LOG! C, 
27 
verfion of the premifes. Nothing can therefore be more 
clear than the ufeleffnefs of the three laft figures, however 
much they may have been efteemed as original modes of 
concluding categorically ; and a greater fervice cannot be 
rendered to the fcience of Logic, than to clear them en¬ 
tirely away, and thus prevent them from confuting argu¬ 
ments, which, when exhibited in the firft figure in their 
perfeCt purity, mull be convincing to every one ; and, if 
logically correCt, apodiCtically certain. 
" Remark. The firft figure admits of a conclufion of any 
Quantity and any Quality. In the other figures conclu¬ 
sions of a reftricted kind only can occur. This proves that 
thefe figures are not complete ; but that certain limita¬ 
tions are to be met, which prevent their concluding uni¬ 
verfally, as in the firft figure. 
Conditions of a Reduction of the three lajl Figures to the firjl. 
70. The reafon why in the three laft figures a right mode 
of concluding is poffible, is this; that the middle-term is 
fo Unrated, that, by means of immediate conclufions , it is 
placed orderly, agreeably to the rules of the firft figure. 
Hence the following rules for the other three figures. 
Rule for the Second Figure. 
71. In the fecond figure the minor is correSl, therefore 
the major mult be inverted, but fo that it (till remains 
univerfal. This is only poffible when it is univerfally ne¬ 
gative-. for, if it is univerfally affirmative, it mult be 
done by contrapofition. In both cafes the conclufion will 
be negative (fequitur partem debiliorem). 
Remark. The rule for the fecond figure is this; What is 
contradicted by the mark of a thing, cantradids the thing itfelf. 
Now I mull firft invert this, and fay, What is contra¬ 
dicted by a mark, contradicts this mark ; or I mult con¬ 
vert the conclufion thus; What is contradicted by the 
mark of a thing contradicts the thing itfelf ; confequently 
the thing is contradicted by it. 
Rule for the third Figure. 
72. In the third figure the major is correct, confequent¬ 
ly the minor muft be inverted ; however, fo that an affir¬ 
mative pofition arifes from it. But this is only poffible 
■when the affirmative pofition is particular, confequently 
the conclufion is alfo particular. 
Remark. The rule for the third figure is this; What 
agrees with or contradicts a mark alfo agrees with or contra¬ 
dicts some that are contained under this mark. Here I muft 
firft fay, it agrees with or contradicts all that are con¬ 
tained under this mark. 
Rule for the Fourth Figure. 
73. In the fonrth figure, neither major nor minor are 
correCt. If the major be univerfally-negative, it admits of 
fimple converfion, but fo that the minor is particular; con¬ 
fequently the conclufion negative. If the major is uni- 
vtrfally-affirmative, it admits either of converfion or contra¬ 
pofition. Therefore the conclufion will be either particu¬ 
lar or negative. But, if the conclufion be not to be in¬ 
verted, (P. S. changed into S. P.) then a tranfpolition of 
the premifes or a converfion of both muft take place. 
Remark (1.) The fourth figure concludes as follows. 
The predicate depends upon the middle term ; the middle 
term upon the fubjeCl (of the conclufion) ; confequently 
the fubjeCl upon the ■ predicate ; which does not at all 
follow, but always the reverie. In order to render this 
poffible, the major muft be made minor, or vice verfa- ; 
and the conclufion muft be converted, becaufe in the firft 
change the major is turned into the minor. 
2. We have dwelt purpofely upon thefe three falfe 
figures of Categorical Rational Conclufions, with a view 
of facilitating the detection of them in complicated ar¬ 
guments, and thus rendering it eafy to reduce them to 
the firft figure, where the fame confequences will flow' in 
a regular and uninterrupted manner, without any imme¬ 
diate conclufions being introduced. 
General Refult of the three laft Figures. 
74. From the previoufly-explained. rules of the three laft 
figures, which w'e have proved to be falfe modes of Conclu¬ 
fion, it is evident, 
1. That in none of them a univerfally-affirmative conclu¬ 
fion can occur, but that the conclufion is always either 
negative or particular. 
2. That in all of them an immediate conclufion is intermixed, 
which, though not evidently expreifed, is fecretly under- 
ftood ; and, on this account, 
3. Thefe three modes of concluding are termed impure 
conclufions, (ratiocinum hybrida, impura,) fince no pure 
conclufion can have more than three chief propofitions, 
(termini.) 
2. Hypothetical Conclufions of Reafon . 
75. An Hypothetical Conclufion is one which has an hy¬ 
pothetical propotition for its Major. It confifts therefore 
of two propofitions; firft an Antecedent, and fecondly a Con- 
fequent ; and here the conclufion takes place either ac¬ 
cording to the modo ponente or the modo tollente. 
Remark (1.) Hypothetical Conclufions of Reafon have 
confequently no middle-term ; for the inference of one judg¬ 
ment from the other is here only denoted. In the Major is 
exprefled the inference of one propofition from another} 
the firft of which is a premife, and the other a conclufion. 
The Minor is the changing a problematical condition into an 
ajfertorical propofition. 
(2.) As an Hypothetical Conclufion confifts only of two 
propofitions without a Middle-term ; it is clear that this is 
properly no conclufion of Reafon, but an irnmediately- 
demonftrable conclufion from Antecedent and Confequent, ei¬ 
ther according to Matter or Form. 
(3.) Every Conclufion of Reafon muft be a Demonftra- 
tion. Now the Hypothetical contains in itfelf only the 
Ground of a Demonftration ; confequently it is clear that 
it cannot be a Conclufion of Reafon. 
Principle of Hypothetical Conclufions. 
76. The principle of Hypothetical Conclufions is the 
propofition of a ground-, (a ratione ad rationatum ; a nega- 
tione rationali ad negationem rationis, valet coniequentia.) 
3. Disjunctive Conclufions of Reafon. 
77. In Disjunctive conclufions, the Major is a disjunctive 
propofition, and muft therefore have members of divifion. 
Here we conclude, 1, from the truth of one member of 
Disjunction upon the falfehood of the reft ; or, 2, from the 
falsehood of all the members except one, upon the truth of 
this one. The former takes place by the modum ponentem 
(or ponendo tollentem) ; the latter by the modum tollentem , 
(tollendo ponentem.) 
Remark (1.) All the members of disjunction except one, 
taken together, conftitute the contradiCtorily-oppofite of 
this one. Here therefore a Dichotomy takes place, agree¬ 
ably to which, If one of the propofitions be true, the other 
is falfe, and conversely. 
(2.) All Disjunctive rational conclufions, confiding of 
more than two members of divifion, are properly polyfyl- 
logijlical. For all true Disjunction can only confift of twi 
members ; and indeed the logical divifion confifts only of 
two members ; but the membra fubdividentia are placed for 
the fake of brevity under the membra dividentia. 
Principle of Disjunctive Conclufions. 
78. The principle of Disjunctive Rational Conclufions 
is the principle of the excluded third. (A contradiCtorie op- 
pofitorum negatione unius ad affirmationem alterius;— 
a pofitione unius ad negationem alterius—valet conie¬ 
quentia.) 
Dilemma. 
79. A Dilemma is an Hypothetic-di junctive Conclufion of 
Reafon, or an Hypothetical Conclufion whole confequent 
is a disjunctive judgment. The Major is an Hypothetical 
propofition 
