excepting the acts of our own mind; so that even when we know, by
discursion, that there are substances really one or simple, we do not
see them in themselves.
Extension consists essentially of parts; whence it happens that we
never encounter real unity or simplicity in the corporeal world as
object of our sensibility. But as the composite must be resolved
into the simple, as it is hard to proceed _ad infinitum_, we infer
that the corporeal universe itself is a union of substances which,
whether called points without extension, or any thing else, cannot be
decomposed into others; for which reason they are really one, or simple.
18. Hence we conclude that substances may be said to be in a certain
manner simple; and that things called composite are unions of
substances, which in their turn form a third substance by virtue of
a law presiding over them and giving them that unity which we call
factitious.
19. We cannot, then, do less than to remark that the transcendental
analysis refutes those who deny simplicity to thinking beings, since we
have seen that simplicity is prior to composition, which can neither be
nor be conceived if it be not presupposed. Simplicity is a necessary
law of every being: a composite being ought to be called a union of
beings, rather than a being.
20. We have said that simple substances are not objects of our
intuition, which has none worthy to be called simple excepting the
acts of our mind. The reason of this is, that the principal medium of
our intuition is sensibility, which is founded upon representations,
themselves based upon extension. There can be no doubt that the acts
of our mind, given us by intuition, in the inward sense are perfectly
simple; for who can decompose a perception, a judgment, an act of the
reason or of the will?
21. The perception of a certain object requires preparatory acts;
and the same may be said of judgments and ratiocinations; yet these
operations are in themselves exceedingly simple, and cannot be divided
into various parts. Simplicity is met with alike in the acts of the
will, whether of the pure, intellectual, or sensible will. How shall we
divide such acts as these into parts: _I desire_, _I do not desire_, _I
love_, _I abhor_, _I suffer_, _I rejoice_?
22. We must take care not to confound the multiplicity of the acts with
the acts themselves; there may be many acts, but in themselves they are
simple. Thoughts, impressions and affections continually succeed one
another in our mind; these phenomena are all distinct from each other,
as is proved by their existing at different times, some at one time
without the others, and by some being incompatible with others, because
contradictory; but each individual phenomenon is by itself incapable of
decomposition, and admits in itself no distinction into various parts;
wherefore, it is simple.
23. True unity, therefore, is only found in simplicity; where there is
no true simplicity, there may be factitious, but not real, unity; since
even when there is no separation, there may be distinction between the
various parts of which the composite is formed.
24. It may be inferred from this that _indistinctum_ ought, perhaps, to
take the place of _indivisum_ in the definition of a one being; because
distinction is opposed to unity of identity, and division to union.
Absence of division is all that factitious unity requires; but real
unity demands that there be no distinction. However closely united two
things may be, if one is not the other they are distinct, and cannot,
in strict metaphysical language, be called one.
25. The object of these observations is only to fix our ideas, not to
modify our language. In common parlance, the idea of unity is used in
a less rigorous sense, and, far from opposing this use, we readily
accord it a reasonable foundation. There results from the union of two
really distinct things, a conjunction, rightly called one so far as it
also is subjected to a certain unity; and, were it not permitted to use
this word in a sense less rigorous than that exacted by metaphysical
analysis, we should be under the necessity of excluding unity from the
great mass of objects. Simple substances, we have said, are not offered
to us in immediate intuition, and we see compositions rather than their
component elements. Could we apply unity only to simple elements,
science would be greatly reduced, language would be impoverished, and
literature and the fine arts would be despoiled of unity, one of their
characteristic perfections.
CHAPTER IV.
ORIGIN OF THE TENDENCY OF OUR MIND TO UNITY.
26. Since we encounter multiplicity in all sensible objects, which are
those chiefly demanding our attention, how does our mind acquire the
idea of unity? In science, in literature, in the arts, and in every
thing, we seek unity; and whence this irresistible tendency towards
unity, which makes us seek a factitious when we cannot find a real
unity, and this, too, notwithstanding the multiplicity presented by all
the objects of our perception?
27. Two origins, if we mistake not, may be assigned to this tendency
towards unity, the one objective, the other subjective. The former
consists in the very character of unity in which the object of the
understanding is mainly comprised; the other is the unity found in the
intelligent being, and which it experiences in itself. We will explain
these ideas more at length.
28. Unity is being; every being is one; and, properly speaking, being
is not found without unity. Let us take a composite object: in it we
discover two things; the simple component elements of it, and the
union of them. The being, properly speaking, does not consist in the
union, but in the united elements. The union is a mere relation, not
even possible without the elements to be united. On the other hand,
these elements in themselves, abstracted from their union, are true
beings, existed before, and will exist after their union. What is an
organized body? An aggregation of molecules united under a certain law,
conformably to a principle presiding over their organization. The
parts existed before their organization, and will continue to exist
after its destruction. The being, therefore, properly consisted in the
elements; and the organization was a relation of them among themselves.
29. Organization requires a principle to rule it, and subject its
functions to determinate laws. Thus we see that even relation is
subject to unity, to the unity of end and to the unity of a ruling and
directing principle.
30. It is inconceivable how the union of distinct things can have any
meaning, or lead to any result, if unity do not preside over it. In
objects submitted to our experience, things are united in three ways:
by juxtaposition in space; by co-existence in time; and by association
in the exercise of their activity. The elements constitutive of
extension are united in the first way; all objects belonging to the
same time, in the second; and in the third all those which unite their
forces and direct them to one and the same end.
31. The union consisting in the continuity of elements in space, has no
value in the eyes of science, save inasmuch as there is an intelligent
being who perceives the forms resulting from this continuity, by
reducing them to unity under ideal types. Four lines of points,
so disposed as to form a quadrilateral figure, have no scientific
meaning until there comes an intelligence and perceives the form of a
quadrilateral figure under the aspect of unity. We do not deny that the
quadrilateral figure exists independently of intellectual perception:
these lines will certainly exist, and be arranged in the same manner,
although we prescind all intelligence; but this disposition in the
quadrilateral form is a relation, not a being distinct from the
aggregation of the elements disposed; and this relation, of itself
alone, is no object of intelligence except inasmuch as presented to it
under the unity of the quadrilateral form.
The intelligence in search of a true being, can find none, save in
elements; and if it wishes to perceive their relation, it must recur to
the unity of form.
32. Co-existence in time, is a relation, which, of itself alone,
neither gives any thing to, nor takes any thing from objects. These
exist independently of this relation; for they must, of necessity,
exist, in order to co-exist. This relation denotes something
perceptible to the understanding, only as it is presented to it under
unity, which, in this case, is unity of time, as in the former it was
unity of space.
33. Neither has the association of activities any meaning, except when
it expresses the convergence of forces towards one and the same object.
If unity be wanting to the point of their direction, their union will
express nothing, and the intelligence will have for its object only
scattered and unrelated activities.
34. We have then shown that unity is a law of our understanding,
founded upon the very nature of things. Absolute being is never found
in the composite, but only in the simple, and relative being is not
even conceivable, if it be not submitted to unity.
35. We discover in the very nature of our mind, the second origin of
its tendency to unity. It in itself is one, is simple, and therefore
disposed to assimilate every thing to itself under this same unity
and simplicity. It feels that it is one in the midst of multiplicity,
permanent even in succession, and under all the immense variety of
sensible phenomena, intellectual and moral, which it unceasingly
experiences. The inward sense attests with irresistible certainty the
identity of the _me_. This unity, this identity, is as certain, as
evident to the child who begins to feel pleasure or pain, and is sure
that he is one and the same that experiences both impressions, as
they are to the philosopher who has spent long years in profoundly
investigating the idea of the _me_ and the unity of consciousness.
The unity and simplicity which we experience in ourselves force us
to reduce the composite to the simple, the multiple to the one. The
perception of things the most composite refers to a consciousness
essentially one: even were we to perceive the whole complicated
universe by a single act, this act would be most simple, since
otherwise the _me_ could not say, _I perceive_.
36. Two reasons, then, exist why our mind in all things seeks unity.
Objects are unintelligible, except so far as subjected to a certain
perceptible unity, to a form, under which the multiple is made one, and
the composite simple. The object of the understanding is being, and
being consists in the simple. The composite involves an aggregation of
simple elements with the relation called _union_; but unless this be
presented under a certain unity, it does not constitute a perceptible
object.
Without the indivisible unity of consciousness, no intelligent subject
is conceivable. Every intelligent being requires this link to unite
the variety of phenomena of which it is the subject. If this unity
fail, the phenomena become an informal aggregation, unrelated among
themselves: intellectual acts without an intelligent being.
The tendency to unity originates in the perfection of our mind, and is
itself a perfection; but it needs to be carefully watched, lest it go
astray, and seek real unity there, where only a factitious unity can be
found. This exaggeration is the cause of pantheism, the fatal error of
our day. Our mind is one, so also is the infinite essence, cause of all
finite beings; but the aggregation of these beings is not one, for even
when united by many ties, they cease not to be distinct. There is in
the world unity of order, of harmony, of origin, and of end; but there
is no absolute unity. Number also enters into unity of harmony, but it
is incompatible with absolute unity, as reason and experience both show.
CHAPTER V.
GENERATION OF THE IDEA OF NUMBER.
37. Unity is the first element of number, but does not of itself alone
constitute number, which is not unity, but the collection of unities.
38. _Two_ is a number. What is our idea of the number _two_? Evidently
it is not confounded with its sign, for signs are many and very
different, but it is one and always the same.
39. It would seem at first sight that the idea of two is independent
of the mode of its generation, and that, being one, it may be formed
by addition or subtraction, by adding one to one, or taking one
from three: 1 + 1 = 2; 3-1 = 2. But if we reflect upon these two
expressions, we shall see that the latter is impossible without the
former. We should not know that 3-1 = 2 if we did not previously know
that two entered into the composition of three, and how it entered. We
could know nothing of this had we not already the idea of two, and this
idea is nothing else than the perception of this sum.
40. The idea of two is no sensation, for it extends alike to the
sensible and the non-sensible, to the simultaneous and the successive.
In itself it is simple, its object is composite.
