570 
usually held necessary for academical 
diséussion in the public, schouls of our 
universities, 
OF THE STRUCTURE AND MANAGEMENT 
OF SYLLOGISMS, 
A syllogism may be defined to bea 
sentence made up of three propositions, 
0) disposed, that the last 1s necessarily 
inferred from those that precede. 
EXAMPLE. 
Our Creator must be worshipped. 
Ged is our Creator ; 
Therefore God must be worshipped. 
The three propositions are called the 
Major, the Minor, and the Consequence. 
The theory of all syllogisms is the 
same, two ideas are compared by means 
ofa third; as the ideas of God and wor- 
Skip ave by the intervention of the idea 
of Creator, for at first we see no con- 
nection between them. 
The kinds of syllogisms now in use, are 
reduced to three, viz. the hypothetical, 
categorical, and disjunctive. 
The hypothetical i is that wherein the 
major includes some condition or suppo- 
sitien, and is known by its begin- 
ning with of 
The Major affirms something condi- 
tionally, 
The Minor confirms that supposition ; 
and 
The Consequence affirms peremptorily 
what the Major affirms only condi- - 
tionally, 
EXAMPLE. 
Major —\f Cesar be a King, he must be 
honoured. 
Minor. —But Czsar is a King ; 
Cons.—Therefore Cesar must be honoured. 
In hypothetical syllogisms sometimes 
the Aimor, and sometimes the Conse- 
guence 1s to be denied: the Minor, when 
the second proposition 3s false ; the Con- 
sequence, when the second proposition is 
true, yet the Consequence dces not ne- 
cessarily follow from it. 
A caiegorical.or positive syllogism is 
that in which the Major includes a posi- 
tive assertion ; thus the Major asserts or 
denies the agreement between two ideas, 
EXAMPLE. 
Major. —Every creature possessed of reason 
and liberty is accountable for his actions. 
Mizor.—Man is a creature possessed of 
yeason and liberty. 
Cons. —=T herefure man is accountable for his 
actions. 
Tu the disjunctive syllogism, the Major 
Contains two or More assertions one of 
which is true.—The Miner denies the 
ri 
On the Structure and Management of Syllogisms. July 15 
truth of the rest.—The Consequence af- | 
firms that one to be true. 
EXAMPL Ee 
Major. —The world is either self-existent, 
or framed by chance, or the workmanship of 
an infinitely powerful and wise being. 
Minor.—But it is neither seit- -existent, nor 
formed by chance. 
Cons.—Theretore it is the work of an infi- 
nit<ly powerful and wise being. 
In disjunctive syllogisms, sometimes 
the disyunctive and sometimes tne minor 
may be denied; the former when all the 
possible suppositions are not enumerated; 
the latter, when any of the suppositions 
are true which are denied to be so. 
An Argument is a series of syllogisms, 
whea each succeeding syllogism proves 
what was denied in the preceding one. 
Suppose the question, to be defended 
by the respondent, was this: 
Duo Jatera cujuscungue trianguli sunt mas 
jora tertio, 
Argument against this: 
Mayor.—Si quadratum hypothenusee trian- “ 
guli rectanguli, summo quadraiorum laterum, 
sit equale, cadit questio. _ 
Minor.—Sed quadratum hypothenuse, fc, 
Cons, —Ergo cadit questio. 
Here, as the Minor is true, the Cons 
sequence must be denied ; the opponent 
therefore proceeds to prove the conses 
quence in the following maaner in the 
next syllogisra. 
Mojo .—Si ubi quadrata quantitatum sint 
zyualia quantitates ips sint eequales—valet 
consequentia. 
Minor.—Sed ubi quadrata quantitatum, &c. 
Cons.—Ergo valet constqueytia. 
This syllogism being true, he proceeds 
in his argument thus: 
Major.—Si ex premissis sequatur hypsthe- 
nusam trianguli rectanguli duobus lateribus 
zqualem, valet consequentia et -argumen- 
tum 
Minor. —Sed ex przemissis sequitur, &c. 
Cons.—Ergo valet consequentia etargumen- _ 
tum. 
Here we must deny the Minor, and 
shew that this last deduction is not fairly 
drawn from the premises before ne. § 
by distinguishing between the square 
root of the sum of the squares, and the 
sum of the square roots of the two quan 
ties. 
‘and not b-+-d, which is the square root of 
b? +d?+-2hd. 
Suppose the question to be, Status 
Juturus patet ex lumine nature. 
‘The following argument, consisting of 
one 
Thus, if a? =A?-+-d?, ther” a= Vie 4d? 
Ry 
