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THE
O F
L O G I C K.
In FOUR BOOKS.
THE
ELEMENTS
L O
C K.
IN FOUR BOOKS.
BOOK I.
Of the Original of our
Ideas, their various Di-
vifians, and the Manner
in which they contribute
to the Increafe of Know-
ledge j with a Philofo-
phical Account of the
Rile, Progrefs, and Na-
ture of human Lan-
guage.
BOOK II.
Of the Grounds of human
Judgment, the Doftrine
of Propofitions, their Ufe
in Reafoning, and Divi-
lion into felf-evident and
demonftrable.
BOOK III.
Of Reafoning and Demon,
ftration, with their Ap-
plication to the Inveiti-
gation of Knowledge,
and the common Affairs
of Life.
BOOK IV.
Of the Methods of Inven-
tion and Science, where
the feveral Degrees of
Evidence are examined,
the Notion of Certainty
is fixed and ftated, and
the Parts of Knowledge
in which it may be at-
tained, demonstrated at
large.
Defigned particularly for Young Gentlemen at the
Univerfity, and to prepare the Way to the Study
of Philofophy and the Mathematicks.
By WILLIAM DUNCAN, |
Profefibr of Philofophy in the Mari/hal College of ABERDEVN*
Doclrina fed Vim promovet infitaoi ;
Reftique cultus Pedora roborant. Hon.
The EIGHTH EDITION.
LONDON:
Printed for J. DODSLEY, in Pali-Mall. 1787..
( V ) (01
A/SA ~ ~ rSfSrS
XXX kjM( XXX
To the RIGHT HONOUR ABU
I
S I R,
F I take this Opportunity of pub-
lifhing to the World the Efteerri I
have for a Character to which Learn-
ing is fo greatly indebted, I hope you
will not think yourfelf injured by
fuch a Declaration from a Man that
honours
Vi D E DI C A T,I O N.
honours you, and who looks upon
the Liberty of putting the following
Work under your Patronage, as one
of the happy Incidents of his Life.
FROM the firft Moment I form-
ed the Defign of it, I had it in my
Thoughts to addrefs it to you ; and
indeed what could be more natural,
than that I fliould be ambitious of
infcribing a Treatife upon the Ele-
ments of Philofophy, to one, who
has fb eminently diftinguifhed himfelf
by his exteniive Knowledge in that,
as well as all the other Branches of
human Learning ?
YOUR great Abilities in every Kind,
have defervedly recommended you to
the Notice of your King and Country,
and occafioned your being courted and
importuned to accept of thofe high
Offices of State, which others purfue
with
Vli
with fo much Eagernefs, and find it
often difficult to obtain, by all the
Arts and Endeavours of Ambition.
Nor have your Talents been confined
to the View of your own Country
alone. Foreign Nations have feen
and admired you, andftill fpeak with
the greateft Applaufes of your wife
and able Conduct, when it was your
Province to act as a Britijh Minifter
abroad.
BUT theQualities of a great Statef-
man are not thofe alone by which
you have rendered yourfelf illuflrious.
The Virtues of private Life no lefs
actuate and adorn your whole Beha-
viour, and add a new Dignity to the
high Station to which your Merit
has raifed you. Affability, Compla-
cency of Manners, and, above all, an
extenfive Humanity and Benevolence,
which takes Pleafure in doing Good,
are
viii DEDICATION.
are diftingui filing Parts of your Cha-
racter, and have contributed no lefs
than your other extraordinary En-
dowments, to that univerfal Acknow-
ledgment which is paid you by your
Country.
THAT you may long live to be an
Ornament and Bleffing to the Nation,
and to enjoy the Pleafure which arifes
from a Confcioufnefs of the.Efteem
and Approbation of all good Men, is
the fincere and hearty Prayer of,
S i R,
Tour much obliged,
and moft obedient
bumble Strvanf,
W. DUNCAN.
( I )
\
THE
ELEMENTS
O F
L O G I C K.
INTRODUCTION.
I. ^""V F all the human Sciences,
fm, r IinperteHft
tnat concerning Man is c f t bi Kem-
V-X certainly the moft wor- jg f // ""'
thy of Mao, and the moft neceflary
Part of Knowledge. We find ourfelves in this
World furrounded with a Variety of Objects ;
we have Powers and Faculties fitted to deal
with them, and are happy or miferable in pro-
portion as we know how to frame a right Judg-
ment of Things, and fhape our Actions agree-
ably to the Circumftances in which we are
placed. No Study therefore is more important
than that which introduces us to the Know-
ledge of ourfelves. Hereby we become ac-
B quainted
quainted with the Extent and Capacity of the
human Mind - y and learning to diftinguifli what
Objects it is fuited to, and in what manner it
muft proceed in order to compafs its Ends, we
arrive by Degrees at that Juftnefs and Truth
of Underftanding, which is the great Perfection
of a rational Being.
II. IF we look attentively into
^Ja"L .f Things, and furvey them in their
Pcrfcaion in f u ll Extent, we fee them rifmg one
Things. , i r-k
above another in various Degrees
of Eminence. Among the inanimate Parts of
Matter, fome exhibit nothing worthy our At-
tention; their Parts feem as it were jumbled to-
gether by mere Chance, nor can we difcover any
Beauty, Order, or Regularity in their Compofi-
tion. In others we difcern the fined Arrange-
ment, and a certain Elegance of Contexture,
that makes us affix to them a Notion of Worth
and Excellence. Thus Metals, and precious
Stones, are conceived as far furpaffing thofe un-
formed Mafles of Earth, that lie every where ex-
pofed to view. If we trace Nature onward, and
purfue her through the vegetable and animal
Kingdoms, we find her ftill multiplying her Per-
ft&ions, and rifmg, by a juft Gradation, from
mere Mechanifm to Perception, and from Per-
ception, in all its various Degrees, to Reafon and
Underftanding.
III. BUT
( 3 )
III. BUT though Reafon be the vfefefaft f
Boundary by which Man is diftin- Culture, and
particularly of
guifhed from the other Creatures the Study of
that furround him, yet we are far L & uk '
from finding it the fame in all. Nor is this Ine-
quality to be wholly afcribed to the original
Make of Men's Minds, or the Difference of
their natural Endowments. For if we look
abroad into the feveral Nations of the World,
fome are over-run with Ignorance and Barbarity,
others flourifh in Learning and the Sciences ;
and what is yet more remarkable, the fame Peo-
ple have in different Ages been diftinguifhed by
thefe very oppofite Characters. It is therefore by-
Culture, and a due Application of the Powers
of our Minds, that we increafe their Capacity,
and carry human Reafon to Perfection. Where
this Method is followed, Knowledge and
Strength of Underftanding never fail to enfue ;
where it is neglected, we remain ignorant of our
own Worth ; and thofe latent Qualities of the
Soul, by which (he is fitted to furvey this vaft
Fabrick of the World, to fcan the Heavens, and
fearch into the Caufes of Things, lie buried in
Darknefs and Obfcurity. No Part of Know-
ledge therefore yields a fairer PTofpecT: of Im-
provement, than that which takes account of
the Underftanding, examines its Powers and
Faculties, and {hews the Ways by which it
B 2 comes
( 4 )
comes to attain its various Notions of Things.
This is properly the DcTign of Logick, which
may be juftly ftyled the Hiftory of the human
Mind, inafmuch as it traces the Progrefs of our
Knowledge, from our firft and fimple Percep-
tions, through all their different Combina-
tions, and all thofe numerous Deductions that
refult from varioufly comparing them one with
another. It is thus that we are let into the natu-
ral Frame and Contexture of our own Minds,
and learn in what manner we ought to conduft
our Thoughts, in order to arrive at Truth, and
avoid Error. We fee how to build one Difco-
very upon another, and by preferving the Chain
of Reafonings uniform and unbroken, to purfue
the Relations of Things through all their La-
byrinths and Windings, and at length exhibit
them to the View of the Soul, with all the Ad-
vantages of Light and Conviction.
Cftrationt of ^- BUT as ^ Undemanding, in
tb Mad. advancing from one Part of Know-
ledge to another, proceeds by r. juft Gradation,
and exerts various Acts, according to the diffe-
rent Progrefs it has made, Logicians have been
careful to note thefe feveral Steps, and have di-
ftinguifhed them in their Writings by the Name
of the Operations of the Mind. Thefe they
make four in Number, and agreeably to that
have divided the whole Syftem of Logick into
four
( 5 )
four Parts, in which thefe Acts are feverally ex-
plained, and the Conduct and Procedure of the
Mind, in its different Stages of Improvement,
regulated by proper Rules and Observations.
Now, in order to judge how far Logicians have
followed Nature, in this Diftinction of the Pow-
ers of the Underftanding, let us take a fhort
View of the Mind, and the manner ofits Pro-
grefs, according to the Experience we have of it
in ourfelves, and fee whither the Chain of our
own Thoughts will without Conftraint lead us.
V. FIRST, then, we find ourfelves
furrounded with a Variety of Ob-
jects, which acting differently on our Senfes,
convey diftinct Impreffions into the Mind, and
thereby roufe the Attention and Notice of the
Underftanding. By reflecting too on what
pafles within us, we become fenfible of the Ope-
rations of our own Minds, and attend to them as
a new Set of Impreflions. But in all this there
is only bare Confcioufnefs. The Mind, without
proceeding any farther, takes notice of the Im-
preflions that are made upon it, and views
Things in order as they prefent thcmfelves one
afcer another. This Attention of the Under-
ftanding to the Objects acting upon it, whereby
it becomes fenfible of the Impreffions they make,
is called- by Logicians Perception ; and the No-
tices themfelves, as they exift in the Mind, and
3 3 are
( 6 )
are there treafured up to be the Materials of
Thinking and Knowledge, are diftinguifhed by
the Name of Ideas.
VI. BUT the Mind does not al-
judgment. . ,
ways reft latisned in the bare View
and Contemplation of its Ideas. It is of a more
a&ive and bufy Nature^ and likes to be aflembling
them together, and comparing them one with
another. In this complicated View of Things,
it readily difcerns that fome agree and others
difagree, and joins or feparates them according to
this Perception. Thus, upon comparing the
Idea of two added to two, with the Idea of four,
we at firft Glance perceive their Agreement, and
thereupon pronounce that two and two are equal
to four. Again, that white is not black, that
five is lefs than feven, are Truths to which we
immediately afTenr, as foon as we compare thofe
Ideas together. This is the firft and fimpleft
Act of the Mind, in determining the Relations
of Things, when by a bare Attention to its own
Ideas, comparing any two of them together, it
can at once fee how far they are connected or
disjoined. The Knowledge thence derived is
called intuitive, as requiring no Pains or Exa-
mination ; and the A6t of the Mind aflernbling
its Ideas together, and joining or disjoining them
according to the Refult of its Perceptions, is
what Logicians tetm Judgment.
