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 pose 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；
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 formulae； 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 formulae。 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。
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
plete 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 〃formulae〃 of the former。
A。 FIRST ANALOGY。
Principle of the Permanence of Substance。
In all changes of phenomena； substance is permanent； and the
quantum thereof in nature is neither increased nor diminished。
PROOF。
All phenomena exist in time； wherein alone as substratum； that is；
as the permanent form of the internal intuition； coexistence and
succession can be represented。 Consequently time； in which all changes
of phenomena must be cogitated； remains and changes not； because it is
that in which succession and coexistence can be represented only as
determinations thereof。 Now； time in itself cannot be an object of
perception。 It follows that in objects of perception； that is； in
phenomena； there must be found a substratum which represents time in
general； and in which all change or coexistence can be perceived by
means of the relation of phenomena to it。 But the substratum of all
reality； that is； of all that pertains to the existence of things；
is substance； all that pertains to existence can be cogitated only
as a determination of substance。 Consequently； the permanent； in
relation to which alone can all relations of time in phenomena be
determined； is substance in the world of phenomena； that is； the
real in phenomena； that which； as the substratum of all change；
remains ever the same。 Accordingly； as this cannot change in
existence； its quantity in nature can neither be increased nor
diminished。
Our apprehension of the manifold in a phenomenon is always
successive； is Consequently always changing。 By it alone we could；
therefore； never determine whether this manifold； as an object of
experience； is coexistent or successive； unless it had for a
foundation something fixed and permanent； of the existence of which
all succession and coexistence are nothing but so many modes （modi
of time）。 Only in the permanent； then； are relations of time
possible （for simultaneity and succession are the only relations in
time）； that is to say； the permanent is the substratum of our
empirical representation of time itself； in which alone all
determination of time is possible。 Permanence is； in fact； just
another expression for time； as the abiding correlate of all existence
of phenomena； and of all change； and of all coexistence。 For change
does not affect time itself； but only the phenomena in time （just as
coexistence cannot be regarded as a modus of time itself； seeing
that in time no parts are coexistent； but all successive）。 If we
were to attribute succession to time itself； we should be obliged to
cogitate another time； in which this succession would be possible。
It is only by means of the permanent that existence in different parts
of the successive series of time receives a quantity； which we entitle
duration。 For in mere succession； existence is perpetually vanishing
and remencing； and therefore never has even the least quantity。
Without the permanent； then； no relation in time is possible。 Now；
time in itself is not an object of perception； consequently the
permanent in phenomena must be regarded as the substratum of all
determination of time； and consequently also as the condition of the
possibility of all synthetical unity of perceptions； that is； of
experience； and all existence and all change in time can only be
regarded as a mode in the existence of that which abides unchangeably。
Therefore； in all phenomena； the permanent is the object in itself；
that is； the substance （phenomenon）； but all that changes or can
change belongs only to the mode of the existence of this substance
or substances； consequently to its determinations。
I find that in all ages not only the philosopher； but even the
mon understanding； has preposited this permanence as a substratum
of all change in phenomena； indeed； I am pelled to believe that
they will always accept this as an indubitable fact。 Only the
philosopher expresses himself in a more precise and definite manner；
when he says： 〃In all changes in the world； the substance remains； and
the accidents alone are changeable。〃 But of this decidedly synthetical
proposition； I nowhere meet with even an attempt at proof； nay； it
very rarely has the good fortune to stand； as it deserves to do； at
the head of the pure and entirely a priori laws of nature。 In truth；
the statement that substance is permanent； is tautological。 For this
very permanence is the ground on which we apply the category of
substance to the phenomenon； and we should have been obliged to
prove that in all phenomena there is something permanent； of the
existence of which the changeable is nothing but a determination。
But because a proof of this nature cannot be dogmatical； that is；
cannot be drawn from conceptions； inasmuch as it concerns a
synthetical proposition a priori； and as philosophers never
reflected that such propositions are valid only in relation to
possible experience； and therefore cannot be proved except by means of
a deduction of the possibility of experience； it is no wonder that
while it has served as the foundation of all experience （for we feel
the need of it in empirical cognition）； it has never been supported by
proof。
A philosopher was asked： 〃What is the weight of smoke？〃 He answered：
〃Subtract from the weight of the burnt wood the weight of the
remaining ashes； and you will have the weight of the smoke。〃 Thus he
presumed it to be incontrovertible that even in fire the matter
（substance） does not perish； but that only the form of it undergoes
a change。 In