of the relations of the beings which form the composite
extended object, than those beings themselves. The sensitive faculties
are the lowest grade in the order of perception. Their sole function
is to make known to their possessor a certain arrangement of external
objects, but they teach him nothing concerning the nature of those
objects. Pure spirits are a grade higher in the scale of perceptive
beings, and one of the characteristics of intelligence is, that it
penetrates to the inward nature of things. Therefore it might easily
happen that the sensible faculties are repugnant to intelligences of
a higher order than ours, not by reason of their simplicity, but on
account of the different manner of their perception.
230. Reasoning by analogy from what takes place within ourselves, we
are confirmed in this opinion. Sensible representations are often
powerful auxiliaries to purely intellectual perception; but they just
as often embarrass and confuse it. In meditating on very abstract
matters sensible representations are a hinderance to the understanding,
from which we should be glad to free ourselves. Every one has
experienced this to be so. They are like shadows which come between
the eye of the intellect and the object: the necessity of continually
removing them delays and weakens our perception. Thus, we propose, for
example, to think of causality. No sensible representation should find
place in this idea in the abstract, yet in spite of all our efforts
the representation haunts us. At one time it is the word _causality_,
written or spoken; at another, the image of a man doing something,
or of any other agent. The sensible representation is always in our
way, and we cannot free ourselves from its presence. The understanding
is forced to repeat continually to itself, "This is not the idea of
causality; it is only an image, a comparison, an expression;" in order
to defend itself against illusions, which would make it confound the
particular with the universal, the contingent with the necessary, the
phenomenal with the real.
231. We must conclude from this that a repugnance of sensitive
faculties to the nature of a pure spirit, might proceed from the
character of its intelligence, which by reason of its perfection
rejects the duality of perception which exists in us. The object of
the understanding is the essence of the thing understood, _quidditas_,
as the scholastics called it. Sensible representations tell us nothing
of this essence. They offer only one aspect of things, and even this
is limited to the perception of extension; for as regards the other
sensations, they are a subjective fact which instinct and reason teach
us to attribute to external causes, rather than a perception of the
real disposition of things.
232. This suggests another observation which supports the conjecture
that the elevation of intelligence above a certain degree makes it
incompatible with sensitive faculties. Sensations would tell us nothing
even of this aspect and disposition of things if they did not have
extension for their basis. To what should we reduce the corporeal world
if we supposed it unextended? Since extension, as we have shown,[59]
although the basis of some sensations, is not the direct and immediate
object of sensation; that which in the sensitive faculties makes us
perceive something of the reality of objects, is not strictly sensible.
Therefore, if it is the character of intellectual perception to know
the reality of the object, the more elevated an intelligence is the
farther it will be from sensation, and there may be a subject in which
intellectual faculties are incompatible with sensitive faculties.
[59] Ch. II.
233. We shall better understand the force of this observation by
casting a glance at the scale of beings, and noting the difference in
them in proportion to their perfection. The isolation of a being is a
mark of its imperfection. The lowest idea of an object is that which we
form when we conceive it absolutely limited to existence, completely
inert, without either internal or external activity. A stone has
existence and a determinate form; it is what it was made, and nothing
more; it preserves the form which was given to it, but it has no
activity to communicate with other beings, no consciousness of what it
is; in all its relations it is passive; it receives but cannot give.
234. In proportion as beings rise in the scale of perfection, this
isolation ceases; active properties are combined with the passive;
such we conceive to be the corporeal agents, which, although they do
not reach the category of _living beings_, take an active part in the
production of phenomena in the laboratory of nature. In these beings we
find besides what they _are_, what they _can do_; their relations with
other beings are many and varied; their existence is not confined to
the circle of their own existence; but it expands and is communicated
in some way to others.
235. In organized beings we find a more expansive nature. Their life
is a continual expansion. The living being extends in a measure beyond
the limits of its own existence; for it bears within it the germs of
its reproduction. Its existence is not for itself alone, but for others
also. It is only an imperceptible link in the great chain of nature;
but the vibrations of this link are felt in the remotest confines of
the universe.
236. Life is still more extended when it becomes sensation. The
sensitive being contains in himself, as it were, the universe. By the
consciousness of its affections, it places itself in new relations
with all that acts upon it. Perception is immanent, that is to say,
it remains in the subject, but with the subjective is combined the
objective, by which the universe is reflected on a point. Being does
not then exist in itself alone, it becomes in some manner other things.
There is a profound truth in the expression of the scholastics:
"That which knows is the thing known." There is a certain order in
sensations; they are more perfect in proportion as they are less
subjective; the most noble are those which place us in communication
with objects considered in themselves,--those which are not limited
to the experience of what the objects cause in us, but include the
knowledge of what the objects are.
237. Extension is the basis of the objectiveness of sensations, but it
is not the direct and immediate object of sensation. Although extension
teaches us something of the reality of beings as regards a certain
arrangement of them among themselves, it is not so much the object of a
sensitive faculty as of intelligence. Here sensation ceases and science
commences. Science is not satisfied with what the objects appear. It
penetrates to the reality; the understanding does not stop with the
subjective, but passes to the objective, and when it cannot reach the
reality, it wanders in the regions of possibility.