41. Since the collection of objects is small in two, the imagination
can easily figure to itself what the understanding perceives; and the
idea seems clearer to us because made sensible by a representation. The
idea of addition made, _in facto_, that is, the idea of the sum, enters
into that of two, but not of addition _in fieri_. Our idea of this
number is perfectly clear, and yet we do not continually think of one
plus one.
42. The idea of two refers to the simultaneous as well as to the
successive; but our mind does not discover it until after it has the
idea of succession. The object of this perception is the relation of
united things; the understanding perceives them as such, and then only
has it the idea of two.
43. Neither the successive nor simultaneous perception of two objects
unaccompanied by relation is the idea of two. Hence the saying: a man
and a horse do not make two, but only one and one; and the reason of
this is that the man and the horse are represented to the understanding
by their difference, not by their resemblance; and things must be
presented to the mind under a common idea in order to give number.
Thus, if we abstract their difference, and consider them only as
animals, or corporeal beings, or beings simply, or things, they will
make two.
44. In objects, then, totally unlike, or not comprehended under some
common idea, there can be no number. Abstract number is number by
excellence; because it eliminates all that distinguishes the things
numbered, and considers them only as beings, consequently as similar,
as contained in the general idea of being. Concrete numbers are
only numbers so far as they participate in this property. _Two_ is
applicable to one horse and another horse, but not to a horse and a
man, unless we identify them under the idea of animal, and abstract
rationality and irrationality. Concrete number requires a common
denomination; otherwise it is not number.
45. The idea of distinction, that is, that the one is not the other,
enters into the idea of two, so that this idea necessarily involves an
affirmation and a negation. The affirmation is of the real, possible,
or imaginary existence of the things counted; the negation is of the
one with respect to the other. Affirmation without distinction or
negation involves identity. The idea of two, as well as that of every
other number, includes the ideas of identity and distinction. The
identity is of each extreme with itself; the distinction is of the
extremes among themselves. Identity in the thing is the thing itself:
identity in the idea is the simple perception of the thing. Distinction
in the thing is the negation of it with respect to others: distinction
in the idea is the perception of negation. We always perceive a thing
as identical, and consequently every perception includes the idea
of unity. But we do not always, when we perceive a thing, observe
its negation with respect to others, and consequently do not always
perceive number. The idea of number originates in comparison, when we
see an object which _is not_ another.
46. The ideas of being, distinction, and similarity enter into that
of two. The idea of being, because nothing cannot be counted: that
of distinction, or negation of the one being the other, because the
identical does not constitute number: that of similarity, because
things are only numbered when abstraction is made of their difference.
Being is the basis of perception; distinction, of comparison; and
similarity, of union. Perception begins with unity, proceeds with
distinction, and ends with similarity, which is a kind of unity. The
perception of this similarity unites what is distinct; but the union
need not always be of the things, but may be in the idea comprising
them. There are two poles of the world, but they are not united. The
perception of the number two requires something more than the simple
perception of objects; they must be susceptible of comparison, and
consequently united in a common idea. This perception, therefore,
demands comparison and abstraction, and this is why animals cannot
numerate; they can neither compare nor generalize.
47. The analysis of the idea of two is the analysis of all numbers; the
difference is not of nature, but of more and less; in the repetition of
the same perception.
48. If any one now ask whether number be in the things, or in the mind
alone, we reply that it is in things as in its foundation, because both
distinction and similarity are in the things; that is, the one is not
the other, and both have something in common; but it is the mind that
sees all this.
49. After having perceived the distinction and union of two objects,
we can also perceive another object, which will be neither the one nor
the other of them, and will yet be comprehended in one general idea
with them. This is the perception or idea of the number _three_. No
matter how many numbers be imagined, nothing will ever be discovered in
any of them except a simultaneous perception of objects, distinction
of objects, and similarity of objects. If these be determinate, we
shall have concrete number; if they be comprised in the general idea of
being, of thing, we shall have abstract number.
50. The limits of our mind prevent it from comparing many objects at
one time, and from easily recollecting the comparisons it has already
made. To assist the memory, and the perception of these relations, we
make use of signs. When we pass beyond three or four, our power of
simultaneous perception fails, and we divide the object into groups
which serve us as new units, and are expressed by signs. Ten is clearly
the general group in the decimal system; but before we reach the number
ten we have already formed other subalternate groups; since to count
ten, we do not say one and one and one, etc., but one and one, two;
two and one, three; three and one, four, etc. Each unit added forms
a new group, which, in its turn, serves to form another. With two,
we form three; with three, four, and so on. This affords an idea of
the relation of numbers with their signs; but, as this matter is too
important to be here dismissed, we will further develop it in the
following chapters.
CHAPTER VI.
CONNECTION OF THE IDEAS OF NUMBER WITH THEIR SIGNS.
51. The connection of ideas and impressions, in a sign, is a most
wonderful intellectual phenomenon, and at the same time of the greatest
help to our mind. Were it not for this connection, we could scarcely
reflect at all upon objects somewhat complex, and above all our memory
would be exceedingly limited.[26]
[26] See L. IV., C. XXVIII. and XXIX.
52. Condillac made some excellent remarks upon this matter: in his
opinion, we cannot, unaided by signs, count more than three or four.
If, indeed, we had no sign but that of unity, we could readily count
two, saying one and one. Having only two ideas, we could easily satisfy
ourselves that we had twice repeated one. But it is not so easy to be
certain of the exactness of our repetition when we have to count three,
by saying one and one and one; still, this is not difficult. It is more
so to count four, and next to impossible to go as far as ten. If we
undertake to abstract the signs, we shall find that it is impossible
to form an idea of ten by repeating one; and that it will be alike
impossible, if we employ no sign, to make sure that we have repeated
one exactly ten times.
53. Suppose the sign two, and one half of the difficulty is obviated;
thus it will be much easier to say two and one, than one and one and
one. In this supposition four will be no more difficult than was two,
since, just as we before said, one and one, two; we now say, two and
two, four. The attention before divided four times by the repetition of
one, is now only divided twice. Six was before a hard number to count,
but, in the present supposition, it is as easy as three was before;
for, if we repeat two and two and two, we shall have six. The attention
before distracted by six signs, is now distracted only by three.
Evidently, if we continue to form the numbers three, four, and so on,
expressive of distinct collections, we shall gradually facilitate
numeration, until we attain the decimal simplicity now in use.
54. It may here be asked if the actual system be the most perfect
possible? And if facility depend upon the distribution of collections
in signs, can there be any thing more perfect than this distribution?
Either there is question of new signs to denote new collections, or
of the combination of signs. There can be no number which we cannot
express with our present system, and consequently there is no need of
inventing any thing to denote new collections. New signs might perhaps
be invented for these collections, and these collections might possibly
be distributed in a simpler and more convenient manner. In this case
we admit an amelioration to be possible, though very difficult; but
none in the former. In a word, the only possible progress would be in
expressing better, not in expressing more.
55. The sign connects many ideas which, without it, would be isolated;
hence its necessity in many cases, its utility in all cases. With the
word hundred, or its numerical representative, 100, we know that we
have one repeated a hundred times. Were this help to fail, we could not
speak of a hundred, base calculations upon it, or even form it. It is,
however, well said that we do not succeed in forming it except by tens,
by repeating the calculation ten ten times.
56. Let it not, therefore, be thought that the idea of the number is
the idea of the sign; for evidently the same idea of ten corresponds to
the word ten, whether written, spoken, or numerically represented by
the figures 10, although these three signs are very different. Every
language has a word of its own to express ten, and all people have the
same idea of it.
57. This last remark creates a difficulty as to what the idea of
ten consists in. We cannot say that it is the recollection of the
repetition of one ten times; first, because we do not think of this
recollection when thinking of ten; and second, because, according to
what has already been said, a clear recollection of this repetition is
impossible. Neither is it the idea of the sign, for the idea signified
existed before the sign was invented, otherwise the invention would
have had no object, and would even have been impossible. There can be
no sign where there is nothing to signify.
The idea of number includes more difficulties than Condillac ever
imagined; who, if he had, after his close analysis of what facilitates
numeration, profoundly meditated upon the idea itself, would not
so readily have censured St. Augustine, Malebranche, and the whole
Platonic school, for having said that numbers perceived by the pure
understanding are something superior to those perceived by the senses.
CHAPTER VII.
ANALYSIS OF THE IDEA OF NUMBER IN ITSELF AND IN ITS RELATIONS WITH
SIGNS.
58. In order clearly to conceive the idea of number, and the way it is
engendered in our mind, let us study its formation in a deaf and dumb
person.
We have no better way of giving such a one an idea of unity than by
presenting an object to him. Now, if we would convey to him the idea of
two, we show him two fingers, then two oranges, then two books, and in
each of these operations make a sign which must be always the same. If
we repeat this operation a number of times, the deaf and dumb person
will associate the idea of two with that of the sign, and one will
suggest the others; and he will endeavor to show us that he has seen
two objects of some kind, by uniting the expression of the object with
the sign of two. The same will take place with three, or four. When we
reach higher numbers, the sign becomes more indispensable; since the
less easily the idea of number is represented, the more necessary is
the sign to secure it. But what we do to convey an idea of number to
the deaf and dumb person, what he himself must do to express the number
which he conceives, we must all do if we would obtain the idea.
59. Numeration is a repetition of operations; and the art of
facilitating it consists in instituting signs which recall to our
memory what we have done. It is an exceedingly complicated labyrinth,
and we cannot trust ourselves to its windings with any expectation of
finding our way out again, if we do not take care to mark the path we
have followed.
It is to the admirable simplicity of the decimal system, united to
its inexhaustible variety, that the facility and fecundity of our
arithmetic are due. Algebra, going a step beyond, expresses without
determining numbers, and presents the results of its operations without
effacing its footsteps on the road travelled, is far superior to
arithmetic, and has made the human mind take gigantic strides. But how?
Solely by aiding the memory. Thus, the very principle that enables the
child to say four and one, five, instead of adding unity five times to
unity, the dumb man to express five by a hand, a hundred by a grain,
enables the algebraist to express the result of his longest operations
by a formula easy of retention by the memory. Both attain their object
simply by aiding the memory. A grain of wheat denotes to the dumb man
the idea of hundred, and this he applies to all similar collections; a
few letters combined in a simple manner designate to the mathematician
a property of certain quantities, and this he applies to all which are
found in the same case.