VII. IN-
( 7 )
VII. INTUITION affords the high-
_ ,_ _ . . - i i . Reafoniitf,
eft Degree of Certainty, it breaks m
with an irrefiftible Light upon the UnderftancU
ing, and leaves no Room for Doubt or Hefitation.
Could we in all Cafes, by thus putting two Ideas
together, difcern immediately their Agreement or
Difagreement, we fhould be exempt from Error,
and all its fatal Confequences. But it fo hap-
pens, that many of our Ideas are of fuch a Na-
ture that they cannot be thus examined in Con-
cert, or by any immediate Application one to
another ; and then it becomes neceflary to find
out fome other Ideas that will admit of this Ap-
plication, that by means of them we may difco-
ver the Agreement or Difagreement we fearch
for. Thus the Mind wanting to know the
Agreement or Difagreement in Extent between
two inclofed Fields, which it cannot fo put toge-
ther as to difcover their Equality or Inequality by
an immediate Comparifon, cafts about for fome
intermediate Idea, which by being applied firft to
the one, and then to the other, will difcover the
Relation it is in queft of. Accordingly it a/Fumes
fome ftated Length, as a Yard, &. and mea-
furing the Fields one after the other, comes by
that means to the Knowledge of the Agreement
or Difagreement in queftion. The intervening
Ideas made ufe of on thefe Occaflons, are call-
ed Proofs i and the Exercife of the Mind in
B 4, finding
finding them out, and applying them for the Dif-
covery of the Truths it is in fearch of, is what
we term Reafoning. And here let it be obferyed,
that the Knowledge gained by Reafoning is a
Deduction from our intuitive Preceptions, and
ultimately founded on them. Thus, in the
Cafe before mentioned, having found by meafur.
ing that one of the Fields makes threefcore fquare
Yards, and the other only fifty- five, we thence
conclude that the firft Field is larger than the fe-
cof)J. Here the two firft Perceptions are plainly
intuitive, and gained by an immediate Application
of the Meafure of a Yard to the two Fields, one af-
ter another. The Conclufion, though it produces
no lefs certain Knowledge, yet differs from tho
others in this, that it is not obtained by an imme-
diate Comparifon of the Ideas contained in it one
with another, but is a Deduction from the two
preceding Judgments, in which the Ideas are fe-
verally compared with a third, and their Relation
thereby difcovered. We fee, therefore, that
Reafoning is a much more complicated Act of
the Mind than fimple Judgment, and neceflarily
prefuppofes it, as being ultimately founded on
the Perceptions thence gained, and implying the
various Comparifons of them one with another.
This is the great Excercife of the human Facul-
ties, and the chief Inftrument by which we pufli
on our Difcoveries, and enlarge our Knowledge.
A Quick-
( 9 )
A Quicknefs of Mind to find out intermediate
Ideas, and apply them fkilfully in determining
the Relations of Things, is one of the principal
Diftinctions among Men, and that which gives
fome fo remarkable a Superiority over others,
that we are apt to look upon them as Creatures
of another Species.
VIII. THUS far we have traced
. Method.
the Progrefs of the Mind in Think-
ing, and feen it rifing by natural and eafy Steps
from its fir ft and fimple Perceptions, to the Sxer-
cife of its higheft and moft diftinguiftiing Faculty.
Let us now view it in another Light, as enriched
with Knowledge, and ftored with a Variety of
Difcoveries, acquired by a due Application of its
natural Powers. It is obvious to confider it in
thefe Circumftances, as taking a general Survey
of its whole Stock of intellectual Acquifitions,
difpofing them under certain Heads and ClafTes,
and tying them together, according to thofe
Connections and Pcpcndencies it difcerns be-
tween them. It often happens, in carrying on
our Enquiries from Subject to Subject, that we
ilumble upon unexpected Truths, and are en-
countered by Difcoveries which our prefent
Train of Thinking gave no Profpect of bring-
ing in our Way. A Man of clear Apprehenfion,
and diftinct Reafon, who after due Search and
Examination has mattered any Part of Know-
B $ ledge,
( 10 )
ledge, and even made important Difcoveries in
it, beyond what he at firft expected, will not fuf-
fer his Thoughts to lie jumbled together in the
fame confufed Manner as Chance offered them ;
he will be for combining them into a regular
Syftem, where their mutual Dependence may be
eafily traced, and the Parts feem to grow one out
of another. This is that Operation of the
Mind, known by the Name of Difpofitlon or Me-
thod) and comes in the laft in order, according to
the Divifion of the Logicians, as prefuppofing
fome tolerable Meafure of Knowledge, before it
can have an Opportunity of exerting itfelfin any
extenfive Degree.
P<r C <p t icna*d IX ' WE fee then that this f U ^
judgment, fold Diftin&ion of the Powers of
"Termi cf a , i r T i
ery txtenfat tn ^ Mind in Perception, Judgment,
ion. Reafoning, and Difpofition, as well
as the Order in which they are placed, have a
real Foundation in Nature, and arife from the
Method and Procedure of our own Thoughts.
It is true, there are many other Actions and Mo-
difications of the Underftandingj befides thofe
above mentioned^ as Believing, Doubting, Af-
jfenting, (ffr. but thefe are all implied in the Adi
f Reafoning, in the like manner as Comprehend-
ing, Abftradling, Remembering, may be referred
to the firft Operation of the Mind, or Perception.
This will appear more fully in the Sequel, when
we
C )
we come to handle the feveral Parts of Logick fe-
parately : at prefent we ftiall content ourfelves
with this general Account of Things j only it
feems neceflary to obferve, that Perception and
Judgment, in the Propriety of the Englijh Tongue,
have a much more extenfive Signification than,
Logicians commonly allow them. We not only
perceive the Ideas in our own Minds, but we are
faid alfo to perceive their Agreement or Dif-
agreement; and hence arife the common Phrafes
of intuitive Perceptions, Perceptions of Truth t
and of the Juftnefs of Arguments or Proofs;
where it is manifeft that the Word is applied
not only to our Judgments, but alfo to our Rea-
fonings. In a Word, whatever comes under
the View of the Mind, fo as to be diftin&ly re-
prefented and taken notice of, whether an Idea,
Propofition, Chain of Reafoning, or the Order
and Connection of Things, is thereby rendered
an Object of Perception, and gives Employment
to this firft and moft fimple of our Faculties. la
like manner the Word 'Judgment is feldom in
common Difcourfe confined to obvious and felf-
evident Truths. It rather fignifies thofe Con-
je&ures and Guefles that we form, in Cafes
which admit not of undoubted Certainty, and
where we are left to determine by comparing the
various Probabilities of Things. Thus a Man of
Sagacity and Penetration, who fees far into the
B 6 Humours
Humours and Paflions of Mankind, and feldorn
miftakes in the Opinions he frames of Charac-
ters and Actions, is faid to judge well, or think
judicioufly. For thefe Reafons, it might not be
improper to change the common Names of the
two firft Operations' of the Mind, calling the
onefimple Apprehenfion^ and the other Intuition ;
which two Words feem better to exprefs their
Nature, and the Manner in which they are con-
verfant about their feveral Objects. This Accu-
racy of Diftinguilhing, where there is any the
leaft Difference, is in a peculiar Manner necef-
fary in a Treatife of Logick, as it is the profeff-
ed Defign of that Science to teach us how to
form clear and diftin& Notions of Things, and
thereby avoid being mifled by their Similitude Or
Refemblancc.
X. HAVING thus given a general
ided into four Idea of the four Operations of the
Uf<fuintfs*r>ti Mind, and traced their Connection
ExciL'eny. an( j Dependence one upon another,
I would next obferve, that in confequence of this
Divifion of the Powers of the Underftanding,
Logick is alfo divided into four Parts, which
treat feverally of thefe A&s, and give Rules and
Directions for their due Conduct and Regulation.
The Operations themfelves we have from Na-
ture, but how to exert them juftly, and employ
them with Advantage in the Search of Truth, is
a Know-
C 13 )
a Knowledge that may be acquired by Study and
Obfervation. It is certain that we meet with
falfe Reafonings as well as juft. Some Men are
diftinguifhed by an Accuracy of Thinking, and
a happy Talent of unravelling and throwing
Light upon moft obfcure and intricate Subjects.
Others confound the eafieft Speculations j their
Underftandings feem to be formed awry, and
they are incapable of either conceiving clearly
themfelves, or making their Thoughts intelligible
to others. If then we fet ourfelves carefully to
obferve what it is that makes the one fucceed fo
well, and how the others come to mifcarry, thefe
Remarks will furnifh us with an Art of the high-
eft Ufe and Excellency in the Conduct of Life.
Now this is the precife Buiinefs of Logtck to
expldn the Nature of the human Mind, and the
proper Manner of conducting its feveral Powers,
in order to the Attainment of Truth and Know-
ledge. It lays open thofe Errors and Miftakes
we are apt through Inattention to run into, and
teaches us how to diftinguifh between Truth, and
what carries only the Appearance of it. By
this means we grow acquainted with the Nature
and Force of the Underftanding, fee what Things
lie within its Reach, where we may attain
Certainty and Demonftration, and when we
muft be contented with bare Probability. Thefe
Confiderations fufficiently evince the Ufefulnefs
and
* i.
( '4 )
and Benefit of this Science, which ought to be
eftablifhed as the Foundation and Ground-work
of all our other Knowledge, if we really wifh to
fucceed in our Enquiries. But we fhall now pro-
ceed to treat of its Parts feparately, according to
the Divifion given of them above.
THE
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( is )
THE
ELEMENTS
O F
L O G I C K.
__ ____ . _ __- -- _____ .- - ---- *
BOOK I.
Of SIMPLE APPREHENSION er PER-
CEPTION.
CHAP. I.