238. Thus we see that the perfection of beings is in proportion to
their expansion. Accordingly as they are more perfect, they go farther
out of their own sphere, and exercise a more extended activity. Hence
the highest degree of perception is the least subjective; the lowest is
sensation, which is limited to the experience of the sentient subject.
Intelligence which is the highest degree, abstracts experience, and
gives its whole attention to reality, its proper object.
239. If we could know the intimate nature of pure spirits, perhaps we
should find that the sensitive faculties are altogether incompatible
with the elevation of their intelligence, and that the analogy founded
on the nature of our perceptions has no value when applied to a more
perfect order of intelligence. However this may be, we must admit that
the question would have been solved in a very incomplete way, if we had
limited it to the single aspect of simplicity. These observations on
the nature of intelligence ought to make us very cautious in affirming
to be possible, what we should perhaps see to be impossible, if our
knowledge of the nature of things were greater.
240. So far we have spoken only of the _intrinsical possibility_; what
shall we say of the reality? This is a question of fact which can only
be solved on data which our experience is unable to furnish, as we are
not in immediate communication either with souls separated from bodies,
or with pure spirits.
241. If we wish to look for an argument to prove that pure spirits
and souls after they are separated from bodies, have no sensitive
faculties, we shall find it in the consideration of the end to which
these faculties are destined, better than by attempting to discover
the essence of things. The body, to which the soul is united in this
life, is an organization subject to the general laws of the corporeal
universe. In order that the soul may rightly exercise its functions,
it must be in constant communication with its own body and the bodies
around it; it must have sensible intuition of the relations of
bodies; it must be notified by pain of any disorder which occurs in
its body, and guided by the sentiment of pleasure as by an instinct
which, directed and moderated by reason, may point out to it what is
profitable or necessary. When the soul is no longer united to the body,
there is no reason why it should have these affections, as it does not
require to be directed in its acts. As this applies equally to pure
spirits, we may form a conjecture as to the cause of the difference
which there must be between the state of our soul in this life, and
that of spiritual beings which are not united to bodies.
This argument, deduced from the final cause, is not to be considered as
a proof; at best it is only a conjecture: for we do not know how far
the soul in its separate existence, or pure spirits, may be in relation
with bodies; and consequently, we do not know whether these sensible
affections would be useful or necessary for ends of which we have no
conception. And even supposing that neither the soul nor pure spirits
have any relations with bodies, we are far from sure that sensible
affections would be useless to them. On the contrary, so far as we can
form an opinion on the subject, it seems that to take from the soul its
imagination and sensation, would be to deprive it of two of its most
beautiful faculties; for they not only assist the understanding, but
are often a strong motive of its acts.
242. It is difficult for us to form an idea of pleasure or pain,
without sensible affections. In the purely intellectual will, we
conceive only _willing_ and _not willing_, acts of a most simple
relation, which do not have for us the same meaning as a pleasant or
unpleasant affection. We often wish a thing in which we experience
pain; and as often find pleasure in what we do not wish. Therefore to
wish and not to wish do not imply pleasure and displeasure, but are
independent of these affections and may exist in opposition to them.
243. It might be said that the cause of this discord is in the
disagreement of the sensitive with the intellectual faculties. This
is true, but it proves nothing against what I have been saying. The
purely intellectual will, in opposition with the sensible affections,
does not involve pleasure or exclude pain. The will triumphs, it is
true, but it does so by virtue of its freedom. Its triumph is like
that of a master obliged to exact obedience by severe punishment, who
experiences pain at the very time when he is obtaining the execution of
his commands. Who can tell, then, whether the will, after this life,
will be accompanied by affections similar to those which it now has,
but purified from the grossness of the body which weighs down the soul?
I see no intrinsical impossibility in it. If questions of philosophy
could be solved by sentiment, I should not hesitate to express my
opinion that this fair and noble union of faculties which we call the
heart, does not go down to the grave, but flies with the soul to the
regions of immortality.
244. As to the imagination,--that mysterious faculty which not only
gives life to the real world, but possesses an inexhaustible activity
in creating new worlds of its own, displaying before the eyes of the
soul rich and splendid panoramas; why should it desert the soul on
its separation from the body? Why may not the harmony of nature be
perceived in a similar manner hereafter? Let us not advance opinions
on secrets of which we are ignorant, but, at the same time, let us
beware of setting bounds to the omnipotence of God. Sound philosophy
should not multiply opinions beyond measure; but neither should
it circumscribe within the limits of human reason the sphere of
possibility.
CHAPTER XXXII.
POSSIBILITY OF THE PENETRATION OF BODIES.
245. The more we meditate on the corporeal world, the more we discover
the contingency of many of its relations, and the consequent necessity
of recourse to a higher cause which has established them. Even those
properties which seem most absolute cease to appear so when submitted
to the examination of reason. What more necessary than impenetrability?
