24 L O < 
(2.) To Problems belong, ift, the OueJUcn, which contains 
what is to he (tone ; 2dly, the Solution, which contains di¬ 
rections how the propofed thing can be done ; and, 3dly, 
the Demon firation, which (hows that, when we have proceed¬ 
ed according to the Directions, the Problem will be halved. 
Theorems, Corollaries, Lemmata, and Scholia, 
39. Theorems, are theoretical propofitions, capable of, 
and requiring, proof. Corollaries are immediate confe- 
quences from preceding propofitions. Lemmata are pro¬ 
pofitions borrowed from other fciences ; with the prefup- 
pofition that they have been demonftrated in the fcience 
to which they naturally belong. Scholia are merely ex¬ 
planatory propofitions, which do not therefore conliitute 
any part of the fyltem. 
Remark. The effential parts of every Theorem are the 
Thejis and Demonjlration. We may remark a farther dif¬ 
ference between Theorems and Corollaries ; namely, that the 
latter are immediately concluded, whereas the former are 
inferred by a feries of confequences from immediately- 
certain propofitions. 
Judgments of Apprehenfon and of Experience. 
40. A judgment of Apprehenfion is merely fubjeftive. 
But an objeElive judgment from Apprehenfion, is a judgment 
of Experience. 
Remark. A Judgment from mere Apprehenfion is not 
eafily poffible; for here I contemplate my objeCt without 
affirming or denying ; for inflance, if I think of a Tower, and 
think it red, I cannot affirm that it is red. The following 
judgment is a Judgment of Apprehenfion : On touching a 
fone, I feel it warm ; and, if I affert that the Jlone is. warm, 
this is an experimental Judgment. But we muff be par¬ 
ticularly careful in experimental Judgments not to attribute 
to the objedl what belongs merely to the fubjed. 
SeClion III. Of Conclusions. 
Conclufion in general. 
41. By conclufion is meant that aft of thinking by which 
one judgment is deduced from another. A conclufion in 
general is therefore the deducing one judgment from ano¬ 
ther. 
Immediate and Mediate Conclufons. 
42. All conclufions are either Immediate or Mediate. 
An immediate conclufion is the deduction of one judg¬ 
ment from another, without the help of an intermediate 
judgment. A mediate conclufion is one which, befides 
the conception involved in the judgment, hill requires 
others in order to deduce a conl'equence. 
Conclufions of Underfunding, of Rcafun, and of Judgment. 
43. Immediate conclufions are alfo called Conclufions of 
Underfanding. All mediate conclufions are either Conclufions. 
of Reafon or Conclufions of Judgment. We fliall firlt treat of 
the immediate, or Conclufions of Underltanding. 
I. Conclusions of Understanding. See Plate II. 
Peculiar Nature of Conclufons of Underfanding. 
44. The effential charafteriltic of all immediate conclufions, 
and the principle of their poffibility, confilts in this, that 
the mere FO.RM of Judgment undergoes a change, whillt the 
matter ot the Judgment, that is, the Suhjeft and Predicate, 
remain unchanged. 
Remark. Immediate conclufions effentially differ from 
mediate. In the former the form only is changed ; in the 
latter the’ matter is altered, for, in order to deduce a con- 
fequencc, we add a new conception as a middle term. 
When 1 , for inltance, conclude thus; All men arc mortal, 
therefore Kant is mortal-, this is no immediate conclufion, 
• but is only pollible by means of the intermediate concep¬ 
tion, Kant is a Man ; but, by the introduftion of this new 
conception, the matter of the judgment is increafed. 
Modes of Conclufions of Underfanding. 
4.J. The conclufions of Underltanding proceed through 
i 1 c. 
all the claffes of the logical funftions of Judgment. They 
are confequently determined by Quantity, Quality, Relation, 
and Modality. 
x. Conclufions of Underfanding as to Quantity ; i. e. by 
SUBALTERNATE JUDGMENTS. 
46. In conclufions of underltanding, per judicia fubaltcr- 
na, both judgments differ as to Quantity. Hence the Par¬ 
ticular judgment is deduced from the Univerfal upon the 
following principle; From the Univerfal t.o the Particular the 
conclufion is valid. 
Remark. A Judgment is termed Jubalternate when it is 
contained under another, as particular under univerfal. 
2. Conclufions of Underfanding as to Quality; i. e. by Judg¬ 
ments of opposition. 
47. Conclufions of underltanding of this kind differ as 
to Quality, and may be confidered in refpeft to their oppo- 
fition, which is indeed threefold. In the firlt, the judg¬ 
ments are Contradictorily oppofed ; in the fecond, Contrarily 
oppojid ; and, in the third, Subcontrari/y oppofed. 
Remark. Conclufions of Underltanding by equivalent 
judgments are properly fpeaking not conclufions, for no 
coniequences follow from them. They may rather be 
confidered as a mere fubftitution of words which denote 
the lame conception. For in fiance; Not ail men are vir¬ 
tuous, and Some men are not virtuous. Both which exprefs 
the fame thing. 
a, Conclufons of Underfanding from Contradictorily- 
opposed Judgments. 
48. In judgments of underltanding that are contradicto¬ 
rily oppofed, which conllitutes real oppofition, the truth of 
one judgment is concluded from the fa Ifhood of the other, 
and converfely. This takes place upon the principle of the 
excluded third. Viz. Two conltadiElory judgments cannot 
both be true, nor can they both he falfe, lince a third 
judgment is impoflible; confequentiy, when one is true, 
the other is falfe, and converfely. 
b, Conclufions of Underfanding from Contrarily-opposed 
Judgments. 
49. In contrarily-oppofed judgments, one is univerfally 
affirmative, the other is univerlally negative. Now one of 
them exprelies more than the other 5 and, as the fall'ehood 
may lie in the excels of the one beyond the mere negation 
in the other, they cannot both be true, but may both be 
falfe. With relpeft to thele judgments, therefore, we 
conclude, from the truth of the one, the falfehcod of ihe other ; 
but not converfely. 
c, Conclufions of Underfanding from Subcontrarily-op- 
posed Judgments. 
50. In fubcontrarily-oppofed judgments, the one particu¬ 
larly affirms what the other particularly denies. As both 
may be true, but both cannot be falle, we have the fol¬ 
lowing conclufion, that, when one of thefc pofidons is falje, the 
other is true-, but not converfely. 
Remark. In lubcontrarily-oppofed judgments, no real 
oppofition takes place; for inftance, in the following con- 
ciufion : Some men arc learned, confequently fame men are not 
learned. For what is affirmed of lome men in the firlt 
judgment, is not denied of the fame men in the fecond. 
3. Conclufons of Underfanding as to Relation; i.e. by Con¬ 
version of Judgments. 
51. Immediate conclufions by Converfion concern the 
Relation of judgments, and confift in the tranjpcfition of 
fubjett and predicate-, fo that the fubjeft in the one judg¬ 
ment becomes the predicate in the ether, and converfely; 
e. g. Some Men are learned, therefore fame learned are men. 
Pure and Altered Chmjcrfon. 
52. By tranfpoftion, the Quantity of a Judgment is ei¬ 
ther altered, or it remains the fame. In the former cafe, 
the converfion is called an altered one, (converfio per ac- 
7, cidens;) 