60. Numeration is only an aggregation of formulas; and the more easy
these are of mutual transformation with a slight modification, the more
perfect will be the numeration. The better one knows the relations of
these formulas and the manner of transforming them, the better will he
know how to count. The greater a person's intellectual power of fixing
simultaneously the attention upon many formulas, and of composing them,
the more perfect arithmetician will he be, because the simultaneous
comparison of many, leads to the perception of new relations.
61. What is our idea of hundred? The union of the units composing it,
a union which we have made more or less frequently when learning to
count. But how do we know that it is the same union? Because we have a
formula called a hundred, expressed by a sign 100. This formula is so
easily recollected that we have no difficulty in recollecting the idea
of hundred and all the properties connected with it. We may be asked
if a hundred is more than ninety. Were we under the necessity counting
one and one and one, we should be bewildered, and never succeed in
distinguishing the greater; but knowing as we do that to reach the
formula hundred, we must pass by another formula ninety, and that this
was in ascending, we know, once for all, that hundred expresses ninety
and something more, that is, a hundred is more than ninety. And if
it be further inquired what is the excess, we shall not undertake to
ascertain this by adding units, but by the two formulas ninety and ten
which compose the formula hundred.
62. By generalization we unite many similar things in one idea. The
general idea is a kind of formula. Numeration unites in one sign many
things contained in a general idea, but this sign has, at the same
time, its own distinctive character. Thus the general idea belongs as a
predicate to each of its particular objects; number belongs to no one
in particular, but to all joined. We perceive in abstraction a common
property, and lay aside all the particular objects which it presents;
in numeration, we perceive similarity, but always with distinction.
Abstraction is the result of comparison, but not comparison. Numeration
implies a permanent comparison, or the recollection of it.
63. The idea of number is not conventional; a hundred is always a
hundred with all its properties and relations, and this, too, prior
to all convention and even to all human perception. The sign, and the
sign only, is conventional. Were there no intellectual creature, and
a hundred beings distinct among themselves were to exist, there would
really be this number. The number three exists in the august mystery
of the Trinity, from all eternity, and of absolute necessity. Number
requires only the existence of distinct things; since, however unlike
they may be, they always have something in common being, which may
be included in a general idea, and consequently they fulfil the two
conditions necessary to number.
64. The perception of being and of distinction, that is, of substantive
being and of relative not-being, is the perception of number. The
science of the relations of every collection, with its measure, which
is unity, is the science of numbers.
BOOK SEVENTH.
ON TIME.
CHAPTER I.
IMPORTANCE AND DIFFICULTY OF THE SUBJECT.
1. The explanation of the idea of time is not a matter of mere
curiosity, but of the highest importance. To convince ourselves of
this we have only to consider that the explanation of the whole
edifice of human cognitions is based upon it. The most fundamental and
indispensable principle which supports all others, includes the idea
of time. A thing cannot be and not be at the same time: "impossibile
est idem simul esse et non esse." The impossibility of being and of
not-being regards only the _simul, the same time_. Therefore, the idea
of time necessarily enters into the very principle of contradiction.
2. The idea of time is involved in all our perceptions; it extends to
many more objects than does the idea of space. We estimate not only the
movements of bodies by time, but also the operations of the mind. We
know that a series of thoughts may be measured by time the same as a
series of corporal movements.
3. The idea of succession necessarily enters into that of time, and
_vice versa_, the idea of time into that of succession. We may conceive
that one thing _succeeds_ another; but this would be impossible without
succession, without a _before and after_, that is, without time. This
reasoning, apparently vicious, shows, perhaps, that we must not
explain the ideas of time and succession, the one by the other, since
they are identical.
4. Time does not seem to be distinct from things; for who can imagine
duration without that which lasts, or a succession without that which
succeeds? Is it a substance? Is it a modification inherent in things,
or distinct from them? Whatever is something exists; and yet we nowhere
meet time existing. Its nature is composed of instants divisible
to infinity, essentially successive, and consequently incapable of
simultaneousness. Imagine the minutest instant you can, and it does not
exist, for it is composed of others infinitely minute, which cannot
exist united. To conceive an existing time, we must conceive it as
actual, and in order to do this, we must surprise it in an indivisible
instant; but even this is not time; it involves no succession; it is
not _duration_, containing _a before and an after_.
5. Nothing is easier than to calculate time, and nothing more difficult
than to conceive it in its essence. As to the former the learned and
the ignorant are on the same footing; both have equally clear ideas;
the latter is excessively difficult even to the most eminent men. The
passage in the _Confessiones_ of St. Augustine, in which the Holy
Doctor endeavors to penetrate this mystery is well known.
CHAPTER II.
IS TIME THE MEASURE OF MOVEMENT?
6. Time is said by many philosophers to be the measure of movement.
This idea is fruitful, but it needs to be illustrated.
When we measure movement we refer to something fixed. Thus we measure
the rapidity with which we have traversed a certain space by noticing
the time denoted by a watch. But how do we measure time by a watch? By
the space passed over by the hand on the dial. If we reflect carefully,
we shall see that this is purely conventional, or rather, that it
depends upon an arbitrary condition. For if we suppose the time marked
to be an hour, the space passed over by the minute hand, that is, the
circumference of the dial, has no relation with the hour except what
the artificer gave it by so constructing the watch that the minute hand
would make one revolution every hour. If the watchmaker had constructed
it differently, as he did the hour hand, the time would be the same,
but the space passed over is very different.
7. The time, therefore, indicated by the watch is no measure, save
as itself is subject to another measure; consequently it is not the
primitive measure. The same can evidently be said of all other watches
which must have been regulated one after another, until we come to the
first of all watches. There was no other watch to regulate this; it
follows, therefore, that no one of the measures furnished by art is the
primitive measure.
8. Not finding this measure in the works of man, we must seek it in
nature; and here we discover fixed measures. If we regard the course
of the sun, and take for unity the time it requires from the time it
leaves the meridian until it returns, we shall have the day; this
divided into twenty-four parts gives us the hours. Here we have a great
watch which will serve to regulate all others.
9. Nevertheless, however lightly we reflect upon this, we cannot help
seeing that the solution is not so satisfactory as it seems at first
sight.
Solar time and sidereal time do not agree. Thus, if we note the moment
when a star is in the meridian conjointly with the sun, we shall the
next day see that the star reaches the meridian a little before the
sun. Which is right? Has the star taken just twenty-four hours, or the
sun? If time be a fixed thing independently of movement, neither of
these measures corresponds exactly to time.
10. This argument, which may be called practical, is corroborated by
another purely theoretical. If we take celestial movement for the
measure of time, will it be true that whenever the movement, which
serves as the rule, shall be verified, that there has passed a fixed
and determinate time? If we be answered in the affirmative, we must
infer, that even were this movement to be accelerated or retarded,
as, for instance, if a solar revolution were to be made with a half,
or with twice its ordinary velocity, it would continue to mark the
same time, which, however, is absurd. If it be said that the movement
is supposed to be uniform, we reply, that this is a begging of the
question. Uniformity of movement consists in equal times recurring
after equal intervals. Did time, then, in its nature depend upon the
movement of the sun, or of any star, as primitive measure, neither
uniformity nor variety would have any meaning. If the space of
twenty-four hours depended upon a revolution's being made, no matter in
what manner whether at a snail's pace, or with the velocity of light,
we should never have more or less than twenty-four hours. But if these
depend upon another measure, if prior to them, there was a time which
measured the velocity of movement, and determined whether it had been
accelerated or retarded, then the movement of the stars is not the
primitive measure; they are in the same category as our watches, they
marked the time passed, but time has not passed because they mark it.
Time is the measure of their movement, not their movement the measure
of time. Movement is in time, not time in movement.
11. To appeal to the movement of the superior heavens, is evidently no
solution of this difficulty, for what has been said of the sun, may
also be said of the remotest star in the firmament. Whether we appeal
to annual, solar, or sidereal movements, the same difficulty remains.
Would sidereal years be the same, if the movement be made with greater
or less velocity. If they would, an absurdity would follow; if not,
this is not the primitive measure.
12. Moreover, we perceive, when considering movement, that we seem to
conceive of greater and less velocity; and thus the idea of time, of
necessity, enters into that of velocity, since velocity is the relation
of space passed over in a given time. The idea of time is therefore
prior to, consequently independent of, _every_ particular measure.
13. We measure time by movement, and in order to measure the velocity
of movement we need that of time. Here then, perhaps, is a vicious
circle; but possibly this only shows that these are correlative ideas,
the one explanatory of the other; or, rather, they are different
aspects of one and the same idea. The difficulty of separating them,
and the intimate union which unites them on the one hand as much as
it divides them on the other, confirms this conjecture. To show this,
we ask, what time has passed? Two hours. How do we know this? By our
time-piece. But what if it be too fast or too slow? The measure fails.
This time is thus to us as a fixed measure, prior to that of the watch
by which we undertake to measure it. But what are these two hours, if
we abstract the measure of the watch, that also of the stars, and every
other measure? Two hours, in the abstract, can be found in no category
of real or possible beings; and we cannot, without a measure, give any
idea of them, nor form one for ourselves. The idea of hour refers to a
determinate movement of known bodies; and this in its turn refers to
others; and finally, we come to one in which we can discover no reason
why it should be exempted from the general law to which the others are
subject. No farther reference being possible, all measure fails; and
this failing, time, by the force of analysis, vanishes.
14. Therefore, the referring of time to movement, explains nothing; it
only expresses a thing known, and that is, the mutual relation between
time and movement, a relation known to the unlearned, and of constant
and common use; but the philosophic idea stands intact; the same
difficulty remains; what is time?
CHAPTER III.
SIMILARITIES AND DIFFERENCES BETWEEN TIME AND SPACE.
15. Time seems to us to be something fixed. An hour is neither more
nor less than an hour, no matter how our time-pieces go, or the world
itself; just as a cubic foot of space is always a cubic foot, neither
more nor less, whether occupied or not occupied by bodies.
