PHILO 
■fubjefitive grounds compel us toa judgment, then thofe ne¬ 
gative judgments have frequently a greater value than 
much pofitive information. 
The conftraint by which the conftant propenfity to de¬ 
viate from certain rules is limited, is called Discipline. 
It differs from Culture, wliofe life is merely to produce a 
readinefs, without deftroying any other already acquired. 
With regard to Knowledge, Difcipline is the limiting of 
the propenfity to determine objects pofitively by negative 
judgments; and it is oppofed to the doftrine which af- 
. fords inftrmftion by pofitive Judgments. 
To conltrudl a Difcipline as a fcience, that is, as a fyf- 
tem of negative judgments, is not neceffary with regard to 
the objects of experience. Experience extends itfelf gra¬ 
dually; and, though it is felf-evident that we'muft here 
alfo by negative judgments poftpone our decifion on the 
various determinations of objects, until our judgment has 
been matured by experience, Kill we expeft from its con- 
fvant progrefs the extenilon of this fort of knowledge, 
which itfelf furnifhes an immediate touchftone by which 
at lead error is averted, though proper inftrudtion is not 
immediately obtained. As to the Mathematics, their 
conceptions can be reprefented in the pure intuition, and 
error therefore cannot remain hidden : but, as to thofe 
conceptions whofe objefls can neither be given in empi¬ 
rical nor in pure intuition, error with regard to them can¬ 
not be fo eafily deteiled; a fcientific Difcipline therefore 
is here indifpenfible, prior to all Doflrine. This we have 
treated of in Transcendental Dialectics; and it 
concerned the matter of knowledge. We have (fill to con- 
fider the knowledge derived from pureReafon; and the 
difcipline of which vve (hall now treat will determine the 
method to be followed in this field. Mathematical 
knowledge agrees with that juft mentioned, that neither 
of them is empirical; and it appears, therefore, that the 
method, by which the former fcience has been brought to 
a confiderable and yet more-and-more-to-be-extended 
compafs, will not be lefs fortunate in the other. We 
fiiall fliow, that the mathematical method cannot be at all 
followed in Philofophy, and confequently not in that 
part of it which aims at a knowledge of objects that lie 
beyond all experience. 
Seek I. The Difcipline of Pure Reafon in its dogmatical 
Ufe. 
The method ufed in the Mathematics leads to apodi&i- 
cal certainty. We eafily comprehend that it can be at¬ 
tained only fo far as it is the certainty of a non-empirical 
knowledge. Now the objedls of Philofophy, as to their 
tranfeendentpart, are of fuch a kind, that they cannot be 
given in any experience. If certainty is to be acquired 
with regard to them, it can be no other than apodidlical. 
From this fimilarity of both lciences, an appearance 
arifes, that the mathematical method in philofophy, where 
it would neceffariiy be called Dogmatical, would lead to 
the fame end, that is, to apodidlical certainty. 
Mathematical knowledge is a rational knowledge by 
means of the conftrudlion of conceptions. To conftrudt 
a conception means to reprefent hpviori the intuition cor- 
refponding to it. The Geometrician conftrudls his own 
conceptions; and he would therefore never attain a new 
infight if he did not proceed further, but remained by 
thefe cpnpeptions. Inftead of this, he creates reprefenta- 
tions that contain infinitely more than thofe conceptions. 
In the conftrudlion of a conception as a general reprefen- 
tation, the Geometrician goes beyond it, and proceeds to 
the reprefentation of what is individual. The queltion 
now is, with what ground he may afterwards recede, and 
apply that to the conception, confequently to the whole 
fphere, which he has only found in the reprefentation of 
the individual. It is felf-evident that this proceeding 
cannot fucceed with empirical conceptions. Thefe arile 
from empirical intuitions; and thefe reprefentations of 
lingle objedls are dated as undetermined in feveral points. 
Vol. XX. No. 1364. 
