1000000030

JOOO

.lkcouclllji1U

ought

this

c:J~

to be ucnieo oí lhe

¡ub–

j (fI.

So lhat the ground of mfoning in aU fyllogilins

.of lite firll ligure is manifeUly lhis.

JIf;'nl,"er lIJa) b:

aJfiflll<d u/JiwI"[,,11y

all)

idM , may b, offil"7IIed

,"er}

or 011}'

11I,,~ber

o[ porlieula1'l

mnprcn:r.d

,,1 u1Ider Ih,,1

.i.lea.

And.•ga¡n:

Whnltwr

may be

d,,,¡'d u/Jivf1fally

an}

id,a, IIIn] b, in

li.le

IlIa1,,;,r rimúd o[

e.ver}

01"

Any nll",b"

o[ iIJ individua/¡:

T hefe IWO

pr~pofitions

.areealled byIllgicians lhe

di{lum d, omn;,

and

d/{Jum de

111.110,

and

a.re

indeeo the gre.! principies of fylloginie

reafoning, in.fmuch as aU conclufions whatfoever eHher

reUimmcdialely

u ~on

them, or

u ~o~

propofitionsdcduced

froOl th:m. But what adas greatly to lheir value is,

that they are

re.Uy

felf- evident

l1 u~hs,

and fuch as we

eannor gainfay \\'ithout

run~ing

ipto an exprefs contq·

diél on . Toa/lirm, for

mn.~ce, .

that

no fIInn

perfe{l,

and yet .rgue that

Jo'!."

me~

Qrl

,,"fin;

or to fay tlm

0/1

al"! 7II0l"lal,

. nd yet lha\[olJu

/IIpn art ml m.orlal,

is to .ílen a thing to be aod ooi tObe at lhe fa me time.

And

~ow

we may a/lirm, that in :JI fyUogifms of the

(¡rn fi gure, if the

" r,mij u

are true, the

eQlIclty,on'

mun

necds

true.

it be

tru~

tltat the

prtdieale o[ Ihe

eoue/lljion,

wlrether aflirmalive or negalive, ' grees uni,er–

fally to fOCle idea, and if it be alfo true that the

[ubjefl

lb.

COUclUji11/

is a pan of or eomprehended under ,hgt

idea,

lh~o

il neeelfarily followl, ¡hat the

pmlicaleo[lb.

conclujou

agrees alfo to lhe

¡úbid?

For 10 af!'en Ihe

eontrary. I'/odd be to ruo coonler to fome one of the

two priocipb before eUablifhed; that is, it would

mlinu io an e.ident contradiélion. Aod thos IVe are

come al tan tO the poiot

\Ve

have been .11 aloog endea·

vOllring 10 efhblifh , oaO)ely, Th.l el'ery propoGtioo

whieh

Cl n

be demonUr.ted is ncceflarily true. For as

c.ery

demon~r.lion

may be refolved ioto a feries of fyl–

logifms all in lhe Rrn figure, and as, in .ny one of thefe

fyllogifms, ir lbe premilfes are true, the cooclufion moa

fa '00 ; it cl'idently follows, that ir all lhe feveral

pren,ilfes are tlue, all lhe feveral conclufions are fo, and

eonfoquendy lhe eondufioo . Ifo of ,hc laU fyllogifm,

whíeh is always the propofiliontobedemonnrated. Now

that all lhe premiO"s of a demon(lration are lrue, will

e.lfi ly appear from the very nature and definilion of lhat

furOl of reafoning. A demonflration is a feries of fyllo.

¡¡ifms, all whofe premiffes are either definitions, fel f

~vi

dent lruths, Or propofi,ions already dlabtifl,ed. Defini–

tioos are

ide~tical

propofi lions, wherein we conneél lhe

defcription of ao idea with thc name by which we chufe

have thal idea ealltu ; and ,herefore as to Iheir truth

lhere can be 00 difpute. Self-evident propofilions appear

true of lhemfelves, and leave no doubl or uncenaioty

the mind. PropoGlions before e(lablin,cd are no o–

ther thao eondufion! gained by ooe or more (Ieps ftom

de6nitions and fel f-evident principies, that is, fruOl tr\le

premilfes, and therefare mu(l oeeds be true. \Vhenceall

the previous propofitions of a demonHratioAbeing mani ·

feélly true, lhe !aU cooduGon or propofilion to be de–

ruoo(lrated muU bc fo too. So that demonnralioo not

ooly lead, to emain truth. bUl we have here alfo a dear

vicw of lhe grouno and foundation of that cenainty.