16. Time exists independent of all movement, of all succession; if
it is something absolute, has a determinate value of its own, is
applicable to all that changes without itself changing, the measure of
all succession without itself being measured, what is it? That it is
something accidental cannot be reconciled with its immutability and
universality. Every thing lives in it, but it lives in nothing; every
thing dies in it, but death has no power over it. When the substance
perishes, the accident perishes; but time continues the same although
no substance exist. Before all created beings, we conceive ages and
ages, that is, time; and after the destruction, the annihilation of all
beings, we still conceive a successive although unending succession,
which is time. The idea, then, of time, does not demand that of the
universe; it existed before it, and will survive it: but without time
the universe is inconceivable.
17. The idea of time seems to be independent of the idea of any being;
of all duration in it; every thing may endure in it; but it does not
begin or end with what endures in itself; it is applicable to all
that endures, but it is not itself an endurable thing. We imagine
it to be one in the multiple, uniform in the various, fixed in the
movable, eternal in the perishable; and it even seems to contain some
features of the attributes of Divinity; but it is, on the other hand,
essentially despoiled of every property excepting that of succession in
its abstractest signification. It is essentially sterile, has no power
of its own, no condition of being or action, and consequently leads to
the highest imaginations of what a pure idea really is, an abstraction,
which, like space, we have imagined in the presence of things.
18. The points of similarity between time and space are worthy of our
attention. Both are infinite, immovable; both are a general measure;
both essentially composed of continuous and inseparable parts. Limit
them you cannot, determine any limit you chose, and beyond it you will
see an ocean extended. Your powers are impotent; beyond the highest
heaven are unbounded abysses of space; before the beginning of things
there was a long chain of interminable ages.
In vain would you undertake to move space; you can only move yourself
in it, or survey its various points. Its points are all fixed; you
may mark out distances and directions with respect to them, but you
cannot change them. The result will be analogous if you attempt to move
time. The present instant is not the one just past, nor the one next
to succeed; they are of necessity distinct, and of necessity exclude
each other. Their very nature is to succeed each other. If their place
be changed with respect to time, it ceases to be the same. Imagine,
if you can, that to-morrow is to-day, that to-day is yesterday. It
is impossible for that which was at a certain time not to have then
been; but this would not be impossible if time could be moved; for in
order that what was yesterday may not be, it is necessary to convert
yesterday into to-morrow; but this would be an absurdity. The past, the
present, and the future, are essentially distinct things.
A simple space, a space without parts, is no space at all, it is a
contradiction; neither is a simple time, a time without parts, a time,
but is a contradiction.
A space whose parts are not continuous, is not a space; neither is
a time whose parts are not continuous, a time. The parts
of space are inseparable; you may distinguish them one from another,
count them one after the other, compare them one with another, and
consider them one after another, but you cannot separate them. All
imaginable bodies may exist in the apartment where we write, one or
many, at rest or in motion; but the space which we conceive is one,
fixed, and always the same; we can estimate its extent in cubic feet,
if we choose, but these feet are fixed and inseparable; we cannot
separate one cubic foot from another, even if we would; for even while
we annihilate it, it is present to us, and in the same distance that we
need in order to conceive separation. We cannot conceive separation,
if we do not conceive distance; nor conceive distance, if we do not
conceive space. We separate bodies from each other, but not one space
from another. Space remains with the same continuity when bodies are
separated, and it is by this continuity remaining unalterable that we
measure the extent of their separation. The same happens with time; it
is a chain which cannot be broken. Can we conceive three successive,
immediate instants, A, B, C, and then suppress B? Certainly not; such
a suppression would be impossible, or it would be a poor diversion.
We destroy B in our caprice, and A and C are continuous; since being
only separated by B, when it disappears the extremes meet. But in this
case it is no longer A, but B, for B is the instant which precedes C.
We have no other distinction than that of priority with respect to C,
and continuity with A. When, then, by the imaginary disappearance of
B, A is brought into contact with C, it is converted into B. Moreover,
A is not only connected with C, but is preceded by others; if, then,
by the disappearance of B, it makes a step, so also must the whole
infinite chain which precedes it. Each one is then a soldier, or rather
no soldiery is possible, for we have taken an instant from the infinite
chain, and so rendered it finite. Or, more distinctly; can we conceive
yesterday or to-morrow without to-day, a future or a past without the
present? Evidently we cannot. Time, then, is essentially composed of
inseparable parts.
19. This similarity between time and space naturally leads us to
believe that time is an abstract idea just as space is. What we have
said of space is applicable to time, only with a few modifications
exacted by the very nature of the thing. It can in no case be without
utility, in scientific investigations, to approximate and compare
these great ideas, which are as immense receptacles wherein our mind
deposits its treasures. The actual corporeal universe, and all possible
universes, are included in the idea of space; and all finite beings,
corporeal or incorporeal, are included in that of time.
20. We may well suspect that these ideas, so intimately united to our
perceptions, are formed in a similar manner; for it is probable that
they belong to the order of those primitive laws which govern the
development of our intellect.
21. The similarity between space and time must not make us ignore the
differences which distinguish them.
I. All the parts of space are co-existent; otherwise, that continuity
which is essential to them, would be inconceivable. Time is composed
of successive parts; to imagine them co-existent, is to destroy the
essence of time.
II. Space refers solely to the corporeal world, under only one aspect,
that of continuity. Time extends to all that is successive, corporeal
or incorporeal.
III. Consequently, the idea of space exists only in the geometrical
order, of which it is the basis. The idea of time is mingled with every
thing, and more especially with our own acts.
IV. Our soul, when reflecting upon itself, can totally prescind space,
and forget all its relations with extended objects; but it cannot
prescind time, which it finds necessary even to its own operations.
This last difference is a great help to the understanding in what the
idea of time consists; and we venture to recommend it to the attention
and memory of the reader.
CHAPTER IV.
DEFINITION OF TIME.
22. Time is duration; but duration without something which endures, is
an absurdity. There can then be no time without something existing. The
duration which we conceive, after reducing every thing to nihility, is
a vain imagination; it is not an idea, but is rather in contradiction
with ideas.
An important consequence flows from this; it is, that time in itself,
cannot be defined with absolute elimination of every thing to which it
refers. Time, then, has no proper existence; and separated from beings
is annihilated.
23. Hence, also, it follows that that infinity which we attribute to
time, has no rational foundation. We have no other reason to affirm
this infinity than a vague conception, which presents it as such; but
we cannot fail to perceive that this conception also exists, even if
we suppose all to be reduced to nothing. If, then, there is in this
supposition a vain diversion of the imagination, it is not an idea, but
a contradiction with ideas; and what has once deceived us, no longer
deserves any credit. Those infinite ages of time which we conceive
prior to the creation, are not nothing; they are an imaginary time,
similar to an imaginary space.
24. Time has no necessary relation with movement, since if nothing
were to move, or even no bodies to exist, we should nevertheless
conceive time in the succession of operations of our soul. This last
is indispensable; we must have some succession of things in order to
conceive time. If we suppose nothing to change or to be altered, a
being subject to no external or internal change, having one single
thought always the same, one single will always the same, having no
succession of ideas or acts of any kind whatever, we conceive nothing
to which the idea of time is applicable.
Time is a measure; but what is it to measure in a being of this kind?
Succession? But there is no succession. Duration? But what is there to
measure in a duration always the same, which is only the same being?
Duration must have parts given to it before it can be measured; but
what parts has it? Those of time? But this would be a begging of the
question, since time is applied to it when we are inquiring whether
time is applicable to it. When theologians say that the existence
of God cannot be measured by time, that there is no succession in
eternity, but that all is united in a single point, they utter a
profound truth; and Clarke, before ridiculing it, should have studied
to understand it.
25. Time commences with mutable things; if they perish, it perishes
with them. There is no succession without mutation; and consequently,
no time.
26. What, then, is time? The succession of things considered in the
abstract.
What is succession? Being and not-being. A thing exists; it ceases to
exist; here we have succession. Whenever time can be calculated, there
is succession; and whenever succession can be calculated a being and
a not-being are considered. The perception of this relation, of this
being and not-being, is the idea of time.
27. Time cannot exist without being and not-being; because in this,
succession consists; wherever there is succession, there is some
mutation; and there is no mutation without something being in another
manner, and this other manner is not possible unless the prior manner
ceases to be.
Substances, modifications, and appearances have no succession without
this being and not-being. What is motion? The succession of the
positions of a body with respect to various points; and this succession
is verified by occupying some of these positions and destroying others.
What is the succession of thoughts or affections of our mind? The
not-being of some which were, and the being of others which were not.
28. Time, then, in things, is their succession, their being and
not-being. Time in the understanding, is the perception of this
mutation, this being and not-being.
CHAPTER V.
TIME IS NOTHING ABSOLUTE.
29. Is time something absolute? The definition given in the last
chapter shows clearly enough that it is not. Time in things is not
being only, nor not-being only, but the _relation_ of being and
not-being. Time in the understanding, is the perception of this
relation.
The measure of time is nothing else than the comparison of mutations
among themselves. To us, those mutations which seem to be unalterably
uniform serve as the primitive measure. For this we have taken the
movement of the sun. This movement varies when compared with that of
the stars, and ceases to be the primitive measure when referred to
this: and it was upon this the scholastics rested when they taught that
the movement of the first heavens was the primitive measure of time.
30. But what if the velocity of the sun were augmented, and it should
make its revolution in one half of its time? Would the hours continue
the same? We distinguish. If this alteration should be verified solely
in the solar movement, we should perceive the discordance between this
and all other movements; and perceiving this alteration in the sun, we
should continue to refer our hours as things fixed to other measures,
to our own movements, to our time-pieces, or to other heavenly bodies.
But if we suppose every thing to be changed at one and the same time,
and in the same proportion; the movement of all the heavens and of
every thing terrestrial to be doubly accelerated, but in such a way as
not to increase the rapidity of our thoughts; we should indeed discover
an alteration, but we should not know whether to attribute it to the
world or to ourselves; we should perceive a discrepancy between our
thoughts and these movements, but should not know whether these were
accelerated or our thoughts retarded.
