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

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here the propofition deduced'from'it, muft be true. ' If
then any propofition is propofed to be demonftrated, and
we ajfume the coniradiftory of that- prjpofition, and
thence direftly inf'en the propofition to be demonftrated,
by this very means we know that the propofition fo in¬
ferred is true. For. fince from an afiumed propofition we
have deduced its coatradiftory, we are thereby certain
that the affumed propofition is falfe ; and if fo, then hs
contradictory, or that-deduced from it, which in this
cafe is the fame with, the propofition to be demonftrated,
muft be true.
We have acurious inftanceeftbis in the twelfth propo¬
fition of the ninth book of the elements. Euclid ihzrt
propofes to demonftrate, that in any fetie's of numbers,
rijing from unity in geometrical progrejjion, all the prime
numbers that meafure the lafi term in t'he feries •will
alfo meafure the nexU-Mfter, unity. ■ In order to this, he
aflumes the contradictory of the propofition to be dehiort-
ftrated, namely; that fame prime number meafuring the
laji term in the feriss, does not meafure the next after
unity; and thence, by a^continued train of reafoning, proves,
that it actually does meafure it . Hereupon -he concludes
the affumed propofition to be falfe, and-that which is de¬
duced from it, or its contradictory, which is the very
propofition he propofed to demonftrate; to be true. Now
Part III. C
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that this is a juft and conclufive way of reafoning, is a*
bundantly manifeft front what we havefo clearly eftablifh-
ed above.
Having thus fufficicntly evinced the certainty of de-
monftration in all it? branches, and fhewn the rules by
which we ought to proceed, in order to arrive at a juft
conclufion, according to. the various ways of arguing made
of ; it is needlefs to enter upon a particular confide-
ration of tjiofe feveral fpecies of falfe reafoning, which
logicians diftinguifh by the name of fophifrns. He that
throughly underftands the form and ftruChire of a good
argument, will.of himfejf readily dif-ern eivsry deviation
from it. And although fophifms have been divided into
many clafies, which are all called by founding names, that
therefore carry in them much appearance of learning; yet
are the errors themfelves fo very palpable and obvious,
that it is loft labour to write for a man eapable of being
mifled by them. Here therefore we chufe. to-conclude
this fecond part of logic, and (hall in the next part give
feme account of method, which, though infeparable from
reafoning, is neyerthe.lefs always ponfidered by logicians
as a diftinCt operation of the mind ; becaufe its influence is
not confined to the mqrp exercife of the-reafoning-faeulty,
but extends,in femp degree to all the tranfadlions of the un-
d erftanding.
/’Method.
Of method in general*-and the divijton’of it into analy-
tick and fynthetick.
We have now done with tlfe two firft operations of the
mind, whofe office it is to fearch after truth,'and enlarge
the bounds of human knowledge. There is yet a third,
which regards the difpofal and arrangement of our thought^,
when we endeavour fe .to put them together that their
mutual connexion and dependence may be clearly feen.
This is what logicians ‘call method, and place always the
laft in order in explaining the powers of the underftand-
ing ; becaufe it neceffarily feppofes a previous exercife of
our other faculties, and feme prbgrefs made in know¬
ledge, before we can exert it in any extenfive degree.
In this view it is plain, that we muft be before-hand
well acquainted with the truths we are to combine toge¬
ther ; otherwife how cohid we difcern their feveral con-
nedfions and relations, or fe difpofe of them as their mu¬
tual dependence may require ? Bat it often happens, that
the underftanding is employed, not in the arrangement and
compofition of known truths, but in the fearch and difco-
very of fuch as are unknown. And here the manner of
proceeding is very different. We affemble at once our
whole ftock of knowledge relating to any fubjedt; and,
after a general furvey of things, begin with examining
them feparately and by parts. Hence it comes to pafs,
that whereas, at our firft fetting out, we were acquainted
only with feme of the grand ftrckes and outlines of truth,
by thus purfuing her through her feveral.windings and
receffes we gradually difcover thofe more inward and fi¬
ner touches whence (he derives all her ftrength, fymme-
try, and beauty. And here it is, that when, by a narrow
fcrutinyinto things, we have unravelled any pait of know¬
ledge, and traced it to its firft and original principles, in-
fomuch that the whole frame'and contexture of it lies
open to the view of the mind; here jt is, that taking it
the contrary way, and beginnipg vmh *hefe principles; WC
can fe adjuft and put together the; parts, as the order and
method of fcience requires.
But as thefe things are beft underftflod when illoftrated
by examples , let us fuppofe any machine, for rnffahce a
watch, prefented to us, whofe ftrmfture and compofition
we are as yet unacquainted with,' but want if poffible to
difcover. The manner of proceeding in this cafe is, by
taking the whole to pieces, and examining the paits' fepa-
rately one after another. When by fuch a fcrutiny we
{save throughly informed ourfelves of the frame and con¬
texture of each, we then compare them together, in order*
to judge.of their mutual adlion and influence. By this
means we gradually trace but the; inward make and dflm-
pofition of the whole, and come at length to difcern, how
parts of fuch a form, and fe put together, as we found in
unravelling and taking them afunder, conftitnte that par¬
ticular machine called a watch, and contribute to all the
feveral motions and phsenomena obfervable in it. This
difcovery being made, vie can take things the contrary way,
and, beginning with the parts, fe difpofe and conheift them,
as their feveral ufes and ftruftures require, until'at length
we arrive at the whole itfejf, from the unravelling of which
thefe parts refelted.
And as it is in tracing and examining the works of art,
fo is it in a great meafure in unfolding any part of human
knowledge. For the relations and mutual habitudes of
things do net always immediately .appear* upon compa¬
ring them one with another. Hence we have recourfe to
intermediate ideas, and by means of them are furniffied