185 
PHILOSOPHY, 
be experience, becmife, in the principle here adduced, the 
fecon'd reprefentation is added to the former one, not only 
with greater nniverfality, but even with the exprefiion of 
neceffity, confequently entirely & priori, and from mere 
conceptions. Now upon fuch fynthetical, that is extend¬ 
ing', principles, the whole of our fpeculative knowledge & 
priori reds; for analytical principles are indeed highly 
important and necefi'ary, but only in order to obtain that 
clearnefs of conception, which is required to a fafely ex¬ 
tended fynthefis, as a really new acquifition. 
V. In all Theoretical Sciences of Hecifon, Synthetical 
Judgments it priori are contained as Principles. 
i. Mathematical Judgments are altogether fynthetical. 
This pofition feems hitherto to have efcapecl the obfer- 
vation of the analyzers of Iranian intel!e6t; nay, to have 
been diredtly oppofed to all their fuppofitions, though it 
is indeed indifputably true, and highly important in its 
confequences. For, as they found that all the conclufions 
of the Mathematician proceed according to'the principle 
of contradidtion,(which the nature of apodidlical certainty 
requires,) they perfuaded themfelves that the principles 
alfo were known from the pofition of contradidtion, in 
which however they erred: for a fynthetical pofition may 
indeed be comprehended according to the principle of 
contradidtion, but only in fuch a manner that another 
fynthetical pofition is pre-fuppofed, from which it may 
be inferred, but can never be underftood by itfelf. 
Firft, it muft be remarked, that mathematical pofitions, 
properly (peaking, are always judgments <1 priori, and 
not empirical, becaufe they carry with them neceffity, 
which can never be derived from experience. But, if it 
fhould not be granted, then I limit my pofition to pure 
mathematics, the very conception of which implies that 
they do not contain empirical but merely pure knowledge 
A priori. 
We fhould certainly at firft be inclined to think that the 
pofition 7 + 5 is a mere analytical pofition, which follows 
from the conception of the fum of 7 and 5 according to 
the pofition of contradidtion ; however, if we confider it 
more clofely, we find that the conception of the fum of 7 
and 5 contains nothing elfe but the union of both thefe 
numbers, whereby it is not at all thought what the (ingle 
number is that comprehend both. The conception of 12 
is not thought by merely thinking the union of 7 and 5; 
and, however far I may analyze my conception of fuch a 
pcffible fum, ftill I (hall never find the 12 in it. We muft 
go out of, or beyond, thefe conceptions; and call the in¬ 
tuition toouraid which correfponc's with one of the two, 
perhaps our five fingers or five points, and thus add by 
degrees the unities given in the intuition of 5 to the 
conception of 7. For I firft of all take the number 7 ; 
and, as I call to my aid, for the conception 5, the fingers 
of my hand as the intuition, I add the unities which I 
had previoufly put together, in order to conftitule the 
number 5, by means of my fingers, fuccefiively to the 
number 7, and thus I fee the number 1 z arife. By ad¬ 
ding 7 to 5,1 have indeed the conception of a fum = 7+5, 
but-n-ot that this fum is equal to the number 12. Arith¬ 
metical pofitions are always fynthetical; this is more evi¬ 
dent when we take larger numbers, for it is then clearly 
perceived, that, though we turn and tvvift our con¬ 
ceptions as much as we pleafe, we never can find the fum 
by their mere analyfis, without calling the intuition to 
our aid. 
Neither is any one principle of pure Geometry analyti¬ 
cal. That the ftraight line between two points is the 
fhorteft, is a fynthetical pofition. For my conception of 
ftraight contains nothing of quantity* but only a quality. 
The conception of the ftiorteft is entirely added, and can 
never be derived by any analyfis from the conception 
ftraight line. Intuition muft therefore be here called to 
our aid, by means of which alone the fynthefis is poftible. 