If this rapidity be also communicated to us, so that such or such
a series of thoughts formerly corresponding to so many minutes is
now made in one half the number, we should then witness a perfect
correspondence in all things; we could perceive no mutation. An hour,
for example, is to us only the perception of the relation of certain
mutations: so long as this relation continues the same, there will be
no alteration in the hour.
31. To take away from time every idea of absolute, seems an absurdity
to the imagination, but not to reason. This case will make this
evident. Not the man, the best skilled in perceiving the succession of
time, can, if he look at no time-piece, nor refer to any measure for
twelve hours, say whether eleven hours and a half or twelve hours have
passed. If he live long in this way, he will become totally incapable
of estimating time; if locked up in a dark dungeon for several months,
he will believe he has spent years there. The idea, therefore, of the
measure of time, is nothing absolute; it is essentially relative; it
is the perception of the relations between various mutations. So long
as these relations remain whole and intact, time will be to us the same.
CHAPTER VI.
DIFFICULTIES IN THE EXPLANATION OF VELOCITY.
32. Here arises a serious difficulty: if time be nothing absolute,
greater or less velocity is inexplicable. This seems to result even
from what we have said, that if the relation of movements be not
changed, any augmentation or diminution of velocity is impossible;
because, if velocity be in necessary relation to time, and time itself
be nothing but the relation of mutations, it is inconceivable how time,
and consequently how velocity, can be changed without changing the
relation of mutations. Thus it would be impossible for the velocity of
the whole mechanism of the universe to be changed, just as it would
be absurd to say that the stars and every thing that exists may now
experience the same changes of velocity. This would destroy the very
idea of velocity; at least if taken as something absolute, wherein
different grades may be considered.
33. Let us now examine this difficulty, which indeed deserves to be
examined, for it seems to contradict our most common ideas.
First of all, we must premise that velocity is not something absolute,
but a relation. Physicists and mathematicians express it by a fraction
whose numerator is the space run over and whose denominator is the time
consumed. Making V the velocity, S the space, and T the time, we shall
have V = S/T. This shows the velocity to be essentially a _relation_;
for it cannot be otherwise expressed than by the ratio of the space to
the time.
34. This mathematic formula expresses the idea we all have of velocity;
it expresses in three letters what the unlettered man repeatedly says
to himself. The velocity of two horses is ascertained not solely by the
space they have passed over, nor solely by the time they have consumed
in their career, but by the greater or less space passed over in a
given time; or by the longer or shorter time required to pass over a
given space.
To deny, then, to velocity an absolute nature, is nothing new; for we
all of us make it essentially consist in a relation.
35. In the expression V = S/T two terms enter, space and time. Viewing
the former in the real order, abstraction made of that of phenomena, we
more easily come to regard it as something fixed; and we comprehend it
in a given case without any relation. A foot is at all times a foot;
and a yard, a yard. These are quantities existing in reality; and if
we refer them to other quantities, it is only to make sure that they
are so; not because their reality depends upon the relation. A cubic
foot of water is not a cubic foot because the measure so says, but
on the contrary, the measure so says because there is a cubit foot.
The measure itself is also an absolute quantity; and in general, all
extensions are absolute, for otherwise, we should be obliged to seek
measure of measure, and so on to infinity. True, to call things large
or small depends upon comparison; but this does not change their own
quantity. The diameter of the earth, compared with an inch measure,
is immense; but it is an almost imperceptible point compared with
the distance of the fixed stars; yet this does not prevent the inch
measure, the diameter of the earth, and the distance to the fixed
stars, from being values in themselves determinate, and independent of
each other.[27]
[27] See Lib. III., Ch. XX.
If the denominator in S/T were a quantity of the same kind as space,
that is, having determinate values, existing and conceivable by
themselves alone, the velocity, although still a relation, might also
have determinate values, not indeed, wholly absolute, but only in the
supposition that the two terms, S and T, having fixed values, are
compared. Thus, if we require a velocity of 4, we have only to take a
fixed quantity of space, and another fixed quantity of time, having the
relation to each other of 4 to 1; and this is quite easy, when S and T
are both absolute quantities. If, in this supposition, an acceleration
or delay be required in the whole universe, nothing more would be
required than to augment or diminish the time in which each part would
have to traverse its respective space. But from the difficulties which
we have on the one hand seen presented to the consideration of time as
an absolute thing, and from the fact that, on the other hand, no solid
proof can be adduced to show such a property to have any foundation, it
follows that we know not how to consider velocity as absolute, even in
the sense above explained.
36. Hence a consequence not less important than striking, as to the
possibility of a universal acceleration or retardation. If we would
have an acceleration or retardation of the whole machine of the
universe, and should abandon all motion to which we might refer time,
should at once change all, not excluding the operations of our own
soul, we should have a problem proposed to us that appears insolvable,
nothing less than the realization of an impossibility; the relation of
many terms would have to be changed without undergoing any change. If
velocity be only the relation of space and time, and time only the
relation of spaces traversed, it is the same thing to change them all
in the same proportion, and not to change them at all; it is to leave
every thing as it is.
37. The singularity of such consequences ought not to be a sufficient
excuse for abandoning them. We must not forget that we are examining
the common ideas of time and velocity in their most transcendental
aspect, and that it is by no means astonishing that our mind finds
itself, as it leaves its ordinary walks, in an entirely new atmosphere,
wherein it seems to discover contradictions. When we examine the
ideas of time and velocity, we unwittingly fall into the error of
uniting them in the same explanation. We would prescind them; but this
we do only with great difficulty, and we often fall into a vicious
circle. Hence it is that when, by a great effort, we succeed in
really prescinding, the consequences that follow seem contradictory;
but this apparent contradiction arises solely from our not having
persevered with due firmness in our prescision; and as, in this case,
the understanding starts from two different suppositions, whereas
it believes that it starts from one alone, the results seem to it
contradictory, which in reality they may not be. The same thing occurs
in the examination of the idea of space.[28]
[28] See Lib. III., Chs. XII., XIII., and XIV.
CHAPTER VII.
FUNDAMENTAL EXPLANATION OF SUCCESSION.
38. The reasons that destroy the absolute nature of time, inasmuch
as it is subject to measure, do not seem fully to obviate another
difficulty, arising from the consideration of time in itself. If indeed
time be succession, what is this succession? It is evident that things
succeed each other; but if there be no _before_ or _after_, that is,
time existing before succession, since succession consists in some
things coming _after_ others, what is the meaning of succeeding each
other? Thus, time is explained by succession, and succession by time.
What is _afterwards_ but a part of time that is in relation with a
_heretofore_?
39. What we said in the fourth chapter does not seem completely to
solve the difficulty; for being and not-being do not form succession,
save only inasmuch as one comes _after_ the other, that is, inasmuch
as it presupposes the time to be explained already to exist. There may
be a simultaneous being and not-being of distinct things; and there is
in one and the same thing no repugnance between being and not-being,
if not referred to the same time. In such a case, therefore, this is
always presupposed so to be; since in one and the same thing, being and
not-being are inconceivable unless at different instants of time. Hence
it follows that being and not-being do not sufficiently explain time.
40. This difficulty is indeed grave; and we must, in order to solve
it, elaborate a fundamental explanation of succession. This we shall
endeavor to do, and without in any sense supposing the idea of time.
41. There are things which exclude, and things which do not exclude
each other. When we have existence of things which exclude each other,
we have succession. If in a line a--------b--------c, a body be at a,
it cannot pass to b, without ceasing to be at a. The situation at b
excludes that at a; and so also that at c excludes that at b. When we
see things exist notwithstanding this reciprocal exclusion, we find
succession.
42. Succession is, in reality, the existence of things mentally
exclusive of each other. What each involves is the being of that which
excludes, and the not-being of that which is excluded.
43. This exclusion prevails in all variations; and therefore, we find
succession in every variation. Variation is the mutation of states;
the loss of one, and the acquisition of another; therefore, there is
exclusion, for being excludes not-being, and not-being, being.
44. When we perceive these distinctions, these exclusions realized,
we perceive succession, time. When we compute these exclusions, these
distinctions in which distinct and exclusive things are offered to us,
such as being and not-being, we compute time.
45. Here arises a difficulty. If succession involves exclusion, and
there is no succession without exclusion, it follows that things which
do not exclude each other are simultaneous; and from this we infer the
absurdity of saying, that the things happening in the time of Adam,
which do not exclude those of our own time, are simultaneous. The
motion of the plants of Paradise excludes not that of plants in gardens
now existing; this motion, then, is simultaneous with that; the motion
that was then is the present; and the present motion was then; which is
inconceivably absurd.
This difficulty is serious: it seems to be based upon a reason founded
in evident truths; but it is not impossible to give a solution of it.
46. Were there to exist one thing which excluded nothing, and was
excluded by nothing, it would be simultaneous with every thing. Know
you what this thing is? There is but one, God. It is therefore that the
theologians say, with great truth, and with a profoundness which has
not, perhaps, been at all times understood even by those who have made
the remark, that God is present to all times; that to him there is no
succession, no _before_ or _after_; that to him every thing is present,
is _now_.
47. Of God alone is this true; in all else there is some exclusion,
being and not-being, and therefore succession. Let us now, for example,
examine how the motion of the plants in our gardens is excluded by that
of the garden of Eden. How are those of our gardens moved? By existing,
and also by being subject to conditions necessary to motion. How do
they exist? By a development of the germs they themselves contain. What
is this development? A series of motions, of being and of not-being,
and consequently of things that exclude each other. There is, then, no
simultaneousness between those of the garden of Eden and those of our
own gardens; for between the former and the first germ, there was no
mediation other than the movement of the first development; whereas,
between the movements of those of our gardens and the first germ, many
others have intervened. Here we have exclusion, being and not-being.
The number of exclusions necessary to existence is very different in
the two cases; therefore, there is no simultaneousness. Considering all
the developments, and all the changes of the orb, as a dilated series
of terms interlaced by a mutual dependence, as in fact they are by the
laws of nature; and calling these terms A, B, C, D, E,--N, the plants
of the garden of Eden belong to the term A, and those of ours, to the
term N.
