Encyclopaedia Britannica; or, A dictionary of arts and sciences, compiled upon a new plan … > Volume 2, C-L

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taftatjee, we coihpare two figures of a different make, in
order to judge of their equality or inequality, it is plain,
that by barely confidering the figures themfelves we
cannot arrive at an exadt determination ; becaufe, by rea-
fon of their difagreeing forms, it is impoffible fo to put
them together, as that their feveral parts {hall mutually
coincide. Here then it becomes neceflary to look out for
fome third idea, that will admit of fuch an application as
the prefent cafe requires ; wherein if we fucceed, all
difficulties vaniffi, and the relation we are in quell of
may be traced with eafe. Thus right-lined figures are
all reducible to fquares, by means of which we can
meafure their areas, and determine exadfly their agree¬
ment or difagreement in point of magnitude.
But how can any third idea ferve to difcover a relation
between two others, by being compared feverally with
thefe others ? for fuch a comparifon enables us to fee how
far the ideas with which this third is compared are con-
nedted or disjoined between themfelves. In the example
mentioned above, of two right-lined figures, if we com¬
pare each of them with fome fquare whofe area is known,
and find the one exadfly equal to it, and the other lefs
by a fquare inch, we imediately conclude, that the area
of the firft figure is a fquare inch greater than that of the
fecond. This manner of determining the relation between
any two ideas, by the intervention of fome third with
which they may be compared, is that which we call rea-
fining. The greft art lies, in finding out fuch interme¬
diate ideas, as, when compared with the others in the
queflton, will furniffi evident and known truths, becaufe
it is only by means of them that we anive at the know¬
ledge of what is hidden and remote.
Hence it appears, that every adt of reafohing neceflarily
includes three diftindl judgments; two wherein the ideas
whofe relation we want to difcover are feverally compared
with the middle idea, and a third wherein they are them¬
felves connedted or disjoined according to the refult of that
comparifon. Now, as, in the firll part of logic, our judg¬
ments, when put into words, were called propofitions ; fo
here, in the fecond part, the expreffionsof ourreafonings are
termedfyllogifms. And hence it follow*, that as every adt of
reafbntng implies three feveral judgments, fo veryfyllogifni
muft include three diftindt propofitions. When a reafbning
is thus put into words, and appears in form of a fyllogifm,
the intermediate idea made ufe of to difcover the agree¬
ment or difagreement we fearch for is called the middle
term ,• and the two ideas themfelves, with which this
third is compared, go by the name of the extremes.
But as thefe things are beft illuftrated by examples ;
let us, for inftance, fet burfelves to inquire, 'whether ti/en
are accountable for their aSlions. As the relation be¬
tween the ideas of man and accountabienefi, comes not
within the immediate view of the mind, our firft care
muft be, to find out fome third idea, that will enable us
the more eafily to difcover and trace it A very fmall
raeafure of reftedtion is fufficient to inform us, that no
creature can be accountable for his actions, unlefs we
fuppofe him-capable of drftinguiffiing the good from the
bad. Nor is this alone fufficient. For what would it
avail him to know good from bad adfions, if he had no
freedgm of choice*, nor could avoid ihe one aud purfue
G I C. 99 *
the other ? hence it becomes necdTary to take in both
confiderations in the prefent cafe. It is at the fame time
equally apparent, that where-ever there is this ability of
diftinguiffiing good from bad adtions, and of purfuing the
one and avoiding the other, there alfo a creature is ac*
countable. We have then got a third idea, with which
accountablenefs is infeparably connedted, viz. reafinand
liberty; which are here to be confidered as making up
one complex conception. Let us now take this middle
idea, and compare it with the other term in the queftion,
viz. man; and we all know by experience, that it may
be affirmed of him. Having thus, by means of the in¬
termediate idea’, formed two feveral judgments, viz. that
man it pojftjfed of reafin and liberty ; and that reafin
and liberty imply accountallenefs ; a third obvioufly and
neceflarily follows, viz. that man is accountable fir his
attions. Here then we have a complete adt of reafoning,
in which there are three diftindt judgments; two that
may be ftyled previous, in as much as they lead to the o-
ther, and arife from comparing the middle idea with the
two ideas in the queftion : the third is a confequence of
thefe previous adts, and flows from combining the ex¬
treme ideas between themfelves. If now we put this rea¬
foning into words, it exhibits what logicians termafyllo*-
gifm, and runs this :
Every creature pojfejfed of redfon and liberty is ac*
countable for his altions.
Man it a creature pojfejfed of reafon and liberty.
Therefore man is accountable for his a 11 ions.
In tills fyllogifm there are three feveral propofitions,,.
expreffing the three judgments implied in the adf of rea¬
foning, and fo difpofed as to reprefent diftindtly what
paffes within the mind in tracing the more diftant rela¬
tions of its ideas. The two firft propofitions anfwer the
two previous judgments in reafoning, and are called the
premijfes, becaufe they are placed before the other. The
third is termed the conclufien, as being gained in confe-
quence of what was afterted in the premifles. The terms
exprefling the two ideas whofe relation, we inquire after,
as here man and accountablenefs, are in general called the
extremes \ and the intermediate idea, by means of which
the relation, is traced,, r/Z. a creature pojjejfidaf reafin
and liberty, takes the name of the middle term Hence
it follows, that by the premijfes of a fyllogifm we are al¬
ways to underftand the two propofitions where the middle
term is fevendly compared with the extremes ; for thefe
conftitute the previous judgments, whence the truth we
are in queft of is by reafoning deduced. The ccnclufton
is that other propofitionj in which extremes themfelves -
are joined or feparated, agreeably to what appears upon
the above comparifon.
The conclufion is made up of the extreme terms of
the fyllogifm ; and the extreme, whichferves as the pre¬
dicate of the conclufion, goes by the name of the major
term ; the other extreme, which makes the fubjeA in the
fame propofition, is-called the minor term. From this
diftinftion of the extremes, arifes alfo a diftinftion be¬
tween the premifles, . where thefe extremes are feverally
compared with the middle term. That propofition which
compares the greater extreme, or the predicate of the
cefficlufi&n, wuh the middle term, is called the major
proportion ;