For al, in demonflwing. we may be faid tOdo nothing

roore tllao combioe a feries of fyllogifms togeilier, aJl

re(lingon the fame

b~"om;

it is

pl.ic

, that aoe uniforOl

ground of emaioty runs through lhe \Vhole, <od lhat lhe

conclufions are every-\Vhere bUtll upoa fome one of· lhe

two principies before ellJb!ifhcd a:: the found'lioo of all

our

r~dfo",ng.

Thefc two

priu~ipb

are e,fily reduceJ

iOlPope, and mal' b, cxprcffcd thus.

W~~/,~er

,r,di–

cale, 'lJJhelh" aJlirlllaliw or I/'galive, ogrea unive1all,

t.~

Qny idea, Ihe¡"lile mujl nud! agree

l .

{very .r '(/n,

lIumb"

.¡

individ/loiJ cOlll/m h",d.d ul/d" Ihnl

id.~

And thus we have rcdueed lhe cerlaintyof demonilratiop

to one fimple aod univerfJI principie; whieh earries ir,¡

OIVO evideoce 310ng Wilh ir, aRd whieh

jndeed the u¡"

limale fou nuation of all fyllogillic. mfooiqg.

Demonllr.Uoo therefore Jérving as ao infaIJible guide

to truth, and (Iaoding no·fo fure aod uoalterable a

bafi~

IVe may 'nolV venlure

alfen, lhat the. r.ules of log'e

furnifh a

fufli cieol erilcrÍ<u

for lhe cWlinguifhing beLweeo

trulh aod falfehood. For fince every proRofiriaofhat cao

be demonílmed is oecclfarily true, he·is able to di!lio–

guifh irum froJU falIehood, who can" ith ,enainlyjudú

when a propofilion is duly demon(lrated: Now a

de~

monllralion is nOlhing more than

coneaten_tion of

fyllog,f8ts, all whofe premilfes aredefioitians. [elf-evrdeot

truths, or propofilioos previoufly eHablifhed_ Tojodge

therefore of lhe validily of a deo)onfl raliOll, we mull be

able 10 diUinlluilh, \\'I\e,her lhe defioitioos rhat eoter it

are genoioe, aod truly deferiplive of the ideas they are

mean! 10 exhioit ; whetber the

pr~pofi,ioas aJf~med

with,

OUl proof as iotuitive truths have really lhat felf-evideoe«

to which lhey lay daim; whether tbe fyIJogifms are

drawa up in due forOl, and agreeable tOthe laws of ar.

gumeolation; io fioe, IVbether they are combined

10.

gether in a jufl and orderly m_noer, fo lhar no demon.

[lrable Vropóf¡ lioos ferve any where as premilfes, unlefs

they are eonduGoos of previous fyllogifms. NolV il is

the bufinefsof logie, io explaining lhe feveral operations

of lhe mind, fully to inOruél us in all thefe points.

teaches lhe nature aoel eod of defi nilions, and lays down

the rules by which lhey ought to be framed.

unfolds

the feveral fptcies of propofi rions, and dillinguinies the

felf e.ideOl fromthe·demoollrable. 11 delineates alfo ,he

dilferent farms of fyllogifms, and explains lhe 1. lOs of

argumenmion proper to each. In fine, it deferibes rhe

manoer of eombioingfyllogifms, fo as ihat theymayform

a lrain of reafooiog, and Icad 10 the fuceeffive difeovery

of truth. Thc preeepts of logie ,herefore, as lhey en–

able us 10 judge Wilh een3inty when a propofi lioo i$

duly gemonllraled, fuminl a fu re

cril" ion

for Ihe

dj[·

tinguifhiog belween trulh and falfehood.

But perhaps it m,y be objeéled, thar demonnration i6

thing tery rare and uncommon, as beiog rhe preroga·

tive of but a feIV feieoees, and therefore the

crileriol:

here given can be of nogreat ufe. But IOhere ever, by

lhe bare eaotemplation01' our ideas, !ruth is

difcolerabl~,

lhere alfo demonflralion nlay be attained. NolV lhal is

an abundantly fullicient

cril"ion,

\Vhich enables Us to

judge \Virh ceminty in all cafes where rhekoowled¡¡e of

truth comes within our reaeh; for \Virh difcoveries, that

lie beyond the limils of the human mind, "e

h~ve

pro–

perly no bufinefs. Wheo a propofition is dfmonnrarcd,

we are cenain of its troth. Wh n, on tbe eODtrary, oor