48. The non-simultaneousness of motion is proved in the same manner
as the non-simultaneousness of existence, for motion is a manner of
existing. Moreover, the air which agitates the plants of our gardens
has been moved by another, and this other by yet another; and these
motions, subject to all the fixed and constant laws of nature, are
all interlinked from the very first motion, just as the wheels are
interlocked in a system of machinery. But as the curvature of one wheel
is not that of the other, so these motions are different, and exclude
one another down to the last, which is the air which moves the present
plants.
49. This explanation of succession and time, throws much light on the
idea of eternity; and shows that eternity, or the simultaneousness of
all existence, belongs only to the immutable being. All mutable beings,
which necessarily imply a transition from not-being to being, and from
being to not-being, involve a succession, if not in their substance, at
least in their modifications.
50. This explains how the idea of time is found in almost all our
conceptions, and is expressed in all languages. Man continually
perceives being and not-being in all around him. He perceives it within
him, in the multitude of his thoughts and affections; at one time
agreeing, at another disagreeing; sometimes connected, and sometimes
separated; but always distinguished from one another, always producing
different modifications in the mind: they therefore exclude each
other, and cannot co-exist; because the existence of one excludes the
existence of the other.
CHAPTER VIII.
WHAT IS CO-EXISTENCE?
51. If the succession of time involves exclusion, there must be
co-existence where there is no exclusion: therefore, supposing that
God has created other worlds, they must necessarily be contemporaneous
with the present; for it is evident that they would not be excluded;
and as they have not the mutual relation of cause and effect like the
phenomena of the present world, we cannot apply to them the explanation
which we gave to show that the motion of the plants of Paradise was not
contemporaneous with the motion of the plants in our gardens. We must,
therefore, hold that it would have been impossible for another world
to exist before the present world; and that though God might create as
many beings as he pleased, yet, so long as they do not exclude each
other, they must be contemporaneous.
52. This difficulty is not easy to solve, unless we have perfectly
understood the meaning of the word exclusion. By exclusion is meant,
not only the intrinsical repugnance of one being to another, but that,
for one reason or another, whether intrinsical or extrinsical, the
existence of one implies the negation of the existence of the other.
This explanation solves the difficulty.
53. Two worlds, entirely independent of one another, could have been
subjected to this exclusion by the will of God. God can create one
without creating the other; in this case, we find the existence of the
first and the negation of the existence of the other. God can cease to
preserve the first, and create the second; we then find the existence
of the second and the negation of the first. In both these cases,
there is _before_ and _after_, a succession in existence. God can
create both; we can conceive the existence of both without the negation
of the existence of either; this is co-existence.
54. We shall understand the whole question much better, if we examine
for a moment the meaning of co-existence. Two beings co-exist, or exist
at the same time, when there is no succession of one to the other, when
both exist, when there is not the existence of one and the negation of
the other. In order to conceive co-existence, we need only conceive the
existence of two beings: we form the idea of succession, by combining
with the idea of the existence of one the idea of the negation of
the other. The co-existence of two beings is their existence; their
succession is the being of one, and the not-being of the other. Being
refers only to the present; the past and the future are not being. That
only is which is, not that which was, or which will be. There is a
profound truth, a sound philosophy, and an admirable ontology in those
words of the sacred text: "I AM WHO AM. He who is, hath sent
me to you."
55. Without being and not-being, there is no succession, there is
no time, there is only the present, there is eternity. To a being
immutable in itself, and in all its acts, one in its intelligence, one
in its will, always its own object, unchangeable, in the plenitude
of its being, without any kind of negation,--to such a being there
is neither _before_ nor _after_; there is only _now_. If you give to
it the succession of instants, you apply to it, without any ground,
the work of your imagination. Reflect well on the meaning of _before_
and _after_, in that which can change in nothing, by nothing, and
for nothing, and you will see that succession is in this case a word
without any meaning. We attribute to it succession because we judge the
object by our perceptions, and our perceptions are successive; they
have an alternative of being and not-being, even when applied to an
immutable object.
56. Every one may experience this in his own mind. Conceive two beings
to exist; add to this thought nothing accessory, neither the negation
of being, nor of time, nor of any thing else,--merely conceive the
existence of two beings, and see if any thing is wanting to complete
your idea of their co-existence. If, on the contrary, you wish to
perceive succession, or difference of instants, you must perceive the
existence of one, and the negation of the existence of the other.
Therefore, the idea of co-existence is simple, and implies only the
existence of the beings, but the idea of succession is composed of the
combination of being with not-being.
57. I must here call attention to the fruitfulness of the idea of
being, which, combined with the idea of not-being, furnishes the idea
of time. We have before seen, that the ideas of unity and number
were favored in the same manner, and we shall soon have occasion to
observe, how, from the ideas of being and not-being, spring others,
which, although secondary in respect to these, are the most important
of all the ideas which the human mind possesses. I call attention to
this, from a desire that the reader may become accustomed to refer all
ideas to a few points where they are united, not by a factitious chain
imposed by arbitrary methods, but by the internal nature of things
themselves. What extension is, in relation to sensible intuitions,
the idea of being is, in relation to conceptions. The intuition of
extension, and the idea of being, are the two fundamental points in
all ideological and ontological science; they are two primitive data
possessed by the mind, by means of which it can solve all problems,
either in the sensible order, or in the purely intellectual. Regarded
from this point of view, every thing becomes clear, and is arranged in
the most logical order, because it is the order of nature.
58. I wish to make one observation on the method which I have followed
in this work. I did not think it well to explain separately my opinion
of these general connections of all ideas; for then it would have been
necessary to treat philosophy in a systematic order, placing at the
beginning what ought to be at the end, and trying to establish as a
preliminary doctrine, what ought only to be the result of a collection
of doctrines. To attain my object, it was necessary to go on analyzing
in succession facts and ideas, without reference to system, without
doing violence to them, in order to make them conform to a system,
but only examining them, in order to ascertain their result. This,
undoubtedly, is the best method. We thus obtain the knowledge of truth
as a fruit of our labors on facts, and are not obliged to alter objects
for the sake of forcing them to bend to the author's opinion. After
the application which we have been making of the ideas of being, and
not-being, to one of the most abstruse points of metaphysics, it is not
out of place to call the reader's attention to this for a moment, so
that he may be able to see the connection of doctrines.
CHAPTER IX.
PRESENT, PAST, AND FUTURE.
59. After explaining the idea of co-existence, we came to the
definition of the various relations which time presents. They
are principally three: present, past, and future. All others are
combinations of these.
60. The present is the only absolute time: by this I mean, that it
needs no relation, in order to be conceived. The present is conceived
without relation to the past or to the future. Neither the past nor the
future can be conceived without relation to the present.
61. The _past_ is an essentially relative idea. When we speak of
the _past_, we have to take some point to which it refers, and in
respect to which we say it is past. This point is the present, either
in reality, or in the ideal order; that is to say, that by the
understanding, we place ourselves in that point, and make it present to
us, and in reference to it, we speak of the past.
To prove that the idea of past is essentially relative, we may observe,
that by varying the points of reference, the past may cease to be
considered as such, and may be presented as present or future. Speaking
of the events of the time of Alexander, they are presented to us as
past, because we consider them in relation to the present moment; but
if we are speaking of the empire of Sesostris, the epoch of Alexander
ceases to be past, and is converted into future. If we were relating
events contemporary with the deeds of Alexander, this epoch would cease
to be past or future, and would become present.
The past, therefore, is always in reference to a present point, taken
in the course of time, and it is only in respect to this, that any
thing is said to have been, to be past; without this relation, the idea
of past is absurd, and it is impossible to conceive it.
62. What is the relation of past? According to the definition which we
have given of time, when we perceive the being of any thing, and then
its not-being, and the being of something else, we say the first is
past in relation to the second.
63. What would take place, then, if we should perceive the being of
something, and then its not-being, without relation to any other being?
This hypothesis is absurd; for we must always have this other being, if
we perceive being and not-being.
But it may be replied that we may suppose the disappearance of
ourselves, and then the objection would be good. Even though we should
disappear, there would still remain intelligences capable of perceiving
being and not-being. If there were no finite intelligence, there would
still be the infinite intelligence.
64. Here arises a new difficulty; for it may be asked whether the thing
would be passed with relation to the infinite intelligence. If we admit
that it would be, we seem to introduce time with the duration of God,
by which we destroy his eternity, which excludes all succession. If we
say that to the eyes of the infinite intelligence the thing would not
be past, then it would not be past in reality; for things are as God
knows them. Then there would be the idea of being and of not-being, and
still there would not be the idea of past. This difficulty arises from
a confusion of terms.
Let us suppose that God had created only one being, and this being
had ceased to exist; and let us see what would be the result of
this hypothesis. God knows the existence and the non-existence of
the object. This intellectual act is most simple; there can be no
succession in it. There is properly no past with respect to God,
and applied to the object this idea can only mean its non-existence
in relation to its existence which is destroyed. When the ideas are
presented in this light it is easy to understand that there is no past
in God, but that there is the knowledge of past things.
65. On this hypothesis, how can the time of only one creature be
measured? By its changes. But if it has none? On this imaginary
supposition there would be no time.
This conclusion is absolutely necessary, although it may at first sight
seem strange. We must either abandon our definition of time, or else
admit that there is no time where there is no change.
66. Whatever conclusions we form on questions founded on imaginary
suppositions, this, at least, is certain--that the idea of past is
essentially relative, and that on no supposition can we conceive the
past, if we take from it all relation. The expression _has been_
implies both being and not-being,--the succession which constitutes
time. In this relation the order is such that not-being is perceived
after being, and this is why it is called past.
67. The idea of the future is also relative to the present. The future
is inconceivable without this relation. The future is that which is
to come,--that which is to be with respect to a real or hypothetical
_now_; for we may apply to the future what we said of the past, that it
is changed by changing the point of its reference. The future for us
will be past to those who come after us; that which was future to those
past, is present or past to us.
The point of reference of the future is always a present moment; it
cannot be referred to the past as its ultimate term; for it is in
itself referred equally to the present.