Of the Original of our Ideas*
I.I B "VHE firft thing we obferve,
I B "V
i XT- c
when we take a View or prcbenfun and
what pafies within us, is, 1*""'
thatw are capable of receiving Impreflions from
a Variety of Objects, that diftinft Notices are
thereby conveyed into the Underftanding, and
that we are confcious of their being there. This
Attention x)f the Mind to the Objects acting upon
it, is what we c^lfimple^pprebenfion^n^ is in fact
the Mind itfelf taking a View of Things, as re-
prefented
( 16 )
prcfcnted to it by its own Confcioufnefs. It is by
this means that we come to be furnifhed with all
thofe Ideas about which our Thoughts are em-
O
ployed. For being fenfible of the Lnprelnons made
upon us, and attending to the Perceptions they
bring, we can renew them again upon Occafion,
even when the Objects that firft produced them
are removed. Now our Ideas are nothing etfe but
thefe renewed Reprefentations of what we have at
any Time perceived and felt, by means of which
Things are again brought under the View of the
Mind, and feem to have a Kind of Exiftence in it.
It is true we can upon many Occafions combine
our Ideas variously together, and thereby form to
ourfelves Reprefentations of Things that never
had an Exiftence in Nature, as when we fancy
a- Centaur, or a Golden Mountain ; but it is (till
certain, that the original Ideas out of which thefe
are made, are fuch as have been conveyed into
the Mind by fome former Impreflions. It remains
therefore to enquire how we come by our fiift
Notions and Perceptions of iThings. Whencedoes
the Underftanding derive thofe original Impref*.
fions and Characters, which it can combine in fo
many different Ways, and reprefent to itfelf un-
der fuch infinite Varieties ? To this I anfweiy
that if we attend carefully to what pafTes in our
Minds, we fliall obferve two Inlets of Know-
ledge, from whence, as from two Fountains,
the
the Underftanding is fupplied with all the Mate-
rials of Thinking.
II. FIRST, outward Obje&s, a&-
ing upon our Senfes, roufe in us a
Variety of Perceptions, according
. ,._ ...
to the different Manner in which
they affect us. It is thus that we come by the
Ideas of Light and Darknefs, Heat and Gold,
Sweet and Bitter, and all thofe other Impreijions
which we term fenfible Qualities. This great
Source and Inlet of Knowledge is commonly
diftinguifhed by the Name of Senfation, as com-
prehending all the Notices conveyed into the
Mind, by Impulfes made upon the Organs of
Senfe.
III. BUT thefe Ideas, numerous
i , ,, , . , Or Reflefltin,
as they are, are wholly derived to us
from without ; there is therefore yet another
Source of Impreflions, arifing from the Mind's
Attention to its own Ads, when, turning in-
wards upon itfelf, it takes a View of the Percep-
tions that are lodged there, and the various Ways
in which it employs itfelf about them. For the
Ideas furnilhed by the Senfes, give the Mind an
Opportunity of exerting its feveral Powers ; and
as all our Thoughts, under whatever Form they
appear, are attended with Confcioufnefs, hence
the Impreflions they leave, when we come to turn
the Eye of the Soul upon them, enrich the Un-
derftandin*
C >8 J
demanding with a new Set of Perceptions, no
lefs diftindl than thofe conveyed in by the Senfes.
Thus it is that we get Ideas of Thinking, Doubt-
ing, Believing, Willing, &c. which are the dif-
ferent Acts and Workings of our Minds, repre-
fented to us by our own Confcioufnefs. This
fecond Source of Ideas is called Refieftlon, and
evidently prefuppofes Senfation, as the Impref-
fions it furnifhes are only of the various Powers
of the Underftanding, employed about Percep-
tions already in the Mind.
Rjt and Pro- ^ THESE Confiderations, if we
vrcfs cf human duly attend to them, will give us a
clear and diftincl: View of the natural
Procedure of the human Intellect, in its Advances
to Knowledge. We can have no Perception of
the Operations of our own Minds, until they are
exerted ; nor can they be exerted before the Un-
derfbnding is furnifhed with Ideas about which
to employ them : and as thefe Ideas, that give the
firft Employment to our Faculties, are evidently
the Perceptions of Senfe, it is plain that all our
Knowledge mult begin here. This then is the
fuft Capacity of the human Mind, that it is fitted
to receive the Imprefllons made upon it by out-
ward Objects affedingthe Senfes ; which Impref-
fions thus derived into the Underftanding, and
there lodged for the View of the Soul, employ it in
various A6ls of Perceiving, Remembering, Con-
(idering,
( 19 )
fidering, &V. all which are attended with an in-
ternal Feeling nd Confcioufnefs. And this
leads us to the fecond Step the Mind takes in its
Progrefs towards Knowledge, viz. that it can by
its own Confcioufnefs reprefent to itfelf thefe its
feveral Workings and Operations, and thereby
furnifh the Underftanding with a new Stock of
Ideas. From thefe fimple Beginnings, all our
Difcoveries take their Rife : for the Mind, thus
.provided with its original Characters and Notices
of Things, has a Power of combining, modify-
ing, and examining them in an infinite Variety of
Lights, by which means it is enabled to enlarge
the Objedls of its Perception, and finds itfelf pof-
fefTed of an inexhauftible Stock of Materials. It
is in the various Comparifon of thefe Ideas, ac-
cording to fuch Combinations of them as feeni
beft to fuit its Ends, that the Underftanding ex-
erts itfelf in the Arts of Judging and Reafoning,
by which the capacious Mind of Man pufhes on
its Views of Things, adds Difcovery to Difcove-
ry, and often extends its Thoughts beyond the
utmoft Bounds of the Univerfe. Thus we fee, as
it were, at one Glance, the whole Progrefs of the
Soul, from the very firft Dawnings of Percep-
tion, till it reaches the Perfe&ion of human
Knowledge ; nor (hall we, among all its vail
Stock of Difcoveries, or that infinite Variety of
Conceptions whereof they confift, be able to
find
( 20 )
find one original Idea which is not derived
from Senfation or Reflection, or one complex
Idea which is not made up of thofe original
ones.
V. HAVING thus fhewn how the
u7'i'jeat into Mind comes to be firft furnifhed
Jiittple and w jth Ideas, we (hall next proceed to
the Confideration of the Ideas them-
felves, and endeavour to give fuch an Account of
them as will beft ferve to explain their feveral Ap-
pearances, and the Manner in which they are
formed. It is evident, from what has been faid
above, that they all fall naturally under thefe two
Heads : Firft, thofe original Imprcffions that are
conveyed into the Mind by Senfation and Reflec-
tion, and which exift there fimple, uniform, aad
without any Shadow of Variety. Secondly,
thofe more complex Notions of Things that re-
fuk from the various Combinations of our fimple
Ideas, whether they are conceived to exift of
themfelves in any particular Subje&, or are
united and joined together by the Mind en-
larging its Conceptions of Things, and purfuing
the Ends and Purpofes of Knowledge. Thefe
two ClaiTes comprehend our whole Stock of
Ideas ; and, when confidered feparately in that
Order wherein they moft naturally feem to offer
themfelves to our Thoughts, will, I hope, give
fuch a View of the Conduct and Manner of the
Mind,
Mind, as may contribute not a little to intro-
duce us to an Acquaintance with ourfelves, and
make us fenfible of the Capacity and Extent of
the human Intellect. We proceed therefore to
a. more particular Account of this Divifion of
our Ideas.
CHAP. II.
Of Simple Ideas.
I. f-r\HE firft Clafs of our Ideas
1 are thofe which I diftin- Simfk
What,
guifh by the Name of fimple Percep-
tion ; becaufe they exift in the Mind under one
uniform Appearance, without Variety or Com-
pofition. For though external objects convey at
once into the Underftanding many different
Ideas all united together, and making as it were
one whole ; yet the Imprefllons themfelves are
evidently diftinc\ and are conceived by the Mind,
each under a Form peculiar to itfelf. Thus the
Ideas of Colour, Extenfion, and Motion, may
be taken in at one and the fame Time, from the
fame Body ; yet thefe three Perceptions are as
diftinct in themfelves, as if they all proceeded
from different Objects, or were exhibited to our
Notice at different Times. We are therefore
carefully
( 22 )
carefully to diftinguifh between our fimple and
primitive Conceptions, and thofe different Com-
binations of them which are often fuggeftcd to
the Mind by fingle Objects acting upon it. The
firft conftitute our original Notices of Thing?,
and are not diftinguifhable into different Ideas,
but enter by the Senfes fimple and unmixed.
They are alfo the Materials out of which all the
others, how complex and complicated foever, are
formed j and therefore ought defervedly to be
looked on as the Foundation and Ground-work
of our Knowledge.
II. Now if we take a Survey of
bimfle Idtat . . .
f Senja- thefe Ideas, and their Icveral Lmi-
'""' fions and Claffes, we ihall find them
all fuggefled to us either by our Senfes, or the
Attention of the Mind to what paffes within it-
felf. Thus our Notices of the different Qualities
of Bodies, are all of the Kind we call fimple
Ideas, and may be reduced to five general Heads,
according to the feveral Organs which are affected
by them. Colours, &c. and Sounds, are convey-
ed in by the Eyes and Ears; Taftes and Smells,
by the Nofe and Palate ; and Heat, Cold, and
Solidity, &c. by the Touch. Befides thefe,
there are others which make Impreffions on feve-
ral of our Senfes, as Extenfion, Figure, Reft, and
Motion, &c. the Ideas of which we receive into
our Minds both by feeing and feeling.
3 III. IF
III. IF we next turn our View
r,, . . . r , Simple TJetl
upon what paites within ourfelves, O f
we fhall find another Set of fimple e "
Ideas arifing from our Confcioufnefs of the Acts
and Operations of our own Minds- Perception
or Thinking, and Volition or Willing, are what
every Man experiments in himfelf, and cannot
avoid being fenfible of. I fhall only obferve far-
ther, that befides all the above-mentioned Percep-
tions, there are others that come into our Minds
by all the Ways of Senfation and Reflection j fuch
are the Ideas of Pleafure and Pain, Power, Exig-
ence, Unity, Succeflion, ff>. which are derived
into our Underftandings both by the Action of
Objects without us, and the Confcioufnefs of
what we feel within. It is true fome of thefe
Ideas, as of Extenfion and Duration, cannot be
conceived altogether without Parts, neverthelefs
they are juftly ranked among our fimple Ideas j be-
caufe their Parts being all of the fame Kind, and
without the Mixture of any other Idea, neither of
them can be refolved into two diftinct and fsparate
Conceptions. Thus they {till anfwer the Defini-
tion given above, of being one uniform Appear-
ance in the Mind, without Variety or Plurality.
But to prevent confounding our fimple Ideas of
Space and Duration, with thofe complex Modes
of them marked out by the feveral Meafures
commonly in Ufe, as Yards, Miles, Days, Years,
&V. it may perhaps be moft proper to confider
the leaft Portions of either whereof we can form
a clear and diftincl Perception, as the fimple Ideas
of that Kind out of which all their other Modes
and Combinations are formed. Such an Inftant,
or Point, may be conceived to be the fame in re-
fpecl of Duration or Space, as Unity is in refpect
of Number; and will ferve beft to (hew, how by
a continued Addition or Repitition our more en-
larged and complex Ideas are made up.
