1000000030

~'o

predicllCs

m.y

be alli,med fcrcrally of mh fubjdl,

when('e

\Ve

llave

tour

oillina propolitions. The olher

furnilhes an exam rle of the neg.ltive kind, \Vhere the

fl.ne

prcdiwe being disjoineJ from bOlh fubjeas, may

be alfo denicd of lhcm in feparate prOrO/ilions.

The olher fpecies of compound

propo~tions

are thofe

ClIled disjunél:vcs; in ",hich, comparing feveral predicms

Wilh lhe !',me fuhjeé!. \Ve allirlll

dlal

one of lhem necc/Ta–

rily bclongs

it, bmlearelhe panicular prcdicate undcler.

mined.

any one. for ex"mpie, fays,

Thil w"U eilh"

txiJl! ,jill"/. "iJlhe w"l

oflon:eoll.wifo

olldJvw:rful

ca/lft;

'il is evident. that One of lhe twO predicatCs mun

belong

the world ; bU! as lhe

propo~tion

determioes

not which, it is therefore of the kind we call

di,jlln{Jive.

Such too are the follolVing.

Thefrmeilha

11I~~(J

round

tbuarlh,

Ihe cenl" ab'1I/ 1vhich Ih, (orlhrro,lv".

fr;,ndJ/¡ip f.ndl "un

(9/1,1,

",al" Ihan

fe.

is lhe

nature of

,11

propofilions of this cla(s,

fuppo~ng

thcm to

be exaél in point of formo that upon determining the par–

ncular predicate, lhe ren are of courfe to be removed

or if

311

thcpredica:e! bU! oneare removed, that one ne–

ce/Tarily takes place. Thus in the example given a–

hove; if we allow the world

be thework of fomewife

and powerful cauCe, we of cour(e deny it to be felr-exin–

ent ; or if we <leny il to be felf·exillent, IVe mu(l nece/Tarily

.dmit that it was produced by fome wife. and pOIVerful

cauCe.

Now this particular manner of linking the predi–

cms togethcr, fo th(t theellablilhing of one di(places all

!he re(l, or the excluding all but One necc/Tarily dtablilhes

that one,. cannot olherwife be effeaed than by means of

diljunai.,

particles. And hcnce it is, that

propo~tion!

this c!a(s take their name from thefe panicles, which

make fo nm/Tary

plrt of them. aod iodeed coofiitute

lheir very nature cocfidercd as a

dinin~

fpecies.

Ih, di"ijion of prop?Jilionl

illt,

ftlf,vidml and

d,monjlrohle.

WH EN

any propofilion is offered to

th~

view of the

miod, if thc terms in which it is expre/Tcd

are

underOood ;

upon comparing the ideas togtther, lhe agreement or dif–

agreem:ot a/Terted is either immediately perceived, or

fouod lOlie bcyond the prefent rm h of thc uoderOaod–

ing. In the firll cafe, lhe propofilion is faid to be

folf

r–

"idM/,

and admits not of any proof, bmufe a barc at–

lention tO Ihe idm themCdves produces full conviélion

and cemioty; nor is it poflible tOcall iD any thing

m~re

cvident, by IVay of

con~rm",ion.

But wbere the COn–

neaioo or rrpl1gnance comes not fo rcadily under lile io–

epeélion of lhc mind, there we mu(l have recourCe to rra·

Coning; and ir by a

c1m

f~ries

of proofs we can make

tut lhc truth propo(ed, in(omu,h that Celf·evidence alall

accompany CI'cry nep of theprocedure, \Ve

are

then able

lOd!mon!lrm ",h" \Ve aaert, and the

propo~tion

il(elf

is raid

lobc drmonjlrnh/e.

\Vhen \Ve allirm, for inHaoce,

Il,,1il

imNJibl(Jor Ih, j.m, Ihing lo bt a/ld /1011, b,;

I·..hoev/C underllands the ternl! made ufe of, pelCei"es at

f" n

ohnce lhe trulh of what is a/Tened; nor CJOhe by

"ny;/ions bring hiOl(clf ,o btlievc the contrary. The

r'opo~lion

lhudore is

ftl[ (viJml•

•

nd fUlh that it is

impolliLlc

rc;¡(llning to m,kc it plainer ; bm u(eIhm

no m th more obviou!, or J::!(C known, from

hich

\.'OL.