68. Therefore all that we find in the idea of time that is absolute is
the present. The present needs no relation. It not only needs none, but
it admits none. We can neither refer it to the past nor to the future,
because these two times both presuppose the idea of the present,
without which they cannot even be conceived.
69. Time is a chain whose links are infinitely divisible. There is no
time which we cannot divide into other times. The indivisible instant
represents something analogous to the indivisible point; a limit which
we approach without ever reaching, an unextended element producing
extension. A geometrical point must be moved in order to generate a
line; but no motion is conceived as possible unless we presuppose
space in which the point moves; or in other words, when we treat of
the generation of extension, we commence by presupposing it. A similar
thing happens in relation to time. We imagine an indivisible instant,
from the fluxion of which results the continuity of duration which we
call time. But this fluxion is impossible, unless we suppose a time
in which it flows. We wish to examine the generation of time, and we
suppose it already existing, prolonged infinitely, as an immense line
on which the fluxion of the instant takes place. What are we to infer
from these apparent contradictions? Nothing but a strong confirmation
of the doctrine which we have established.
Time distinguished from things is nothing. Duration in the abstract,
distinguished from that which endures, is a being of reason,--a work
which our understanding produces from the materials furnished by
reality. All being is present. That which is not present is not-being.
The present instant, the _now_, is the reality of the thing; it is not
sufficient to constitute time, but it is necessary to time. There can
be present without either past or future; but there can be neither past
nor future without the present. When besides being there is not-being,
and this relation is perceived, time begins. To conceive past and
future without the alternation of being and not-being, as a sort of
line infinitely produced in two opposite directions, is to take an
empty play of the phantasy for a philosophical idea, and to apply to
time the illusion of imaginary space.
70. Therefore, if there is only being, there is only absolute, present
duration; therefore no past nor future, and, consequently, no time.
Time is in its essence a successive, _flowing_ quantity; it cannot be
seized in its actuality; for it is always divisible, and every division
in time constitutes past and future. This is a demonstration that time
is a mere relation, and in so far as it is in things, it only expresses
being and not-being.
CHAPTER X.
APPLICATION OF THE PRECEDING DOCTRINE TO SEVERAL IMPORTANT QUESTIONS.
71. This theory will be much better understood by its application to
the solution of several questions.
I. How long a time had passed before the creation? None. As there was
no succession, there was only the present, the eternity of God. All
else that we imagine is a mere illusion, contrary to sound philosophy.
II. Was it possible for another world to have existed when this world's
existence began? Undoubtedly it was; this would only require that God
had created it, without creating this world; it would only require
the being of the one and the not-being of the other. And as there was
not-being because there was no creation, it follows that if God had
created the one without creating the other, and had ceased to preserve
the first when he created the second, there would have been succession
and priority of time.
III. Here is another question which is somewhat strange, and at
first seems very difficult. Was the existence of a world _prior_
to this possible _in any time_? or, in other words, could another
world have _ceased_ to exist _some time before_ the beginning of the
existence of this world? This question implies a contradiction. It
supposes an interval of time, that is, of succession, without any
thing to succeed. If a world had ceased to exist, and no new world
should exist, there would be nothing but God; there would then be no
succession, there would be only eternity. To ask, therefore, how long a
time they were apart, is to suppose that there is time, where there is
none. The proper answer is, that the question is absurd.
But we shall be asked, were they distant, or were they not? There
is no distance of time where there is no time; this distance is a
mere illusion, by which we imagine time, while, by the state of the
question, we suppose that there is no time.
Then it may be objected, that the two successive worlds must be
necessarily immediate, that is to say, that the first instant of one
must be immediately connected with the last instant of the other.
I deny it. For immediateness of instants supposes the succession
of beings mutually connected in a certain order; the two worlds in
question would have no mutual relation; consequently, there would be
neither distance nor immediateness between them.
But, it may be replied, there is no medium between being and not-being,
and distance being the negation of immediateness, and immediateness the
negation of distance, by denying one, we affirm the other; they must,
therefore, either be distant or immediate. This reply also supposes
something which we deny. It speaks of distance and immediateness,
that is, of time, as though it were something positive, distinct from
the beings themselves. The principle, that every thing is, or is
not, _quodlibet est vel non est_, is applicable only when there is
something; but when there is nothing, there is no disjunctive. The time
of the two worlds is nothing, as distinguished from them; it is the
succession of their respective phenomena; the succession of the two
worlds, the one to the other, is nothing distinguished from them; it is
the being of the one, and the negation of the other, and the being of
the second and the negation of the first. God sees this; an intelligent
creature would also see it, if he could survive the annihilation of
the first world. To the eyes of God, who sees the reality, succession
would be simply the respective existence and non-existence of the two
objects. The intelligent creature would say, that the two worlds are
immediate, if to the perception of the last instant of the annihilated
world, the perception of a new existing world had followed without
another intermediate perception; and he would say, that there is
distance, if he had experienced various perceptions between the
annihilation of the old and the perception of the new creation. The
measure of this time would be taken from the changes of perceptions of
this creature, and would be longer or shorter, according to the number
of these perceptions.
72. The idea of time is essentially relative, as it is the ordered
perception of being and not-being. The mere perception of one of the
two extremes, would not be sufficient to produce the idea of time in
our mind; for this idea necessarily implies comparison. The same is
true of the idea of space, which has always a great resemblance to
time. We cannot conceive space, or extension of any kind, without
juxtaposition; that is to say, without relations of various objects.
Multiplicity necessarily enters into the ideas of both space and time.
Hence, we may say, that if we conceive a being, absolutely simple,
with no multiplicity, either in its essence, or in its acts, but in
which all is identified with its essence, there is no room for the
ideas of space and time; and, consequently, they are mere fictions of
the imagination, when we attribute to them any thing real, beyond the
corporeal world, and before the existence of the created.
CHAPTER XI.
THE ANALYSIS OF THE IDEA OF TIME CONFIRMS ITS RESEMBLANCE TO THE IDEA
OF SPACE.
73. Having explained the idea of time, and applied it to the most
difficult questions, we may explain this doctrine still farther, by
examining what we have already intimated concerning the resemblance
between time and space.[29] There is analogy in the difficulties;
analogy in the definitions of both ideas; analogy in the illusions
which hinder the knowledge of the truth. What we announced before with
respect to these two ideas, considering the idea of time as only what
it appeared at first sight, we may now assert as the secure result
of analytical investigations. I call attention in particular to the
following parallel, because it greatly explains the ideas of both.
[29] See Ch. III.
74. Space is nothing in itself, distinguished from bodies; it is only
the extension of bodies: time is nothing in itself, distinguished from
things. It is only the succession of things.
75. The idea of space is the idea of extension in general; the idea of
time is the idea of succession in general.
76. Where there are no bodies, there is no space: where there are no
things which succeed each other, there is no time.
77. An infinite space, before the existence of bodies, or outside of
bodies, is an illusion of the imagination: an infinite time before the
existence of things, or outside of them, is also an illusion.
78. Space is continuous: so is time.
79. One part of space excludes all others; one part of time also
excludes all others.
80. A pure space, in which bodies are situated, is imaginary: a
succession, a time, in which things succeed, is also imaginary.
81. That which is entirely simple has no need of space, and can exist
without it: that which is immutable has no need of time, and can exist
without it.
82. The simple and infinite is present to all points of space, without
losing its infinity: the immutable and infinite is present to all
instants of time, without altering its eternity.
83. Two things are distant in space, because there are bodies placed
between them; this distance is only the extension of the bodies
themselves: two beings are distant in time, because there are other
beings placed between them; this distance is the existence of the
beings which are placed between.
84. Extension needs no other extension, in which to be placed,
otherwise we should have a _processus in infinitum_: the succession
of things, for the same reason, needs no other succession in which to
succeed.
85. Just as we form the idea of continued succession in space by
distinguishing different parts of extension, and perceiving that one
excludes the others, so we also form the idea of continued succession
of time by distinguishing different facts and perceiving that one
excludes the others.
86. In order to form determinate ideas of the parts of space, we must
take a measure and refer to it: to form an idea of the parts of time we
also need a measure. The measure of space is the extension of some body
which we know: the measure of time is some series of changes which we
know. To measure space we seek for fixed things, as far as possible;
for the want of something better, men have recourse to the parts of
the body, the hand, the foot, the yard, and the pace, which give an
approximate, if not an exact measure. The exact sciences having
advanced, they have taken for their measure the forty-millionth part
of the meridian of the earth: time is measured by the motion of the
celestial bodies, by the diurnal motion, the lunar, solar, and sidereal
year.
87. The idea of number is necessary in order to determine space and
compare its different parts: the same idea is necessary in the same
manner to time. The discrete quantity explains the continuous.
CHAPTER XII.
RELATIONS OF THE IDEA OF TIME TO EXPERIENCE.
88. If time is nothing distinct from things, how does it happen that
we conceive it in the abstract, independently of things themselves?
How does it happen that it presents itself to us as an absolute being,
subject to no transformation or motion, while within it every thing
is moved and transformed? If it is a subjective fact, why do we apply
it to things? If it is objective, why is it mingled with all our
perceptions? Because it contains a necessity sufficient to be the
object of science.
The idea of time, whatever it may be, seems prior to all perception of
transformation, the consciousness of all internal acts included. It is
impossible for us to know any of these things, unless time serves as a
receptacle in which we may place our own changes and those of others.
89. The idea of time is not the result of observation; for in that case
it would be the expression of a contingent fact, and could not be the
principle of science. We measure time with the same exactness as we
do space, and it is one of the most fundamental ideas of the exact
sciences, in so far as they have any application to the objects of
nature.
90. It might seem to follow from this that the idea of time is innate
in our mind; and that it is prior to all ideas, and even sensations;
for both are necessarily involved in successive duration.
91. The necessity of the idea of time seems to prove that time is
independent of transitory things; in this case we are obliged to
convert it into a purely subjective fact, or else to grant it an
objective reality, independent of that which is changeable. By the
former we destroy it; by the latter we make it an attribute of the
divinity. To deny time is to deny the light of the sun; to raise it to
the rank of an attribute of divinity is to admit change in an immutable
being. If we make it purely subjective, we deny it; if objective, we
make it divine: is there no middle way?