Simph id*** IV ' HAVING thus g iven a S eneral
ttve no Ad- View of our fimple Ideas, I have ftill
fuffioa bat by /-M /
tbt proper h- two Obfervations to make concern-
ktitfNaiurt. j ng t h em . The firft is, that they
are fuch as can only be conveyed into the Mind
by the proper Channels and Avenues provided by
Nature ; infomuch that if we are deftitute of any
of thofe inlets, by which the Impreffions that
produce them are wont to be admitted, all the
Ideas thence arifing areabfolutely loft to us ; nor
can we, by any Quicknefs of Understanding, find
a Remedy for this Want. A Man born blind is
incapable of the Ideas of Light and Colours ; in
like manner as one who is deaf can form no No-
tion or Conception of Sounds. Hence it ap-
pears, thatthefe our fimple Ideas are juft fuch as
Nature has furnifhed them, and have no Depen-
dence on our Will j we can neither deftrojr
them when in the Understanding, nor fafliioa
8 or
( 25 )
or invent any new one, not taken in by the or-
dinary Means of Perception. So that we here
fee the utmoft Bounds of human Knowledge,
which, however mighty and enlarged, cannot ex-
ceed the Limits of thofe our fimple original Ideas,
and their various Combinations.
V. AXD this leads me to the fe-
, / -^., r - r r i fbey furnijb
cond Oblervation 1 propoled to ampitM&tt-
make, which is, that though the h ' 6 S .
... Knowledge,
Mind cannot, in multiplying its
Conceptions of Things, advance one Step be-
yond the Materials furnifhed it by Senfe and
Confcioufnefs ; yet as it has a Power of com-
bining, modifying, and enlarging them, in all
the different Ways in which they can be put to-
gether, it therefore finds itfelf in Pofleflion of an
inexhauftible Treafure of Ideas, fufficient to em-
ploy it to the full Extent of all its Powers, and
furnifh Matter for all thofe various Opinions,
Fancies, and Views of Things, that make up the
Subject of its Thoughts and Contemplations. Let
us but reflect upon the fingle Idea of Unity or
One,. and obferve what a Variety of Combina-
tions are formed, by continually adding it to it-
felf j infomuch that the Underftanding finds no
Stop or Boundary, in its Progrefs from Number
to Number. In what an Infinity of different
Lights may Extenfion alone be confidered ! What
Limits can be fet to that endlefs Diverfity of
C Figures,
( 26 )
Figures, which it is in the Power of the Imagi-
nation to fafhion and reprefent to itfelf? If to
thcfc we add thofe numberlefs other Combina-
tions that refult from varioufly compounding and
comparing the reft of our fimple Ideas, we fhall
have little Reafon to complain of being limited
to a fcanty Meafure of Knowledge, or that the
Exercife of the human Faculties is confined
within narrow Bounds. But having traced the
Progrefs of the Mind thro' its original and fim-
ple Ideas, until it begins to enlarge its Concep-
tions by uniting and tying them together ; it is
now time to take a Survey of it as thus employ-
td in multiplying its Views, that we may fee by
what Steps it advances from one Degree of Im-
provement to another, and how it contrives to
manage that infinite Stock of Materials it finds
itfelf poflefled of.
VI. WHOEVER attentively con-
*** flders his own Thoughts, and takes
e a View of the feveral complicated
.
tiofe framed thcmfelves to his Understanding ;
ty the Mind.
will readily obferve that many of
them are fuch as have been derived from without,
and fuggefted by different Objects affecting his
Perception; others again are formed by the Miud
itfelf, varioufly combining its fimple Ideas, as
feems bcft to anfwer thofe Ends and Purpofes it
has
f *7 )
has for the prefent in View. Of the firft Kind
are all our Ideas of Subftances, as of a Man, a
Horfe, a Stone, Gold. Of the fecond are thofe
arbitrary Collections of Things, which we on
many Occafions put together, either for their
TJfefulnefs in the Commerce of Life, or to fur-
ther the Purfuit of Knowledge : fuch are our
Ideas of dated Lengths, whether of Duration or
Space ; as Hours, Months, Miles, Leagues, &c.
which Divifions are apparently the Creatures of
the Mind, inafmuch as we often find therrfdiffe-
rent in different Countries j a fure Sign that they
are taken from no certain and invariable Stand-
ard in Nature. Many of our Ideas of human
Actions may be alfo referred to this Head j as
Treafon, Inceft, Manflaughter, &c. which com-
plex Notions we do not always derive from an
a<5hial View of what thefe Words defcribe, but
often from combining the Circumftances of them
in our Minds, or, which is the moft ufual Way,
by hearing their Names explained, and the Ideas
they ftand for enumerated. Thefe two ClafTes
comprehend all our complex Conceptions, it be-
ing impoilible to conceive any that are not either
fuggefted to the Underftanding by fome real Ex-
iftences, or formed by the Mind itfelf arbitra-
rily uniting and compounding its Ideas. We
fhall treat of each in Order.
C * CHAP.
CHAP. III.
Of our Ideas of Subjtances.
I. '"T^ H E firft Head of complex
yw;i Calltc- *" Ideas mentioned in the fore-
timi offimpit going Chapter, is that of Bubjlqnce^
Heat, held to- . J
gttbcr by feme which I choofe to handle before the
ynw.ut- other . bccaufe) as wm afterwards
appear, the Notices derived from
this Source very much help us in forming thofe
arbitrary Collections, which make up the fecond
Divifion. For in many of them we take our
Hints from the Reality of Things, and combine
Ideas that actually exift together, though often
with an Exclufion of others, as will be explain-
ed when we come to treat of abftract and uni-
verfal Notions. It has been already obferved,
that the Impreflions conveyed into the Umler-
ftanding from external Objects, confift for the
mod part of many different Ideas joined together,
which all unite to make up one Whole. Thefe
Collections of various Ideas, thus co-exifting in
the fame common Subject, and held together by
fome unknown Bond of Union, have been dif-
tinguifhed by the Name of Sub/tarices^ a Word
which implies their fubfifting of themfelves, with-
out Dependence (at leaft as far as our Know-
ledge reaches) on any other created Beings. Such
are
( 29 )
are the Ideas we have of Gold, Iron, Water,
a Man, &c. For if we fix upon any one of
thefe, for inftance Gold, the Notion under which
we reprefent it to ourfelves is that of a Body
yellow, very weighty, hard, fufible, malleable,
&V. : where we may obferve, that the fevc-ral
Properties that go to the Compofition of Gold,
are reprefented to us by clear and evident Per-
ceptions; the Union too of thefe Properties, and
their thereby constituting a diftinct Species of
Body, is clearly apprehended by" the Mind : but
when we would pufti our Enquiries farther, and
know wherein this Union confifts, what holds
the Properties together and gives them their Self-
fubfiftence, here we find ourfelves at a Lo^.How-
ever, as we cannot conceive Qualities, without
at the fame Time fuppofing fome Subject in which
they adhere, hence we are naturally led to form
the Notion of a Support, which fervirtg as a
Foundation for the Co-exiftence and Union of
the different Properties of Things, gives them that
feparate and independent Exiftence under which
they are reprefented to our Conception. This
Support we denote by the Name Subjlance- y and
as it is an Idea applicable to all the different Com-
binations of Qualities that exift any where by
themfelves, they are accordingly all called Sub-
ftances. T-hus a Houfe, a Bowl, a Stone, &c.
having each their diftinguifhing Properties, and
C 3 being
( 30 )
being conceived to exift independent one of an-
other, the Idea of Subftance belongs alike to
them all.
The Di-vijion II. IN Subftances therefore there
gfiUT are two Thi "S s to be confidered :
Firft, the general Notion of Self-
lubfiftence, which, as I have faid, belongs equally
to them all j and then the feveral Qualities, or
Properties, by which the different Kinds and
Individuals are diftinguifhed one from another.
Thefe Qualities are othcrwife called Modes, and
have been diftinguifhed into eflcntial and acci.
lcntal, according as they are perceived to be fe-
parable or infeparable from the Subjecl to which
they belong. Extenfion and Solidity are eficntul
Modes of a Stone, becaufe it cannot be conceiv-
ed without them ; but Roundnefs is only an ac-
cidental Mode, as a Stone may exift under any
Shape or Figure, and yet flill retain its Nature
and other Properties.
NO,** of HI. ! MIGHT run farther into
thefe Divifions and Sub-divifions, in
injef arable . T . . , .
frem Sut- which Logicians have been very fcr-
fonce,. t jj e . b ut as they tend little to the
Advancement of real Knowledge, and ferve ra-
ther to fill the Memory with Words and their
Significations, than furnifli clear and diilincl
Apprehenfions of Things, I fhall not trouble the
Reader with them. It is more material to ob-
fcrve, that the Change of Properties in any Sub-
itance,
fiance, tho' it oft- times changes the Nature of that
Subftance, that is, its Species or Kind ; yet it
never deftroys the general Notion of Self-fubfift-
cnce, but leaves that equally clear and applicable,
as before any fuch Alteration happened. Wood
by the Application of Fire is turned into Charcoal;
but Charcoal, however different from Wood, is
ftill a Subftance. 1 In like Manner, Wax may be
converted into Flame and Srnoke, a human Body
will moulder into Duft, yet thefe Alterations de-
ilroy not their Being or Exigence ; they are ftill
Subftances as before, tho' under a different Form
and Appearance. In the feveral Experiments
made by Chemifts, Bodies undergo many
Changes, and put on fucceflively a great Variety
of different Shapes ; and yet, by the Skill and
Addrefs of the Operator, they are often brought
back to their firft and primitive Form. What
Alteration can we fuppofe the Fire, or the Ap-
plication of any other Body, to make, unlefs on
the Configuration, Texture, or Cohefion of the
minute Parts ? When thefe are changed, the
Body is proportionably changed ; when they re-
turn to their original State, the Body likewifo
puts on its firft and natural Appearance.
IV. ALL that is effential to Matter ,
Foundation cf
therefore, is the Cohefion of folid ex- the different
tended Parts ; but as thefe Parts are f^jlf
capable of innumerable Configura- flances.
tions j as their Texture may be very various, and
C 4 the
( 3* )
the internal Conflitution thence arifmg be of
confequence extremely different in different Bo-
dies ; we may from thefe Considerations conceive
pretty clearly the Source and Foundation of all
the different Species of corporeal Subftances.