SOPHY. 241 
The feveral determinations in the reprefentation of the 
fingle, reft here however on apprehenfion ; and we fhould 
therefore unjuftifiably apply that to a whole fphere, from 
which we had abft railed in the conception. The in tuition of 
Space, however, and of every feparate part of it, is a pure 
intuition. Now, though, in the conftrudlion of a geome¬ 
trical conception, I fubftitute for the conception a repre¬ 
fentation which contains more than it, Kill I maydifeover, 
becaufe nothing has here been borrowed from apprehen¬ 
fion in a fingle objedl, certain determinations which are 
common to a whole fphere. If I take the geometrical 
axiom, that two ftraight lines cannot enclofe a fpace, I 
certainly do not find this impoflibility in the conception 
of a bilineal figure. It is nothing but the impoffibility 
of the conftrudlion of this conception. Juft as little are 
we able to comprehend with apodidiical certainty any 
other axiom, fo long as we confine ourfelves to the mere 
conception. That two ftraight lines interfedl each other 
only in one point, we never (hall find in the conception 
of two ftraight lines. But whoever reflects upon this po- 
fition, draws in his imagination two interfedling lines. 
Now this reprefentation, as intuition, certainly contains 
more than the conception : but, as it contains nothing 
empirical, we may explain from this, that all the other 
particular determinations of thefe lines, as for inftance 
their length and their pofition, may be fet afide; and that 
we may Kill remark the univerfal determination wdiich 
belongs to every pair of interfering lines, namely this, 
that they interfedl each otheronly \n one point. Thisisthe 
cafe w ith all geometrical propofitions. It would be a ufelefs 
endeavour, from mere conceptions to comprehend the pro- 
pofition, that the three angles of aredtilineal triangle are to- 
getherequal to two right. The geometrician conftrudls for 
himfelf a triangle in the pure intuition. Now he does not 
indeed perceive fo immediately the truth of the propofi- 
tion as that of the axioms ; but he avails himfelf of thefe 
univerfal propofitions already comprehended, and alfo of 
other propofitions grounded on them ; and, by applying 
them to any cafe in the intuition, he difeovers, at the fame 
time, that through the point of every triangle a ftraight 
line may be drawn parallel to the bale, (a propofition of 
which he has likewife affured himfelf by means of a.pure 
intuition;) and gives univerfality to his dernonftration by 
means of this reprefentation. 
This is alfo the method throughout the mathematics. 
In Arithmetic and Analyfis there is not indeed found this 
geometrical and ojlenfive method, namely, the conftrudlion 
of the cbjedl itfelf; that is,'of the fize together with its 
figure (of a quantum); but ftill the conftrudlion of the 
mere fize (quantitas); that is, the conftrudlion of the mere 
fynthefis ot the various homogeneous parts, by means of 
certain figns; confequently the fymbolical conftrudlion. 
We fhould take a very incorredt view of the laft-named 
fcience, if we fhould take it for an analyticalJcience in the 
fame fenfe in which pure univerfal Logic is taken. It is 
merely the Method that has given it the name of Analj>fis 
That which is to befought, it treats of as fomething given, 
and goes back to the conditions under which it can be 
given ; which procedure is called the analytical method. It 
is neverthelefs a J'yntlieticalfcience; but its method is op¬ 
pofed to the fynthetical method, in whofe courfe that 
which is fought for is not already taken up, but left as it 
were untouched ; and vve do not here afeend, as in the 
analytical, from the conditioned to the condition, but 
converfely defeend from the condition to the conditioned. 
Let us take any pofition in this fcience; for inftance, the 
binominal pofition. By refledling on this conception, 
The fum of two numbers is railed to any power, we fliall 
never find the rule according to which each of thefe 
powers is to be expreffed. The Mathematician proceeds 
to the fymbolical conftrudlion. He indicates by determi¬ 
nate figns the two numbers as well as the index of the 
power. Now perhaps vve may fancy that, becaule, 
inftead of determinate numbers, he choofes univerfal 
3 Q . 
