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there results merely an aggregate of several phenomena, and not

properly a phenomenon as a quantity, which is not produced by the mere

continuation of the productive synthesis of a certain kind, but by the

repetition of a synthesis always ceasing. For example, if I call

thirteen dollars a sum or quantity of money, I employ the term quite

correctly, inasmuch as I understand by thirteen dollars the value of a

mark in standard silver, which is, to be sure, a continuous

quantity, in which no part is the smallest, but every part might

constitute a piece of money, which would contain material for still

smaller pieces. If, however, by the words thirteen dollars I

understand so many coins (be their value in silver what it may), it

would be quite erroneous to use the expression a quantity of

dollars; on the contrary, I must call them aggregate, that is, a

number of coins. And as in every number we must have unity as the

foundation, so a phenomenon taken as unity is a quantity, and as

such always a continuous quantity (quantum continuum).

Now, seeing all phenomena, whether considered as extensive or

intensive, are continuous quantities, the proposition: "All change

(transition of a thing from one state into another) is continuous,"

might be proved here easily, and with mathematical evidence, were it

not that the causality of a change lies, entirely beyond the bounds of

a transcendental philosophy, and presupposes empirical principles. For

of the possibility of a cause which changes the condition of things,

that is, which determines them to the contrary to a certain given

state, the understanding gives us a priori no knowledge; not merely

because it has no insight into the possibility of it (for such insight

is absent in several a priori cognitions), but because the notion of

change concerns only certain determinations of phenomena, which

experience alone can acquaint us with, while their cause lies in the

unchangeable. But seeing that we have nothing which we could here

employ but the pure fundamental conceptions of all possible

experience, among which of course nothing empirical can be admitted,

we dare not, without injuring the unity of our system, anticipate

general physical science, which is built upon certain fundamental

experiences.

Nevertheless, we are in no want of proofs of the great influence

which the principle above developed exercises in the anticipation of

perceptions, and even in supplying the want of them, so far as to

shield us against the false conclusions which otherwise we might

rashly draw.

If all reality in perception has a degree, between which and

negation there is an endless sequence of ever smaller degrees, and if,

nevertheless, every sense must have a determinate degree of

receptivity for sensations; no perception, and consequently no

experience is possible, which can prove, either immediately or

mediately, an entire absence of all reality in a phenomenon; in

other words, it is impossible ever to draw from experience a proof

of the existence of empty space or of empty time. For in the first

place, an entire absence of reality in a sensuous intuition cannot

of course be an object of perception; secondly, such absence cannot be

deduced from the contemplation of any single phenomenon, and the

difference of the degrees in its reality; nor ought it ever to be

admitted in explanation of any phenomenon. For if even the complete

intuition of a determinate space or time is thoroughly real, that

is, if no part thereof is empty, yet because every reality has its

degree, which, with the extensive quantity of the phenomenon

unchanged, can diminish through endless gradations down to nothing

(the void), there must be infinitely graduated degrees, with which

space or time is filled, and the intensive quantity in different

phenomena may be smaller or greater, although the extensive quantity

of the intuition remains equal and unaltered.

We shall give an example of this. Almost all natural philosophers,

remarking a great difference in the quantity of the matter of

different kinds in bodies with the same volume (partly on account of

the momentum of gravity or weight, partly on account of the momentum

of resistance to other bodies in motion), conclude unanimously that

this volume (extensive quantity of the phenomenon) must be void in all

bodies, although in different proportion. But who would suspect that

these for the most part mathematical and mechanical inquirers into

nature should ground this conclusion solely on a metaphysical

hypothesis- a sort of hypothesis which they profess to disparage and

avoid? Yet this they do, in assuming that the real in space (I must

not here call it impenetrability or weight, because these are

empirical conceptions) is always identical, and can only be

distinguished according to its extensive quantity, that is,

multiplicity. Now to this presupposition, for which they can have no

ground in experience, and which consequently is merely metaphysical, I

oppose a transcendental demonstration, which it is true will not

explain the difference in the filling up of spaces, but which

nevertheless completely does away with the supposed necessity of the

above-mentioned presupposition that we cannot explain the said

difference otherwise than by the hypothesis of empty spaces. This

demonstration, moreover, has the merit of setting the understanding at

liberty to conceive this distinction in a different manner, if the

explanation of the fact requires any such hypothesis. For we

perceive that although two equal spaces may be completely filled by

matters altogether different, so that in neither of them is there left

a single point wherein matter is not present, nevertheless, every

reality has its degree (of resistance or of weight), which, without

diminution of the extensive quantity, can become less and less ad

infinitum, before it passes into nothingness and disappears. Thus an

expansion which fills a space- for example, caloric, or any other

reality in the phenomenal world- can decrease in its degrees to

infinity, yet without leaving the smallest part of the space empty; on

the contrary, filling it with those lesser degrees as completely as

another phenomenon could with greater. My intention here is by no

means to maintain that this is really the case with the difference

of matters, in regard to their specific gravity; I wish only to prove,

from a principle of the pure understanding, that the nature of our

perceptions makes such a mode of explanation possible, and that it

is erroneous to regard the real in a phenomenon as equal quoad its

degree, and different only quoad its aggregation and extensive

quantity, and this, too, on the pretended authority of an a priori

principle of the understanding.