Nor is this a Notion taken up at random, or one
of thofe chimerical Fancies in Philofophy, de-
rived rather from a Warmth and Livelincfs of
Imagination, than Obfervations drawn from
Things themfelves. Do we not daily fee our
Food, by the Changes it undergoes in the dif-
ferent Avenues of the Body, converted firft into
Blood, and thence employed in nourishing,
building up, and enlarging, the feveral Parts of
that wonderful Fabrick ? Rain defcending from
the Clouds, and mixing with the Mold or Earth
of a Garden, becomes Aliment for Trees df va-
rious Kinds, puts on a Diverfity of Forms, ac-
cording to the different Channels and Convey-
ances thro' which it paffes ; and at laft, after in-
numerable Changes and Tranfmutations, fprouts
forth in Leaves, opens in Buds, or is converted
into the Subftance of the Tree itfelf. Can we
conceive any greater Difference between the
component Parts of Gold, and thofe of Stone,
than between the moiftened Particles of Garden
Mold, and thofe new Forms and Figures under
which they appear, after they have been thus
fafhioncd by Nature for the Purpofes of Growih
and Nourifhment ?
V. IF
( 33 )
V. IF this be duly attended to, it .
, r , ir EfftrceofSub-
will not appear wonderful to allert, j- tancct no ,bing
that the Variety of material Subftan- but . *' ''"'""
J tial S'rufiure
ces arifes wholly from the different and Conft'nu-
Configuration, Size, Texture, and
Motion of the minute Parts. As thefe happen
to be varioufly combined, and knit together un-
der different Forms, Bodies put on a Divcrfity of
Appearances, and convey into the Mind by the
Senfes all thofe feveral Impreflions, by which
they are diftinguifhed one from another. This
internal Conflitution or Structure of Parts, from
which the feveral Properties that diflinguifh any
Subftance flow, is called the Eflence of that Sub-
ftance, and is in FadT: unknown to us, any far-
ther than by the perceivable Impreflions it makes
upon the Organs of Senfe. Gold, as has been
faid, is a Body yellow, very weighty, hard, fufi-
ble, malleable, &c. That inward Structure and
Conformation of its minute Partides, by which
they are fo clofely linked together, and from
which the Properties above mentioned are con-
ceived to flow, is called its Eflence ; and the Pro-
perties themfelves are the perceivable Marks that
make it known to us, and diftinguirti it from all
other Subftances ; for, our Senfes are not acute
enough to reach its inward Texture and Con-
flitution. The Parts themfelves, as well as their
Arrangement, lie far beyond the utmgrt Penetra-
C 5 tion
C 34 )
tion of human Sight, even when a/Tifled by Mi-
crofcopes, and all the other Contrivances of
Art.
VI. THUS, as to the EfTence or
h vbclly *n- interna i Conftitution of Gold, we
kmivn to us, '
nor f,r*,ei to are wholly in the dark ; but many
Sfau". ' f tne Properties derived from this
Eflence, make obvious and diftin&
Impreflions, as the Weight, Hardnefs, and yellow
Colour, sV. Thefe Properties combined together,
and conceived as co-exifling in the fame common
Subject, makeup our complex Idea of Gold. The
fame may be faid of all the other Species of cor-
poreal Subftances, as Lead, Glafs, Water, &"c.
our Ideas of them being nothing elfe but a
Collection of the ordinary Qualities obferved in
them.
VII. THIS however ought to be
r " r " ,**'? o^ferved, that tho' the Efience or
f re fumed to be
<nj}ir.fi in all inward Structure of Bodies is al-
xf/j* together unknown to us, yet we
rightly judge that, in all the feve-
ral Species, the EfTences are diftinft. For each
Species being a Collection of Properties, which
taken together are different from thofe of every
other Species, the Conformation of Parts, on
which thefe Properties depend, muft in like man-
ner be different ; and this, as we have faid, con-
ttitutes the Eflence. Iron and Glafs are evi-
dently diftinft Kinds of Body, their perceivable
Qualities
( 35 )
Qualities have little or nothing common ; and
therefore the inward Structure or Conftitution
from which thefe Qualities flow, cannot be the
fame in both. But after all, this is the only Thing
we can with Certainty affirm concerning thefe
Eflences, which lying fo wholly in the Dark, we
fhall do well to lay them afide in our Reafonings
about Things, and ftick to thofe more intelligi-
ble and fettled Ideas got by joining together their
various Properties and Powers. For thus only
js true Knowledge promoted, when we argue
from known Qualities, and not from a fuppofed
internal Conftitution, which, however real in it-
felf, yet comes not within the Reach of our Fa-
culties, and therefore can never be a Ground to
us for any Difcoveries or Improvements.
VIII. MATERIAL Subftance, asl By what S(eff
have faid, includes the Idea of folid, *t arrive at
cohering, extended Parts, and is di- LLr"'w ^
vided into different ClafTes, accord- $*%?*"?
ing to the different Impreffions made upon the
Organs of Senfe. But, befides thefe fenfible Ideas
received from without, we alfo experiment in
ourfelves Thinking and Volition. Thefe Actions
have no Connection with the known Properties of
Body ; nay, they feem plainly inconfiftent with
fome of its moft eflential Qualities. For the
Mind not only difcovets no Relation between
Thinking, and the Motion or Arrangement of
C6 Parts;
( 36 )
Parts ; but it alfo perceives that Confcioufnefs,
a fimple individual Act, can never proceed from,
a compounded Subftance, capable of being di-
vided into many. Let us fuppofe, for inftance, a
Syftem of Matter endowed with Thought ; then
either all the Parts of which this Syftem is com-
pofed muft think, which would make it not one,
but a Multitude of diftindt confcious Beings ; or
its Power of thinking muft arife from the Con-
nection of the Parts one with another, their Mo-
tion and Difpofition, &V. which, all taken toge-
ther, contribute to the Production of Thought.
But it is evident that the Motion of Parts, and
Manner of combining them, can produce no-
thing but an artful Structure, and various Modes
of Motion. All Machines of human Compo-r
fiticn, as Watches, Clocks, sV. however art-
fully their Parts are fet together, however com-
plicated their Structure j tho' we conceive in-
numerable different Motions, varioufly conjoin-
ed, and running one into another with an endlefs
Diverfity, yet never produce any Thing but Figure
and Motion. If a Clock tells the Hour and Mi-
nute of the Day, it is only by the Motion of the
different Hands, pointing fuccefllvely at the Fi-
gures marked on the Hour-plate for that Purpofe.
We never imagine this tobe the Effect of Thought
or Intelligence ; nor conceive it poflible, by any
t of Structure, fo to improve the
Com-
( 37 )
Compofition, as that it fhall become capable of
Knowledge and Confcioufnefs. The Reafon is
plain : Thought is fomething altogether diffe-
rent from Motion and Figure, there is not the
Jeaft Connexion between them ; and therefore
it can never be fuppofed to icfult from them.
IX. THIS then being evident,
, , ... ..... Which tee
that Intelligence cannot ante from et ker<wijt all
an Union or Combination of unin- #/>'""
telligible Parts ; if we fuppofe it to belong to
any Syftem of Matter, we muft neceflarily attri-
bute it to all the Parts of which that Syftem is
compofed ; whereby, inftead of one, we fhall, as
was before obferved, have a Multitude of diftindl
confcious Beings. And becaufe Matter, how far
foever we purfue the Minutenefs of its Parts, is
ftill capable of repeated Divifions, even to Infi-
nity; it is plain that this Abfurdity will fol-
low us through all the Suppofitions that make
Thought inherent in a material Subftance.
Finding, therefore, Confcioufnefs incompatible
with the Cohefion of folid feparable Parts, we
are neceflarily led to place it in fome other Sub-
ftance of a diftincl: Nature and Properties, which
we call Spirit.
X. AND here it is carefully to be
i r 11 i f in- r ^"Jy an ^ Spi m
obierved, that the leveral bpecies or r \ t djkn&
corporeal Subftances, though diftin- Subjijncts.
guiflied one from another, and ranked under dif-
ferent Names - t yet, agreeing in fome common
Properties,
( 33 )
Properties, which taken together make up the
Notion of Body, are thence all conceived to par
take of this general Nature, and to differ only
as different Modifications of the fame Subftance.
Whatever confifts of folid extended Parts, is
called Matter ; and as all the various Species of
Body, however diftinguifhed from one another
by their feveral Properties, have yet this in
common, that they are made up of fuch folid
feparable Parts, hence they fall naturally under
the general Denomination of material Beings,
and are not conceived to differ but in their
Form. Thus Gold, Antimony, Wood, &c.
alike partake of the Notion of Bodyj they are
all equally material Subftances, and have no
other Difference but what arifes from the dif-
ferent Structure and Conformation, C3?t\ of
Parts, as we have fhewn above. But Spirit is
fomething altogether diftinft from Body, nay,
and commonly placed in Oppofition to it j for
which Reafon, the Beings of this Clafs are
called immaterial; a Word that implies not any
Thing of their Nature, but merely denotes its
Contrariety to that of Matter.
XI. BODY and Spirit, therefore,
Then may le Differ not as Species of the /fame
many vartcus
SptdetofSub- Subftance, but are really diftincc
ft tboj"tba?c d <,mt Kinds of Subftances, and ferve as
within tit general Heads under which to rank
all
( 39 )
all the particular Beings that fall R eac i f tttr
within the Compafs of our Know- Faculties.
ledge. For we having no Ways of Perception
but Senfe and Confcioufnefs, can have no No-
tices of Things, but as derived from thefe two
Inlets. By our Senfes we are informed of the
Exiftence of folid extended Subftances, and Re-
flection tells us that there are thinking confci-
ous ones. Beyond thefe our Conceptions reach
not ; and therefore, though there may be many
other Kinds as different from them as they are
from one another, yet having no Faculties fuited
to them, they are as remote from our Know-
ledge, as Light and Colours from the Appre-
henfion of a Man born blind. I believe it will
hardly be doubted but the Subftance of the Cre-
ator differs more from that of his Creatures, than
any two created Subftances can from one an-
other ; and therefore when we call God a Spirit,
we ought not rafhly to prefume that he is fo in the
fame Senfe in which the human Soul is a Spirit.
The Word is indeed ufed by us, to denote in
general all thinking intelligent Subftances, in
which Senfe God is very fitly called a Spirit.