Yet from the moment it is carefully analyzed, it becomes reduced
to a fact of experience not founded on the nature of things, which
consequently may exist or cease to exist without any contradiction.
246. Impenetrability is that property of bodies by which two or more
cannot be in the same place at the same time. For those who do not
make pure space a reality independent of bodies this definition has no
meaning; for if place like pure space is nothing, to speak of _the same
place_ abstracted from bodies, is to speak of nothing. In that case,
impenetrability can only be a certain relation either of bodies or of
ideas.
247. Above all, we must distinguish the real order from the purely
ideal. We may consider two kinds of impenetrability; physical
impenetrability, and geometrical impenetrability. The physical is that
which we see in nature; the geometrical that which is found in our
ideas. Two balls of metal cannot be in the same place: this is physical
impenetrability. The ideas of the two balls present two extensions
which mutually exclude each other in the sensible representation: this
is geometrical impenetrability. If we imagine two balls which perfectly
coincide, they are no longer two, but only one; and if we imagine one
ball to occupy a part of the other, we have a new figure, or, rather,
one is considered as a portion of the other, and is consequently
contained in the idea of the other, as a small ball inside of a larger
ball. On either supposition the balls are regarded as penetrating
each other in whole or in part; but by penetration is here meant
only that there are certain parts in one, considered as pure space,
which the other, also considered as pure space, occupies. Geometrical
impenetrability exists only when the two objects are supposed to be
separated, and only inasmuch as they are separated; in which case
impenetrability is absolutely necessary, because penetration would
be to confound what is by the supposition separated, and would imply
separation and non-separation, which are contradictory. Therefore,
geometrical impenetrability is no argument in favor of physical
impenetrability; for the former exists only in case it is presupposed
or required under pain of contradiction. The same would occur in
reality; for if we suppose two bodies separated, they cannot be in the
same place whilst they are separated, without a manifest contradiction.
On this point, therefore, the ideal teaches us nothing as to the real.
248. Can penetration exist in reality? Can one ball of metal, for
example, enter another ball of metal, as we make one geometrical ball
enter another? We are not treating of the regular order of things which
is repugnant to such suppositions, but of the essence of things. On
this supposition, I maintain that there is no contradiction in making
bodies penetrable, and that an analysis of this matter proves that the
impenetrability of bodies is not essential.
We have seen that the idea of place as pure space is an abstraction.
It is therefore an entirely imaginary supposition on which we give to
every body a certain extension to fill a certain place, necessarily,
and in such a manner that it is impossible for it to admit another body
into the same place at the same time. The position of bodies in general
is the sum of their relations; the particular extension of each body is
only the sum of the relations of its parts among themselves, until we
come by an infinite division to unextended or infinitesimal points.
The sum of the relations of indivisible or infinitesimal beings
constitutes what we call extension and space, and all that is contained
in the vast field of sensible representation. Who can assure us that
these relations are not variable? Is our experience, perhaps, the limit
of the nature of things? Evidently not. The universe was not planned
after our experience, but our experience is obtained from the universe.
To say that it contains, and can contain only what our experience sees
in it, is to make the _me_ the type of the universe; to affirm that
its laws are derived from us, that they are emanations from our being.
Foolish pride of an imperceptible atom, which appears for an instant
on the great theatre of nature, and goes out like a spark of fire;
foolish pride for a spirit which, despite its great idea of its own
importance, feels that it is unable to withdraw itself from these laws
and phenomena, which it pretends to consider as its own creation!
CHAPTER XXXIII.
A TRIUMPH OF RELIGION IN THE FIELD OF PHILOSOPHY.
249. There are two things in extended objects: multiplicity and
continuity. The first is absolutely necessary to extension; it supposes
distinct parts, and that which is distinct cannot be identical without
evident contradiction. The continuity represented in the sensible
impression is not essential to extension, because it is only the
result of a union of relations inseparable in the present order of
sensibility, but not absolutely necessary in the order of reality.
Transcendental philosophy rising above sensible representations,
and leaving phenomena to enter on the contemplation of beings in
themselves, nowhere discovers the necessity of these relations, and
is obliged to consider them as simple facts which might cease to be
without any contradiction. In this manner the correspondence of the
phenomenon with the reality is saved, and the internal world harmonized
with the external, but the subjective conditions of the former are
not all transferred to the latter in such a way as to make what is
necessary for our representations, absolutely necessary in itself.
250. Arrived at this point of transcendental philosophy, the mind
beholds new worlds unfolded to its view. We rejoice to say that this
discovers to us a new proof of the divinity of the Catholic religion,
and teaches us to distrust that proud philosophy which finds a
contradiction in every thing which it cannot understand.
251. There is a mystery which the Church celebrates with august
ceremonies, and the Christian adores with faith and with love. The
unbeliever sees the holy Tabernacle, and exclaims, in the pride of his
ignorance: "Here is a monument of superstition; here man adores an
absurdity."