Nevertheless, this principle of the anticipation of perception

must somewhat startle an inquirer whom initiation into

transcendental philosophy has rendered cautious. We must naturally

entertain some doubt whether or not the understanding can enounce

any such synthetical proposition as that respecting the degree of

all reality in phenomena, and consequently the possibility of the

internal difference of sensation itself- abstraction being made of its

empirical quality. Thus it is a question not unworthy of solution:

"How the understanding can pronounce synthetically and a priori

respecting phenomena, and thus anticipate these, even in that which is

peculiarly and merely empirical, that, namely, which concerns

sensation itself?"

The quality of sensation is in all cases merely empirical, and

cannot be represented a priori (for example, colours, taste, etc.).

But the real- that which corresponds to sensation- in opposition to

negation = O, only represents something the conception of which in

itself contains a being (ein seyn), and signifies nothing but the

synthesis in an empirical consciousness. That is to say, the empirical

consciousness in the internal sense can be raised from 0 to every

higher degree, so that the very same extensive quantity of

intuition, an illuminated surface, for example, excites as great a

sensation as an aggregate of many other surfaces less illuminated.

We can therefore make complete abstraction of the extensive quantity

of a phenomenon, and represent to ourselves in the mere sensation in a

certain momentum, a synthesis of homogeneous ascension from 0 up to

the given empirical consciousness, All sensations therefore as such

are given only a posteriori, but this property thereof, namely, that

they have a degree, can be known a priori. It is worthy of remark,

that in respect to quantities in general, we can cognize a priori only

a single quality, namely, continuity; but in respect to all quality

(the real in phenomena), we cannot cognize a priori anything more than

the intensive quantity thereof, namely, that they have a degree. All

else is left to experience.

3. ANALOGIES OF EXPERIENCE.

The principle of these is: Experience is possible only

through the representation of a necessary connection

of Perceptions.

PROOF.

Experience is an empirical cognition; that is to say, a cognition

which determines an object by means of perceptions. It is therefore

a synthesis of perceptions, a synthesis which is not itself

contained in perception, but which contains the synthetical unity of

the manifold of perception in a consciousness; and this unity

constitutes the essential of our cognition of objects of the senses,

that is, of experience (not merely of intuition or sensation). Now

in experience our perceptions come together contingently, so that no

character of necessity in their connection appears, or can appear from

the perceptions themselves, because apprehension is only a placing

together of the manifold of empirical intuition, and no representation

of a necessity in the connected existence of the phenomena which

apprehension brings together, is to be discovered therein. But as

experience is a cognition of objects by means of perceptions, it

follows that the relation of the existence of the existence of the

manifold must be represented in experience not as it is put together

in time, but as it is objectively in time. And as time itself cannot

be perceived, the determination of the existence of objects in time

can only take place by means of their connection in time in general,

consequently only by means of a priori connecting conceptions. Now

as these conceptions always possess the character of necessity,

experience is possible only by means of a representation of the

necessary connection of perception.

The three modi of time are permanence, succession, and

coexistence. Accordingly, there are three rules of all relations of

time in phenomena, according to which the existence of every

phenomenon is determined in respect of the unity of all time, and

these antecede all experience and render it possible.

The general principle of all three analogies rests on the

necessary unity of apperception in relation to all possible

empirical consciousness (perception) at every time, consequently, as

this unity lies a priori at the foundation of all mental operations,

the principle rests on the synthetical unity of all phenomena

according to their relation in time. For the original apperception

relates to our internal sense (the complex of all representations),

and indeed relates a priori to its form, that is to say, the

relation of the manifold empirical consciousness in time. Now this

manifold must be combined in original apperception according to

relations of time- a necessity imposed by the a priori

transcendental unity of apperception, to which is subjected all that

can belong to my (i.e., my own) cognition, and therefore all that

can become an object for me. This synthetical and a priori

determined unity in relation of perceptions in time is therefore the

rule: "All empirical determinations of time must be subject to rules

of the general determination of time"; and the analogies of

experience, of which we are now about to treat, must be rules of

this nature.

These principles have this peculiarity, that they do not concern

phenomena, and the synthesis of the empirical intuition thereof, but

merely the existence of phenomena and their relation to each other

in regard to this existence. Now the mode in which we apprehend a

thing in a phenomenon can be determined a priori in such a manner that

the rule of its synthesis can give, that is to say, can produce this a

priori intuition in every empirical example. But the existence of

phenomena cannot be known a priori, and although we could arrive by

this path at a conclusion of the fact of some existence, we could

not cognize that existence determinately, that is to say, we should be

incapable of anticipating in what respect the empirical intuition of

it would be distinguishable from that of others.

The two principles above mentioned, which I called mathematical,

in consideration of the fact of their authorizing the application of

mathematic phenomena, relate to these phenomena only in regard to

their possibility, and instruct us how phenomena, as far as regards

their intuition or the real in their perception, can be generated

according to the rules of a mathematical synthesis. Consequently,

numerical quantities, and with them the determination of a

phenomenon as a quantity, can be employed in the one case as well as

in the other. Thus, for example, out of 200,000 illuminations by the

moon, I might compose and give a priori, that is construct, the degree

of our sensations of the sunlight. We may therefore entitle these

two principles constitutive.

The case is very different with those principles whose province it

is to subject the existence of phenomena to rules a priori. For as

existence does not admit of being constructed, it is clear that they

must only concern the relations of existence and be merely

regulative principles. In this case, therefore, neither axioms nor

anticipations are to be thought of. Thus, if a perception is given us,