But it were the Height of Folly to imagine, be-
caufe this Name is applied as well to the Mind
of Man as the Creator, that therefore they par-
take of one common Nature, and differ only as
different Modifications of the fame Subftance.
This
( 40 )
This I mention here, to check the Preemption
of the human Mind, always forward to conclude
that every Thing comes within its Reach, and
to deny Exiflence to whatever exceeds the Com-
prehenfion of its fcanty and limited Powers.
Beings of a fuperior Clafs may enjoy many
"Ways of Perception unknown to us, from
which they receive Notices as different from
thofe in our Minds, as the Ideas we apply
to Spirit are from the Ideas we apply to Body.
Solid and thinking Beings are, it is true, the
only Ideas of Subftance that ifre are able to
frame j but this is no more an Argument againft
the Exiftence of other Kinds, than the Want of
the Ideas of Light and Colours in a blind Man
would be a good Argument againft the Reality
or Poflibility of fuch Perceptions.
XII. BEFORE I difmifs this Sub-
Difftrttcc in . . ,
the Manner jeer, it may not be improper to take
I^StrSl notice of a remarkable Difference
ff initial Sub- as to the Manner of our conceiving
corporeal and fpiritual Subftances.
Thofe of the firft Kind convey themfelves into
the Mind by Impreflions made upon the Organs
of Senfe ; and as thefe Impreflions are different in
different Bodies, the Ideas they produce muft of
courfe vary in Proportion. Thus we get Percep-
tions of diftincl Powers and Properties, and range
Bodies into daffes, according as we find them to
agree
agree or difagree in thefe their obfervable Quali-
ties. But it is not fo in our Notion of Spirits ;
for having no Conception of their Powers and
Operations but by what we feel and experience
within ourfelves, we cannot afcribe to them
Properties or Ways of Knowledge, diftinct from
thofe fuggefted to us by our own Confcioufnefs.
And hence it is, that though we readily own
there may be various Ranks of fpiritual Beings,
yet we are not to imagine them divided from
one another by any Diverfity of Powers and
Operations, but merely by poflelTing the fame
Powers, C5"c. in a higher or lower Degree. It is
not however repugnant to Reafori, that they
fhould be diftinguifhed by their feveral Properties
in like Manner as fenfible Things are by the dif-
ferent Qualities obfervable in them ; but Proper-
ties of intellectual Natures, diftincl: from thofe
of our own Minds, being altogether remote
from our Conception, cannot ferve us as a
Means whereby to diftinguifli their different
Orders. We are therefore neceflitated to con-
ceive of them in a Manner fuited to our Way of
Knowledge; and when we would rank them into
Species, according to the Degrees of Superiority
they are imagined to poffefs in the Scale of Be-
ing, we afcribe to them what we find moft ex-
cellent in ourfelves, as Knowledge, Thinking,
Forefight, &c. ; and thofe in different Meafures,
propor-
( 42 )
proportioned to the Station peculiar to each Rank
or Species. But that this is a very imperfect Way
of diftinguifhing the various Orders of intellec-
tual Beings, will not, I think, need many Words
to make appear j efpecially if we confider, that
the Manner of communicating their Thoughts,
without the Intervention of bodily Organs, is a.
Thing to us altogether incomprehenfible, and
necefiarily leads us to fuppofe that they have
Ways of Perception and Knowledge which our
Faculties cannot give us any Notice of.
XIII. BUT I fhall not purfue
Tot Boundi (if
Know/edge in thefe Reflections farther ; what has
'sitttilry b ecn k^ fufficing to give us fomc
nwu.; jj tt ] e Infight into the Extent and
Capacity of our own Minds j to convince us
that our prefent State will not admit of a perfect
and adequate Comprehenfion of Things ; and to
let us fee that there may be other Ways or"
Knowledge, beyond the Reach of the Faculties
we now enjoy ; which yet, in fucceeding Stages
of our Exiftence, we may arrive at, when being
freed from the prefent cumberfome Load of the
Body, we fhall mount up to Stations of greater
Eminence, and advance by a perpetual Series of
Approaches towards Him, who is the Standard
of Perfection and Happinefs,
CHAP.
( 43 )
CHAP. iv.
"Of Ideas framed by the Mind.
1. TTITHERTO we have con- Jn p am \ ns
JLA fidered only fuch Combina- fX comfit*
r / 1*1 Utai, the
lions of our ample Ideas as have a Mmd iiiobolly
real Union in Nature, and are fug- ^y"^'
gefted to the Mind by Things them- i**tary Choice.
felves varioufly affecting our Perception : it is
-now time to take a View of the other Clafs of
our complex Notions j I mean thofe arbitrary
Collections of different Ideas, which we on
many Occafions bring together by that Power
which we find in ourfelves, of uniting, com-
paring, and diverfifying our Notices of Things.
In the Reception of fimple Ideas, and even in
thofe of Subftances, the Underftanding is wholly
paffive, and the Perceptions produced correfpond
to the Impreffions made upon it. When we fee
a Houfe, or a Tree, they necefTarily appear each
under its proper Form j nor is it in our Power
to receive from thefe Objects other Ideas than
what they are fitted to produce. But in this fe-
cond Clafs of complex Conceptions, the Mind
acts voluntarily and of Choice ; it combines only
fuch Ideas as are fuppofed beft to fuit its prefent
Purpofe 5
( 44 >
Purpofe ; and alters or changes thefe Combina-
tions, by inferring fomc, and throwing out others,
according as the Circumftances of Things re-
quire their being viewed in different Lights.
Now as this is by far the moft comprehenlive
Branch of our Ideas, and includes thofe that moft
frequently occur in the Search and Purfuit of
Knowledge, I fhall endeavour to treat of them
in the exadteft Order and Method ; and for that
Purpofe range them under feveral Heads, accord-
ing to the different A&s of the Mind exerted in
framing and putting them together.
II. THESE A els may in the gene-
1 brtt ft-veral , , .,
Aditxtrttd ral be all reduced to three, i. Com-
tytbtMind pofaw}, w hen we join many fimple
t* framing It I * J J J
arbitrary. Ideas together, and coniider them,
', as one Piclure or Reprefentation.
Such are our Ideas of Beauty, Gra-
titude, a Furlong, ^<r. And here let it be< ob-
ferved, that the Mind fometimes confines itfelf
to the various Confideration of the fame Idea,
and, by enlarging it in different Degrees, exhi-
bits it under a Diverfity of Forms. Thus by
adding Units together, in diftinct feparate Col-
lections, we come by all the feveral Combina-
tions of Numbers, as a Dozen, a Score, a
Million. At other Times we unite Perceptions
of different Kinds; in which Cafe the Compofition
is more manifeft, and the Idea itfelf becomes of
courfc
( 45 )
courfe more complicated. Harmony, for in-
fiance, is a compound Idea, made up of many
different Sounds united; all which the Mufician
muft have, and put together in his Mind, before
the Ear can be entertained with the actual Per-
formance. Now although the Act of the Mind
K in fome meafure exerted in the framing of all
our complex Notions, yet as many of them in-
clude certain limited and particular Confidera-
tions, arifing from other Operations of the Mind
employed about them, it is neceflary to take ac-
count of thefe Acts alfo, if we would conceive
clearly the Manner in which the feveral Species
of our compound Ideas are formed.
III. 2. The next Operation there-
fore of the Mind, about its Ideas, is .
AbjlraftiGn^ when we feparate from any of our
Conceptions all thofe Circumftances that render
it particular, or the Reprefentative of a fingle
determinate Object ; by which Means, inftead
of {landing for an Individual, it is made to denote
a whole Rank or Clafs of Things. Thus upon
feeing, for inftance, a Square, or Circle, we
leave out the Confideration of their Bulk,' and
every Thing elfe peculiar to them, as they im-
mediately affect our Sight, retaining only the
Notion of their Figure and Shape. In this Man-
ner we get our general Ideas ; for fuch naked
Appearances, (eparated from the Circumftances
of
of Time, Place, &c. ferve the Mind as Standards
by which to rank and denominate particular Ob-
jects. When therefore we meet with a Figure
anfwering to that Shape and Form we had laid
up in our UndeHtandings, it is immediately re-
ferred by the Mind to this Pattern, and called by
its Name, which by this Means becomes proper
to the whole Species. Thus a Square, or Circle,
are univerfal Terms, common to all Figures of
that particular Shape, and alike applicable to
them wherever they exift ; in like Manner as
the Ideas themfelves are general^ and Reprefen-
tatives of all of the Kind.
IV. 3. THE third and laft A& of
fiffn. Coff!fa ~ the Mind about its Ideas, is the com-
paring them one with another, when
we carry our Confideration of Things beyond the
Objects themfelves, and examine their Refpects
and Correfpondences in Reference to other
Things which the Mind brings into View at
the fame Time. It is thus we get all our Ideas of
Relations, as of Greater, Lefs, Older, Younger,
Father, Son, and innumerable others. This
threefold View of our Ideas, as either compound-
ed of many others put together, or made univer-
fal by the Abftra&ion of the Mind, or as repre-
fcnting the various Relations and Habitudes of
Things, will give us an Opportunity of obferv-
ing whatever is mofl curious and ufefu] in this
1 1 fun-
( 47 )
fundamental Branch of Knowledge, and of ex-
plaining the Manner and Procedure of the Un-
derftanding in enlarging its Views, and multi-
plying the Objects of Perception. That we may
therefore conceive of this Matter with the
greater Order and Clearnefs, we fhall make each
of thefe feveral Ideas the Subject of a diftinct
Section.
SECT. I.
Of Compound Ideas.
I, "T T T E begin therefore with
VV L r TJ v u CcmpoanJ
V V tnofe Ideas which may jj ea , corfJereJ
be properly termed compound, as be- b r ere " ere! y at
r r j t L-omoiTiatiOKt
ing derived from that Power the if the Undir-
Mind has of uniting many Concep- * "'
tions into one. Though this Clafs comprehends,
in fome Sort, all our complex Notions, yet they
are at prefent confidered merely as they are Com-
binations of the Understanding, and with a View
to thofe particular Ideas out of which they are
framed. Here, as was already obferved, the
Mind fometimes proceeds by enlarging and di-
verfifying the fame Idea ; at other Times it brings
together Ideas of different Kinds ; and in both
Ways finds infinite Scope and Variety. But that
we may follow the natural Procedure of the In-
tellect, and trace it in its Advances from fimple
to
to more complicated Acts, we fhall firft take a
View of it as employed about one and the fame
Idea, where perhaps we may meet with fuch In-
ftances of Addrefs, Management, and Contri-
vance, as will appear perfectly aftonifhing to one
who has never fet himfelf ferioufly to confider the
Manner and Conduct of his own Mind.
