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 sun—light.* We may therefore entitle these
two principles constitutive.
[*]
Kant's meaning is: The two principles enunciated under the heads of "Axioms of Intuition,"
and "Anticipations of Perception," authorize the application to phænomena of determinations of size and
number, that is, of mathematic. For example, I may compute the light of the sun, and say, that its
quantity is a certain number of times greater than that of the moon. In the same way, heat is measured by
the comparison of its different effects on water, &c., and on mercury in a thermometer. — Tr.
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,
in a certain relation of time to other (although undetermined)
perceptions, we cannot then say
a priori,
what and
how great (in
quantity) the other perception necessarily connected with the former
is, but only
how it is connected,
quoad its existence, in this given
modus of time. Analogies in philosophy mean something very different
from that which they represent in mathematics. In the latter they
are formulæ, which enounce the equality of two relations of quantity,
*
and are always
constitutive, so that if two terms of the proportion
are given, the third is also given, that is, can be constructed by the
aid of these formulæ. But in philosophy, analogy is not the
equality of two
quantitative but of two
qualitative relations. In this
case, from three given terms, I can give
a priori and cognize the
relation to a fourth member,
* but not this fourth term itself, although
I certainly possess a rule to guide me in the search for this fourth
term in experience, and a mark to assist me in discovering it. An
analogy of experience is therefore only a rule according to which
unity of experience must arise out of perceptions in respect to
objects (phenomena) not as a
constitutive, but merely as a
regulative principle. The same holds good also of the postulates of
empirical thought in general, which relate to the synthesis of mere
intuition (which concerns the form of phenomena), the synthesis of
perception (which concerns the matter of phenomena), and the synthesis
of experience (which concerns the relation of these perceptions).
For they are only regulative principles, and clearly distinguishable
from the mathematical, which are constitutive, not indeed in regard to
the certainty which both
possess
a priori, but in the mode of evidence
thereof, consequently also in the manner of demonstration.
[*]
Known the two terms 3 and 6, and the relation of 3 to 6, not only the relation of 6
to some other number is given, but that number itself, 12, is given, that is, it is constructed.
Therefore 3 : 6 = 6 : 12. — Tr.
[*]
Given a known effect, a known cause, and another known effect, we reason, by analogy,
to an unknown cause, which we do not cognize, but whose relation to the known effect we know from the
comparison of the three given terms. Thus, our own known actions : our own known motives = the known
actions of others : x, that is, the motives of others which we cannot immediately cognize. — Tr.
But what has been observed of all synthetical propositions, and must
be particularly remarked in this place, is this, that these
analogies possess significance and validity, not as principles of
the transcendental, but only as principles of the empirical use of the
understanding, and their truth can therefore be proved only as such,
and that consequently the phenomena must not be subjoined directly
under the categories, but only under their schemata. For if the
objects to which those principles must be applied were things in
themselves, it would be quite impossible to cognize aught concerning
them synthetically a priori. But they are nothing but phenomena; a
complete knowledge of which— a knowledge to which all principles a priori
must at last relate— is the only possible experience. It
follows that these principles can have nothing else for their aim than
the conditions of the empirical cognition in the unity of synthesis of
phenomena. But this synthesis is cogitated only in the schema of the
pure conception of the understanding, of whose unity, as that of a
synthesis in general, the category contains the function
unrestricted by any sensuous condition. These principles will
therefore authorize us to connect phenomena according to an analogy,
with the logical and universal unity of conceptions, and
consequently to employ the categories in the principles themselves;
but in the application of them to experience, we shall use only
their schemata, as the key to their proper application, instead of the
categories, or rather the latter as restricting conditions, under
the title of "formulæ" of the former.