Some few principles which the Geometrician prefuppo- 
fes are indeed really analytical, and reft upon the princi- 
Vol. XX. No. 1360. 
pie of contradiction ; they ferve, however, only as identi¬ 
cal pofitions for the concatenation of method, but not 
as principles ; for inftance, a—a, the whole is equal to 
itfelf, or (a-fh) Z. cr > that is, the whole is greater than its 
part. Even theie, though they are valid according to 
mere conception, are admitted into the mathematics only 
becaufe they can be exhibited in the intuition. What 
commonly makes us imagine that the predicate of fuch 
apodidlical judgments is already implied in our concep¬ 
tion, and that the judgment is therefore analytical, is 
merely the ambiguity of the exprefiion. When we think 
a certain predicate added to a given conception, tills ne¬ 
ceffity already adheres to the conception. But the quel- 
tion is not what we are compelled to think in addition to 
a given conception, but what we really think in it, 
though but obfeurely ; and here it is evident, that the 
predicate adheres neceffarily to the conception, but is not 
thought in the conception itfelf, but by means of an 
intuition that muft be added to the conception. 
2. Natural Philofophy (Phyfica) contains fynthetical 
judgments a priori as principles in itfelf. I (hall only 
adduce a few pofitions as examples. For inftance ; “ that, 
in all changes in the material world, the quantity of mat¬ 
ter remains the fame;” or “that, in all communicated 
motion, the adtion and re-adtion muft be equal.” In 
both cafes the neceffity is evident, confequently their 
origin ii priori. But they are alfo fynthetical pofitions : 
for, in the conception of matter, I do not think perdura- 
bility, but merely its prefence in Space, by filling it ; 
therefore I go out of the conception o 1 matter, in order to 
think fomething a priori in addition to it, that was not 
thought in it. The pofition is therefore not analytical, 
but fynthetical, and yet thought A priori; and this is the 
cafe with the other pofitions of the pure part of Natural 
Philofophy. 
3. In Metaphyfics, if we even confiderthem as a fcience 
hitherto merely'attempted, ftill however indifpenfable by 
the nature of human reafon, fynthetical knowledge il priori 
muft be contained, and they do not merely undertake 
analytically to illuftrate the conceptions which we form 
d priori of things ; they feek to extend our knowledge 
ft priori, for which purpofe we avail ourfelves of fuch prin¬ 
ciples as add fomething that was not contained in the 
given conception, and by fynthetical judgments cl priori 
we go fo far beyond it, that experience itfelf cannot 
follow us. For inftance, in the pofition “ the world muft 
have had a beginning;” and thus Metaphyfics, at leaft 
according to their end, confift of nothing but fynthetical 
pofitions a priori. 
VI. Universal Problem of Pure Reason: How are 
fynthetical Judgments d priori pojftble l 
It is certainly a great advantage to be able to bring a 
variety of inveftigations under the formulary of a (ingle 
problem. This facilitates not only our own operations, 
as it precifely determines them, but alfo that of others 
who are willing to prove the faff, whether our underta¬ 
king be fatisfadtery or not. The proper problem of Pure 
Realon is contained in the queftion, “ How are fynthetical 
judgments a priori poftible ?” 
That Metaphyfics have hitherto remained in fo waver¬ 
ing a ftate of uncertainty and contradidtion is to be af- 
cribed folely to the caufe, that this problem, and perhaps 
even the difference of analytical and fynthetical judgments, 
did not fooner enter into the mind. Upon the lolution 
of this problem, or upon a fatisfadtory proof that no fuch 
poffibility as metaphyfics require to have explained adtually 
occurs, this whole fcience either (lands or falls. David 
Flume, who, of all philofophers approached this problem 
the neareft, did not, however, by any means fufficiently de¬ 
termine it, nor think it in its univerfality, but merely exa¬ 
mined the fynthetical pofition of the connexion of th eCaufe 
with its Effctt, (the principle of Caufality.) He thought 
he could prove that fuch a pofition was entirely impoffible 
A priori; and, according,to his conclufions, all that we 
3 B call 