11. No. 68.

as a con(equencc it may be dtducco.

n'JI

if '\Vc Cal',

Thi!

1V~I-Id

had n brpil/ni"e ;

lhe ani.nion is indccd e–

qually true, but

n,inc~

not [orlh "ilh the fame degree of

cvid~nce.

We fi nd a great dilli;ullY in concci..ing how

Ihe world could be maele out of 1l01hing ; and are not

brought to a free and full conf,nt. unlil by rca(oning IVe

mive at a clear view nf the abCurdily iO"olved in the

contrary fllppofilion. Hcnce lhis

prop~~lion

is of the

kiod we call

Jemonjlr.;!e,

in as much as ilSteuth is not

immediately pereeive,! by lhe mind, bUl yet may be made

appear by means of othcrs more koown and obrious,

whenee it follows as In unavoidable confequcnce.

From what has been (aid il appears, lhat r(a(oning is

employed only aboUl demoonrable

propo~lioos,

and lhat

our intuili,e aod felf.evideot pereeptions are the uhimalé

foundationOn which it re/Is.

Self·evident

propo~tions

furnilh thc hrn principies

reaConing; and it is cemin, that if in our refemhes

\Ve employ only Cuch principies as have this charaaer of

fdf evidence. and apply them . ccordng to lhe rule,' to

be afmwards explained, we /hall be in no danger of er–

ror in advancing froOl one difeovery to another. For

this we may appeal

the writings of the

mathematician~,

which being conduaed by lhe exprefs model here meo–

tioned, are an incontenable proof of the

~rmnefs

and

nability of humanknowledge, wheo built upon fo (ure a

fnundation. For not only have lhe

propo~tions

of this

Ccience 1I00d theten of age!; but arefour.dattended IVith

thM invincible evidence, as forces the a/Tent of all who

duly

con~der

lheproofs upon which they

are

ena'Jlilhed.

Fir(l lhen it ís to be obCerved, that they have been

ve,y cmful in afcemining their idea;, and

~xing

the fig–

nification of their terms. For this purFo(e they begin

Wilb

dr}nili"'I,

in which the meaning of tbeir words i$

dininaly explained, that they cannot fail to excile itl

the mind the veryfame ideas as are annexed to Ihem by

the wriler. And indeed the clearnefs and

irrc~lIable

e–

vidence of mathematical knowledge is owing tO nOlhing

fo much as this care in Iaying the foundation. Where

the rela:ion between any tIVO idcas is accuratelyand jurr–

Iy traceJ, it will not be di/lieult for aoother to compre–

hend that relation, ir. in feninghimfelf tO di(cover it, he

brings the very

f.me

ideas inlo comparifon. But if, on

the contraey, hea/lixes tOhis words i¿eas different from

thofe that Il'ere in lhe mindof him

n advaneed the

demonnration; it is erident, thlt, as the Came ideas are

nOl compared, the Camerdalion cannOl fub@, in(omuch

that a

propo~tioo

will be rejeéled as falle, \Vhieh, had

the terms been rightly unoerOood, mun have appeared

unexcC?lion"blytrue.

fquare, for inllance. is a figure

bounded by four equal right lines, joined tngelher at

riAht angles Here lhe nalure of the angles makes

lefs a

t of lhe ide., thao the eqllalily of lhc

~Jes ;

and many

pr~per1ies

dcmnn(lr.,tcd

lhe fquare Oowen–

tirely from its being a "l'langular figure. If lherefore

IVC

(~rpo(e

aman, \Vho h.s /ormed a pmial nOlion of

fquare, cOO1prehending only Ihe equalily or ilS fi¿es

without regard to lhe anglcs, readill;l fi,me demonllratinn

th.,t iOlplies airo dlis Imer conlidwl;on; it is plain hc

wbuld "jeél il .s not unive,(ally truc, in " much as ir

co~IJ

not be applied where the

~JCI

lme jo:ned 10-

gcllle.