SI 
LOGIC. 
Co-divifion and Sub-divifion. 
Txa. ne firft divifions of a conception are called Co- 
divifions, and the divifions of thefe divifions are termed 
Sub-divifions. 
Remark (i.) Sub-divifions can be continued to infi¬ 
nity, but they may be comparatively finite. Co-divifions pro¬ 
ceed alfo to infinity , particularly in conceptions of experi¬ 
ence; for we can never afeertain all the relations among 
conceptions. 
(2.) We may alfo term co-divifion a divifion according 
to the different conceptions of the fame objeX, (points 
of view ;) fub-divifion a divifion of the points of view 
themfelves. 
Dichotomy and Polytomy. 
113. A divifion into two members is called Dichotomy, 
into more than two, Polytomy. 
Remark (1.) Polytomy is empirical, Dichotomy is the 
only divifion from principles a priori-, confequently, the 
only primitive divifion ; for the members of divifion ought 
to be oppofed to each other: now the oppofite of A is lim¬ 
ply non A. 
(2.) Polytomy cannot be taught in Logic ; for itre- 
quires a Knowledge of the Objedls ; but Dichotomy requires 
only the pofition of contradiction, and not the knowledge 
of the Contents of the Conception which we intend to di¬ 
vide. Polytomy requires either intuition a priori as in the 
Mathematics, (e. g. the divifion of the conic feXions,) 
or empirical intuition, as in Natural Philofophy. However, 
the divifion front the principle of Jynthefis a priori is luf- 
ceptible of Trichotomy ; namely, 1, the Conception as the 
Condition ; 2, the Conditioned ; and, 3, the derivation 
of the latter from the former. 
Various Divifions of Method. 
114.. We may ftill further remark on the fubjeX of Me¬ 
thod, in fcientific Knowledge ; that there are various kinds, 
which may be arranged under the following heads. 
x. Scientific and Popular. 
115. The Scientific or Scholafiic method is thus diflin- 
guifhed from the Popular. The former proceeds from 
fundamental and elementary propofitions; the latter de¬ 
pends on Cufiom and Habit. The former has for its object 
Soundncfs, confequently difpels every thing that is hetero¬ 
geneous to it; the latter aims at entertaining. 
2. Syfiematic and Fragmentary. 
116. The Syfiematic is oppofed to the Fragmentary or 
Rhapfodical Method. When we think according to a cer¬ 
tain method, in which the tranfition from one pofition to 
another is perfpicuoufly denoted, we treat Knowledge 
fyjlematically. If, on the other hand, we think indeed ac¬ 
cording to a method, but have not arranged our thoughts, 
fuch a method may be called Rhapfodical. 
Remark. The fyftematic mode of treatment is oppofed 
to the fragmentary in the fame manner as the methodical 
to the tumultuary. He who thinks methodically can treat 
a fubjeX either in a fyftematic or fragmentary manner. 
The externally-fragmentary but intrinfically.-methodical 
mode of treatment is called the Aphorifiical. 
3, Analytical and Synthetical. 
117. The Analytic is oppofed to the Synthetic method. 
The former commences from the conditioned, and pro¬ 
ceeds to the condition, or to firlt principles (a pnncipiatis 
ad principia) ; the latter proceeds from principles to their 
confequences, or from tne fitnpi. to the compoled. The 
former may be termed Regrejivc f »nd the latter Progrejfive «. 
\ 
Remark. The Analytic method is alfo called the Inven¬ 
tive and is belt fuited to the end of popularity; the Syn¬ 
thetic is calculated for the fcientific and fyftematic treat¬ 
ment of Knowledge. 
4. Syllogifiic and Tabular. 
118. The Sv/log?Jlic is that method in which a fcience is 
propounded by a feries of conclufions; the Tabular that 
which exhibits at once an entire fyftem in its whole con¬ 
nexion. 
5. Acroamatic and Erotematic. 
119. Acroamatic is that method by which we merely 
teach ; Erotematic that by which we alfo queftion. The 
latter may be again divided into the Dialogical or Socratic ; 
and the Catechetical, as the Queftions are direXed either to 
the Underfianding or merely to the Memory. 
Remark. We cannot teach erotematically otherwife than 
by the Socratic Dialogue, in which the Pupil and the 
Teacher mutually propofe Queftions and anfwer them ; fo 
that the pupil feems alfo to be a teacher, and is thus ren¬ 
dered attentive to the principles of his own reafon. By 
the catechetical method we do not teach, but only examine 
what has already been taught by the acroamatic method. 
The Catecketic, therefore, can only be applied to empirical 
and hiltorical knowledge; the Dialogic only to rational 
knowledge. 
Meditation. 
120. Meditation is thinking methodically, which Should 
accompany all our reading and ftudy. To this it is re- 
quifite that we make previous inveftigation, and afterwards 
reduce our thoughts to order, or conneX them according 
to a certain method. 
Conclusion. 
That the preceding fyftem is a Pure Univerfal Logic muft 
be evident, as it concerns itfelf with the form of Know¬ 
ledge only, and not at all with its matter. It can, there¬ 
fore, be only of a regulative life; but, in this light, it 
muft be allowed to be indifpenfable, fince it contains the 
Rules of the Agreement of Knowledge with the Laws of 
Understanding and of Reason. 
But, as all Knowledge confilts both of matter and form, 
and as logic can only criticize the form, it muft be evi¬ 
dent that another fcience is ftill requifite, in order to examine 
or criticize its matter : and this fcience is Transcen¬ 
dental Philosophy. Thus, in order to be certain that 
our Knowledge is genuine, we muft abfolutely examine 
it, both by the Rules of Logic, and by the Laws of Tran- 
fcendental Philofophy, or of true Metaphysics. (See 
that article.) Without the latter. Logic may become a 
mere play of thoughts, which entangles icfelf in its own ill u— 
fions. The diltinXion between the Original and Logical 
ufc of Underltanding is more particularly explained in 
vol. xi. p. 6 i 5 . in that view of the Critical or Tranfcen- 
dental Philofophy which accompanies the life of its au¬ 
thor, the immortal Kant. 
The Logic here given, has the great merit of expofing 
the falfe fubtilties of the fyliogiftic figures, on which fo 
much feeming learning has been lavifhed ; and of efiabli/h - 
ing the only pure and legitimate Form of Categorical Conclufion y 
which is the highelt principle erf reafoning. Thus fim- 
plified, and confined within its proper limits. Logic may 
juftly be expeXed to refume its rank among the ufeful 
l'ciences, and be again, confidered as an effential part of » 
jiberal education. 