. . II. The moft obvious and fimple
TOriz'tnai and Idea we have, is that of Unity or
Foundation of /-\ T> j v .. . ^r ir
milevr ideai ^ ne ' "J adding it to itfelf continu-
jNumbtr. a iiy j anc i retaining the feveral Col-
lections in our Minds, we come by all the diffe-
rent Combinations of Numbers, in which we rea-
dily perceive an endlefs Diverfity. All thefe
Ideas are neverthelefs evidently diftinct among
themfelves, the Addition of a fmgle Unit con-
ftituting a Number as clearly different from that
immediately before it, as any two the moft re-
mote Ideas are.from one another. But that the
Underftanding may not. lofe itfelf in the Con-
fideration of thofe infinite Combinations of
which Unity is capable, it proceeds by regular
Steps ; and beginning with the original Idea it-
felf, purfues it through all its Varieties, as they
are formed by the repeated continual Addition of
Unit after Unit. Thus Numbers are made to
follow one another in an orderly Progrefljon,
and the feveral fucceffive Collections are diftin-
guifhed by particular Names,
III, AND
( 49 )
III. And here we may take Notice rte att p ut
of a wonderful Artifice, made ufe cp*f-t\on
r ... of the Namet
of by the Mind, to facilitate and e f Numbers, *
help it forward in its Conceptions. jS* t9
For as the Advance from Number to tint.
Number is endlefs, were they all to be diftin-
guifhed by different Denominations that had no
Connection or Dependence one upon another,
the Multitude of them muft foon overcharge the
Memory, and render it impoflible for us to go
any great Way in the Progrefs of Numbering,
For this Reafon it is fo contrived, that the
Change of Names is reftrained to a few of the
firft Combinations, all the reft that follow being
marked by a Repetition of the fame Terms, va-
rioufly compounded and linked together. Thus
thirteen is ten and three, fourteen ten and four,
and fo on to twenty^ or two tens, when we begin
again with one, two, ffr. until we advance to
thirty, or three tens. In this Manner the Progref-
fion continues j and when we arrive at ten tens,
to prevent Confufion by a too frequent Repetition
of the fame Word, that Sum is diftinguifhed by
the Name of a Hundred. Again, ten hundred is
called a Thoufand, at which Period the Computa-
tion begins anew, running thro' all the former
Combinations, as ten thoufand, a hundred thou-
fand, ten hundred thoufand; which laft Collec-
tion, for the Reafons mentioned above, has the
D Name
( ,50 )
Name of a Million appropriated to it. With this
Million we can- begin as before, until it is re-
peated a Million of Times j when, if we change
the Denomination to Billions^ and advance in
the fame Manner through Trillions, ^uartillions^
the Series may be carried on, without Confufion,
to any Length we pleafe.
IV. THIS artful Combination of
Ad ontoftbe N arn es, to mark the gradual Increafe
priitciptil i\3-
fon that our o f Numbers, is perhaps one of the
Ideal of Kum- n T\ r r i
ten are jo re- greatelt Refinements or the human
*2'fy W- ' Underftanding, and particularly de-
ferves our Admiration for the Man-
ner of the Compofition; the feveral Denomina-
tions being fo contrived, as to diftinguifh exactly
the Stages of the Progreflion, and point out their
Diftance from the Beginning of the Series. By
this Means it happens, that our Ideas of Num-
bers are of all others, the moft accurate and dif-
tincr,; nor does the Multitude of Units aflembled
together, in the leaft puzzle or confound the
Underftanding. It is indeed amazing that the
Mind of Man, fo limited and narrow in its Views,
fhould yet here feem to fhake off its natural
Weaknefs, and difcover a Capacity of managing
with Eafe the. moft bulky and formidable Collec-
tions. If we errquire particularly into theReafon
of this, we fhall find it wholly owing to the Ad-
drefs of the Mind in thus diftinguifhing Numbers
'
by different Names, according to the natural Or-
der of Progreffion. For as thofe Names are made
to grow one out of another, they may be aptly
compared to .a Chain, all whofe Parts are linked
together by an obvious and vifible Connexion.
Hence it comes to pafs, that when we fix our
Thoughts upon any Number, however great and
feemingly unmanageable; yet, if it isonce deter-
mined to a particular Name, we find it eafy to run
back through all the Stages of the Progreflion,
even till we arrive at Unity itfelf. By this Means
we fee, with a fingle Glance of our Minds, not
only the two Extremes of the Number under
Confideration, but alfo the feveral intermediate
Parts, as they are united to make up the Whole.
V. Now it is to this clear and
accurate View of the interjacent At '^v Mf
J us to a cler
ideas, that we owe our fo diftmct Pcrtepthnof
Perception of the various Com'bi- '%??
nations of Numbers. And indeed
we may obferve, in the general, that all our Ideas
of Quantity, efpecially when they grow to be.
very large, are no-otherwife afcertained than by
that Perception we have of the intervening Parts,
lying, if I may fo fay, between the Extremes.
When we look at any Object considerably dif-
tant from us, if we have a clear View of the in-
terjacent Lands and Houfes, we are able to de-
termine pretty nearly of its Remotenefs but if,
without fuch a Knowledge of the intervening
Da Spaces,
( 5* )
Spaces, we ihould pretend to judge of the Dif-
tance of Objects, as when we fee the Spire of a
Steeple behind a Wall, or beyond a Mountain,
every one's Experience is a Proof how liable we
are, in thefe Cafes, to be deceived. Juft fo it is in
judging of Duration. When we carry back our
Thoughts to any paft Period of our Lives, with-
out Confideration of the Number of Years or
Months, we find that our Idea of the Time
elapfed grows more diftinft, in proportion as
we become fenfible of the intermediate Parts of
our Exiftence. At firft we are apt to judge the
Diftance extremely fliort j but when we fet our-
felves to confider our feveral fuccefllve Thoughts
and Actions, the Idea of the Duration grows
upon us, and continues to increafe as the Atten-
tion of the Mind brings new Periods of Life into
View.
VI. HENCE it will be eafy to
Without conceive how much the Mind is
Names, tot . , .
cannot makt helped forward in its Perception of
'" Number, by that ready Comprehen-
fion of all the feveral Stages in a
Progrefllon, which peculiarly belongs to Ideas of
this Clafs. But this, as I have before intimated,
Vic derive from the orderly Series and Connection
of Names j infbmuch that where they ceafe, the
Computation of Numbers alfo ceafes with them,
We can have no Idea of any Sum, without a
Knowledge of all the Terms that go before, ac-
cording
( 53 )
cording to the natural Order in which they fol-
low one another ; fo that he who cannot, in a
regular Way, count to ninety-nine, will never,
while that Incapacity continues, be able to form
the Idea of a Hundred j becaufe the Chain that
holds the Parts together, is to him wholly unfer-
viceable, nor can he reprefent to his Mind the
feveral interjacent Combinations, without which
it is impoifible in this Cafe to arrive at a diftinl
Perception r
VII. I HAVE infifted the more
largely upon this, not only becaufe
it is by Number that we meafure all A**
(tiffing our
other Things, as Duration, Exten- //<* C B -
fion, Motion, &c. but alfo becaufe '*"'""
it lets us into the moft natural View of the Con-
duel and Procedure of the Underftanding, and
makes us fenfible of the great Art and Addrefs
that is neceflary in the claflrng our very complex
Conceptions. He that can fo put together the
component Parts of an Idea, as that they fliall
lie obvious to the Notice of the Mind, and pre-
fent themfelves, when Occafion requires, in a
juft and orderly Connection, will not find it very
difficult to obtain clear and accurate Percep-
tions, in moft of thofe Subjects about which our
Thoughts are converfant. For the great Art of
Knowledge lies in managing with Skill the
Capacity of the Intellect, and contriving fuch
Helps as, if they ftrengthen not its natural Pow-
D 3 ers,
( 54 )
ers, may yet expofe them to no unneceflary Fa-
tigue, by entangling and perplexing them with
Confiderations remote from the Bufmefs in
hand. When Ideas become very complex, and
by the Multiplicity of their Parts grow too un-
wieldy to be dealt with in the Lump, we muft
cafe the View of the Mind, by taking them to
Pieces, and fetting before it the feveral Portions
feparately, one after another. By this leifurely
Survey we are enabled to take in the whole ; and
if we can draw ic into fuch an orderly Combina-
tion, as will naturally lead the Attention, Step
by Step, in any fucceeding Confideration of the
fame Idea, we fhall ever have it at Command,
and with a fingle Glance of Thought -be able
to run over all its Parts. I have therefore ex- .
plained here, at fome Length, the Conduct of
the Mind in numbering ; it feeming to me the
beft Model in this Kind, whether we confider
the many Advantages derived from fuch an order-
ly Difpofition of our Ideas, or the great Art and
Skill difplayed in binding thefe Ideas together.
This alfo is farther remarkable, in the Confide-
ration of Number, that from it chiefly we de-
rive the Notion we have of Infinity ; it being
apparent that, in adding Number to Number,
there is no End ; the Poflibility of doubling, or
increafmg our Stock in any Degree, remaining ,
as obvious to the Understanding, after a great and
continued
( 55 )
continued Run of Progreflions, as when it firft
began, the Computation.
VII. IF we now turn our
Thoughts towards Space and Dura- **/j
tion^ here too we (hall find that we hr, of great
r i i i i r UJ* '" "/"
very feldom arrive at clear and oil- cert aimr.g our
tinft Ideas of either, but when we #'
and Duration,
introduce the Confideration of Num-
btr. The more obvious and limited Portions, it
is true, eafily flide into the Mind, in the na-
tural Way of Perception ; but it was the Necef-
fity of comparing thefe together, that put us up-
on the Contrivance of certain ftated Meafures,
by which precifely to determine the Quantity in
each. Thus Inches, Feet, Yards, Miles, 2^
afcertain our Ideas of Extenfion ; as Minutes,
Hours, Days, Years, &c. meafure the Progrefs
of Duration. The lefler -Parts, as lyittg moft
open to the Notice of the Underftanding, and
beino; more on a level with its Powers, 'are re-
C? *
tained with tolerable Exa&nefs ; and the larger
Portions, when the Number of Repetitions of
which they are made up is known, are thereby
alfo reduced into clear and determinate Concep-
tions. A Foot, and Yard, are Meafures eafi'y
- comprehended by the Mind j nor do we find any
Difficulty in conceiving a Mile, when we con-
fider it as equal to a certain Number of Yards. If
we are ftill for increafing the Standard, we may
take the Semidiameter of the Earth, and fuppof-
D 4 in S
( 56 )
ing it equal to 8000 Miles, make ufe of it as a
Meafure by which to afcertain the Diftance of
the Sun or fixed Stars. Juft fo it is in Dura-
tion ; from Hours we. rife to Days, Months, and
Years.} by thefe repeated, and added together,
we meafure Time paft, or can run forward at
pleafure into Futurity, and that without any
Confufion or Perplexity.