92. I agree that the idea of time is not derived from mere experience;
for experience could not furnish an element so solid and so fixed,
on which we may with perfect security rest all the observations of
science. Still less can it be maintained, that the idea of time is
derived from purely sensible experience, or that it is in itself a
sensation.
93. The idea of time is not a sensation; for it is relative, and
sensation is an affection of our being, without any reference to or
comparison with any thing. When we experience sensations, if we had
only the sensitive faculty, we should be limited to pure sensation,
without any consideration of before or after, or any relation of any
kind. Sensation, being limited to certain objects, cannot, like the
idea of time, extend to all objects. By time, we measure not only the
external world, but also the internal; not only the affections of the
body, but also the most concealed and abstract actions of our mind.
Time is, in itself, succession, and, in our mind, it is the perception
of this succession; it cannot, therefore, present any object to the
mind; even when time refers to objects, and is, as it were, the link
between them, it is not itself either these objects themselves, nor the
intuition of them. The idea of the time which measures the succession
of a sound or of a sight, clearly is not either the sound or the sight,
but the perception of their succession, of their connection. If it were
the sight alone, or the sound alone, either the sight or the sound
would alone be sufficient in order to perceive time, which is absurd;
for there is no time without succession, and consequently there can
be no time which measures two sensations without these sensations.
The idea of time is independent of either of the two; it is superior
to them; it is a sort of universal form, independent of this or that
matter; so that, if after the sound, instead of the sight, another
sound should be perceived by us, the measure of the succession would
be the same, and this measure is nothing more than the idea of time.
Sensations being mere contingent facts, cannot be the foundation of
necessary and universal truths, they cannot serve as the basis of a
science. But the idea of time is one of the principal ideas in all the
physical sciences, and, like extension, is subjected to a very rigorous
calculation; therefore, it is not a sensation, and it is not derived
from sensation.
94. Purely experimental cognitions are confined to the sphere of
experience; the idea of time extends to the whole real and possible
order, it teaches us not only what _is_, but what _may_, and what
_must_ be; its relations are of absolute necessity, and may be
subjected to the strictest calculation; therefore it contains something
more than the elements furnished by sensible or insensible experience.
It is not otherwise possible to explain the necessity which it
involves, or to pass beyond a collection of contingent facts to arrive
at the possession of an element of science.
95. Let us observe, as we pass, that here is found another proof that
the system of Condillac is neither true nor subsistent. His system
has been found insufficient to explain any fundamental idea, and it
does not explain the idea of time, any more than the rest, although it
seems as though this idea must have the most intimate relations to the
sensible order.
96. If the idea of time is not merely experimental, how explain the
priority and necessity of time?
CHAPTER XIII.
KANT'S OPINION.
97. Kant uses the same theory to explain time that he used to explain
space. Time, according to him, is nothing in itself, neither is it any
thing in things; it is a subjective condition of intuition, a form of
the internal sense, by means of which phenomena are presented to us
as successive, just as space was the form by which they are presented
as continuous. To speak frankly, it seems to me that this is saying
nothing; it affirms a well-known fact, but does not explain it. Who
does not know that what we perceive we perceive in succession--that
we perceive even our own perceptions in succession? But what is
succession? This is what he ought to have explained.
98. Kant says that time is only in us; but I should like to ask him,
if succession is only in us. He pretends that we know nothing of the
external world, but that we perceive certain appearances, or phenomena;
but he does not deny that beyond the appearance there may be a reality.
If this reality is possible, changes are possible in it; and change
cannot be conceived without succession, nor succession without time.
99. According to Kant, the ideas of space and time are _à priori_, they
cannot be empirical, or experimental; for in that case they could not
be the basis of science; we could only affirm what we had experienced,
and this only with respect to the cases in which we have experienced
it. This is true, and I have demonstrated it in the last chapter; but,
conceding this priority, it proves nothing in favor of Kant's system.
The ideas of space and time, although _à priori_, may nevertheless
correspond to something in reality, as follows from the theory by which
I have explained them.
100. Time is not any thing which subsists by itself, but it is not
equally certain that it does not belong, as an objective determination,
to things, and that nothing remains of it, if we abstract it from all
the subjective impressions of intuition. I have demonstrated that time
does not subsist by itself, and that a duration without any thing
which endures, is an absurdity; but it does not follow from this that
the order represented by the idea of time is not something real in
the objects. Abstracting it from our intuition, there still remains
something which verifies the propositions by which we express the
properties of time.
101. The German philosopher makes time purely subjective, and relies
on the following argument: "If time were a condition belonging to the
things themselves, or an order, it could not precede the objects as a
condition of them, and be known and perceived _à priori_ by synthetical
judgments. This last is easily explained if time is nothing but the
subjective condition under which all intuitions are possible in us. For
then this form of the internal intuition can be represented before the
objects, and consequently _à priori_....
"If we abstract our manner of perceiving ourselves internally, and of
embracing, by means of this intuition, all external intuitions in the
faculty of representation, and consequently take objects just as they
may be in themselves, time is nothing....
"I can say that my representations are successive, but this only means
that we are conscious of them in a succession,--that is, in a form of
the internal sense. Time would not therefore be any thing in itself,
nor a determination inherent in things."[30]
[30] Trans. Æsth. II., A. § 6. w. f.
102. It is easy to see that the philosopher is struggling between two
difficulties. The first is, how to explain the necessity involved in
the idea of time, if he makes it proceed from experience. The second
is, how, if it is not derived from experience, it can be found really
in things, or, at least, how we can know that it is found in them.
Hence, he concludes, that it is not possible to save the necessity
involved in the idea of time, unless by making it a purely subjective
fact, a form of an intuition, entirely independent of the reality of
things.
It seems to me, that by attending to the principles established above,
we can give an objective value to time, independently of our intuition,
and explain its relations to experience, without destroying the
necessity contained in its idea.
CHAPTER XIV.
FUNDAMENTAL EXPLANATION OF THE OBJECTIVE POSSIBILITY AND OF THE
NECESSITY OF THE IDEA OF TIME.
103. Things in themselves, abstracted from our intuition, are
susceptible of change. Where there is change, there is succession, and
where there is succession, there is a certain order in the things which
succeed,--an order which is really in the things themselves, although
it does not subsist by itself, separated from them.
Kant might object to this, that perhaps the changes are not in things,
but in the phenomena, or the manner in which they are presented to our
intuition. But he cannot deny, that whether these changes are in the
reality, or not, they are, at least, possible, independently of the
phenomena. Therefore, he asserts, without reason, that time in the
things is nothing, and that it is only the form of our internal sense.
If he admits the possibility of real changes, he must also admit the
possibility of a real time; if he denies that it is possible for the
things in themselves to be really changed, we would ask him how he came
to know this impossibility,--he, who limits all our knowledge to the
purely phenomenal order. We cannot know that a thing is impossible in
an order, if we know nothing of this order; if Kant maintains that we
know nothing of things in themselves, he cannot prove that we know the
impossibility of their really changing.
104. It is then demonstrated that time, or a real order in things, is,
at least, possible. Therefore, we cannot say that time is a purely
subjective condition, to which nothing can correspond in the reality.
105. Admitting the possibility of an objective value of the idea of
time, not only in reference to the purely phenomenal order, but also to
the transcendental, or rather to things considered in themselves, and
abstracted from our intuition; we shall see how the objectiveness of
the idea of time and its relations to experience can be shown, without
destroying the intrinsic necessity which makes it one of the principal
elements of the exact sciences.
106. Time, considered in things, is the order of their being, and their
not-being. The idea of time is the perception of this order in its
greatest generality and abstracted from the objects which are contained
in it. As our understanding evidently can consider a purely possible
order of things, the idea of time extends to the possibility as well as
the reality. This is why we conceive time before and after the present
world, similar to the space which we imagine beyond the limits of the
universe. The idea of being, elevated to a purely possible region, in
which it is abstracted from all individual phenomena, is freed from the
instability to which the objects of our experience are subject: it can
then be an absolutely necessary element of science; for it expresses
a relation which is not affected by any thing contingent. These
observations are a solution of all difficulties.
CHAPTER XV.
IMPORTANT COROLLARIES.
107. Is the idea of time derived from experience? This question is
answered by what we said of the idea of being. It is not a type
existing previous to all sensation and to all intellectual act; it is
a perception of being and not-being which accompanies all our acts,
but is not presented to us separately until reflection eliminates from
it all that does not belong to it. This perception is the exercise of
an innate activity, which is subjected to the conditions of experience
in all that concerns the beginning and the continuation of its acts,
but not with respect to its laws which are characteristic of it, and
correspond to the pure intellectual order. This activity is unfolded in
the presence of causes or occasions which excite it, and its exercise
ceases when these conditions are wanting; but while the activity acts,
it exercises its functions in accordance with fixed laws which are
independent of the objects exciting it.
108. It is therefore clear that the idea of time is not strictly
derived from experience, except inasmuch as the mind is excited to
develop its activity by experience. Neither is it entirely independent
of experience; for without experience we should have no knowledge of
change, and consequently the intellect would not perceive the order of
being and not-being, in which the essence of time consists.
109. Hence the idea of time is not a form of the sensibility, but of
the pure intellectual order; and although it descends to the field
of sensible experience, it does so after the manner of other general
conceptions.
110. The idea of time is one of the most universal and indeterminate
ideas which our mind possesses; for it is the combination of the two
most general and most indeterminate ideas, being and not-being. Here is
the reason why the idea of time is common to all men, and is presented
to us as a form of all our conceptions and of all the objects known.
The ideas of being and not-being, entering as primitive elements into
all our perceptions, generate the idea of time. We therefore find this
idea in the inmost recesses of our soul as a condition from which we
cannot withdraw ourselves, and from which we exempt the Infinite Being
himself only by an effort of reflection.
111. The transition from the purely intellectual order to the field
of experience takes place in the idea of time, in the same manner as
in the other intellectual conceptions. I have, therefore, nothing
to add to what I have already said on this point when explaining it
elsewhere.[31]
[31] See Bk. IV., Chapters XIV. and XV.