IX. IT is however to Number
Without it ,
tbty ere apt alone that we owe this Dmincmefs
todwntrat, of p crc ep t ion, inafmuch as Space
into a confujfa
ad irregular and Time, coiifidered apart from
the regular and orderly Repetition
of Miles or Years, leave no determinate Impref-
fions in the Mind, by which to know and dif-
tinguifh their feveral Portions. Ideas of either,
thus taken in at a Venture, are a confufed and
irregular Heap, efpecially where we endeavour
to enlarge and magnify our Views, and give full
Play to the Powers of the Intellect. Something
indeed the Mind conceives, vaft and mighty, but
nothing that is precife, accurate, and juft. But
when it begins to confider thefe Ideas as made
up of Parts, and fixing upon fuch as are propor-
tioned to its Reach, fets itfelf to examine how
often they are repeated to make up the Whole,
the Perceptions of the Underftanding put on a
new Form, and difcover their exacl Bounds and
Limits.
X. AND
( 57 )
X. AND thus, as before in Num- . ,
7 Infinity an
ber, fo here in Extenfion and Du-
ration, the Mind begins with fimple
and obvious Notices, advancing by human Mind.
Degrees to more enlarged and intricate Concep-
tions. A Day, or a Furlong, are of eafy Appre-
henfion to the Underftanding, and by their Sub-
divifions into ftill lefler Spaces exhibit them-
felves diftinly in all their Parts. With thefe
varioufly repeated, we travel through Space and
Time ; fo that being able to reduce all our Ideas
of this Clafs, however mighty and enlarged, to
the clear and determinate Perceptions of Num-
ber, we can conduct our Thoughts without Per-
plexity, and never find ourfelves puzzled, but
when, prefuming too much on our own Strength,
we launch into Speculations that ftretch beyond
the Powers of the human Intellect. Number
may be compared to a Line, that fetting out
from Unity, runs on in a continued Increafe of
Length, without a Poffibility of ever arriving at
its ultimate Period. So far as we purfue it incur
Thoughts, and trace its regular Advances, fo
far our Ideas are accurate andjuft. But when
we let loofe our Underftandings after a bound-
lefs Remainder, and would fathom the Depth of
Infinity, we find ourfelves loft amidft the Great-
nefs of our own Conceptions. Some Notions it
is true we have, but fuch as, exceeding the Di-
D 5 menfions
-menfions of the Mind, lie involved in Darknefs
and Obfcurity ; and being deftitute of Order,
Method, and Connexion, afford no Founda-
tion whereon to build any juft and accurate
Conclufion.
XI. AND this perhaps may be
Ntwr^n. the R eafon why many mo dern Phi-
Jen tea in itt * *
full Dimm- lofophers, in their Difcourfes con-
/.'-.', bat / y T r* i
an endiefi and ceming Infinity, have run into ap-
wrgrnoiig parent Contradidions ; becaufe, en-
countering with an Object too large
for the Survey of the Understanding, they found
themfelves furrounded with inextricable Diffi-
'culties, which their fcanty and defective Ideas
were by no means able to diffipate or remove.
The Truth of it is, finite Ideas alone are propor-
tioned to a finite Understanding; and although
we are not wholly without a Notion of the Infi-
nity of Number, yet it is not fuch a one as com-
prehends and exhaufts its Object, or exhibits it
to the Mind in its full Size and Dimenfions.
We only fee the Idea, as capable of an endlefs
Increafe, but cannot by any Effort of Thought
take in the whole Profpect; and indeed it is
properly that Part of it which lies beyond the
Reach of our Perception, and flill remains to
be taken into the Account, to which we give
the Name of Iftfinity,
XII. THIS
( 59 )
XII. THIS Idea of the Infinity of Durat!
Number, impsrfecl: as it may feem, -whether con,
.... , i i i filtered as paS
is neverthelefs that by which the 6r to come r t *
Mind afcends to the Conception of ^""^f 1 >
ivbcnce our
Eternity and Immenfity. For when IdeaofEttr-
we confider Duration, either as paft " tty "
* i
or to come, we find nothing to ftop the Progrefs
of our Thoughts, in the Repetition of Years, or
Millions of Years : the farther we proceed, the
more the Idea grows upon us ; and when we
have wearied ourfelves with vain Efforts, we
muft own at laft that we can no more arrive
at the End of Duration, than at the End of Num-
ber. It is true, the feveral Generations of MeR
rife and difappear in very quick Succeffions ;
Earth itfelf may decay ; and thofe bright Lumi-
naries that adorn the Firmament of Heaven, be
extinguifhed. But the Courfe of Time will not
be thereby difturbed j that flows uniform and
invariable, nor is bounded by the Period of their
Exiftence, This double View of Duration, as
having already revolved thro' numberlefs Ages,
and yet (till advancing into Futurity in an end-
lefs Progreflion, properly conftitutes our Idea
of Eternity. We fpeak indeed of an Eternity
paft, and an Eternity to come, but both thefe
are bounded at one Extreme : the former ter-
minates in the prefent Moment, and therefore
has an End ; the latter fets out from the fame
Period, and therefore has a Beginning; but,
D 6 4 taken
taken together, they form a Line both ways in-
finitely extended, and which reprefents Eterni-
ty in its full Dimenfions.
Tt>eldt of XIII. As, in the Confideration of
Time, we fix upon the prefent Mo-
r
n-vtd from the .
thn ment, regarding it as the middle
i Point which divides the whole
Sidn ofut. Line of Duration into two equal
Parts j fo, in the Confideration of Space, that
particular Place in which we exift is looked
upon as a Kind of Center to the whole Expan-
fion. From thence we let loofe our Thoughts on
every Side above, below, around and find we
can travel on, in the Repetition of Miles, and
Millions of Miles, without ever arriving at the
End of the Progreffion. It is not difficult, indeed
to carry our Conceptions to the utmoft Bounds
of the Univerfe ; at leaft fo far as it falls with-
in our Notice. But then the Imagination refts
not here j it fees immeafurable Spaces beyond,
capable of receiving new Worlds, which it can
purfue, as rifing one above another in an end-
]efs Succeffion. This Confideration of Space
ever growing on all Sides of us, and yet never
to be exhaufted, is that which gives us the Idea
of Immenfity, which is in fa& nothing elfe
but the Infinity of Number, applied to certain
Portions of Extenfion, as Miles, or Leagues,
&c. and thefe conceived as extended every Way
around
( fri 7
around us, in infinite and innumerable right
Lines.
XIV. HITHERTO we have con-
fidered the Mind as employed about
one and the fame Idea, enlarging fr** Union
rc . . . . T? of Perception*
and diverhfymg it in various i< orms. of different
We have feen it rifing from the moft Kindi '
fimple and obvious Notices to the Conception'
of Infinity itfelf j and taken a View of it in all
the different Stages of its Improvement. Let us
now proceed to the more complicated A6t of
Compofition, when the Mind brings feveral Ideas
ef different Kinds together, and voluntarily
combines them into one complex Conception.
Such, for inftance, is our Idea of a Tune^ as com-
prehending a Variety of Notes, with many dif-
ferent Modulations of Sound. And here it is ta
be obferved, that tho' the complex Idea may be-
excited in us, by hearing the Air itfelf ftruck off
upon a proper inftrument j yet,- confidered origi-
nally, it ftill belongs to this Clafs of Percep-
tions, which are diftinguifhed as the arbitrary
Collections of the Mind. It was the Mufician,
or Compofer, that combined the feveral Notes,,
and determined the Order in which they were to
follow one another j nor had that peculiar Com-
pofition of Sounds any real Union in Nature,
before they were thus brought together in his
Mind. Of the fame Nature are mofl of our
Ideas of human A&ions ; for tho' many of them
come
( 62 )
come to our Notice by feeing the A&ion^ them*,
felves, or hearing them defcribed by others, as
Dtftilling) Carving, Treafon, &c. yet it is plain
that they muft have been projected and contriv-
ed in the Mind of Man before they had a real
Exiftence.
,. . ... , XV. Ir is here that the Under-
Hoto the Mind
it determined {landing has the greateft Scope, and
'tbtfeComto- k nc ' s mo ^ Employment for its active
nations. Powers : nor indeed is it pofllble
to fet any Bounds to the Ideas of this Clafs j
the Combinations already made being almoft in-
numerable, and thofe, yet in the Power of the
Mind affording an endlefs Diverfity. It may not
however be amifs to confider how we condudl
ourfelves amidft fo great a Variety, and by what
Rules we proceed in making thofe Combina-
tions to which we have affixed particular Names,
while others, perhaps, no lefs obvious, are ne-
gledted. The Idea of Killing, for inftance, joined
to that of a Father, makes a diftincl: Species of
Action, known by the Name of Parricide. It was
doubtlefs as obvious to diftinguifli between the
killing of an old Man and a Child, which yet w
find is not done j both thefe Adlions being compre-
hended under the general Name of Murder. By
what Views therefore does the Mind regulate thefe
its Combinations ? Why is it determined to one
Collection of Ideas rather than another ? This
cannot
( 63 )
cannot be well underftood, without obferving^
that it is the End of Language to communicate
our Thoughts one to another. Words are the
Signs of our Ideas, and ferve to exprefs the Con-
ceptions of the Mind. NOW it is apparent that
fuch Conceptions as are moft apt to occur in
the Commerce of Life, would be firft diftin-
guifhed by particular Names ; the frequent Oc-
cafion Men have of mentioning, thefe among
themfelves, rendering this abfolutely neceflary.
But as many of thefe Conceptions are Collec-
tions of different fimple Ideas, hence we are
infenfibly led to fuch peculiar Combinations,
as are moft ferviceable to Purpofes of mutual
Intercourfe and Communication.
XVI. LET us fuppofe, in the firft
!- c o si Ideal of bu-
JSegmnings of bociety, a Company man Am*
of Leeiflators met together, in order *f ttn f '"**
before the
to confult of proper Regulations ^fiiom them-
for the Government of the Commu- ^"* IX '^'
nity. If they are. Men of Prudence and Fore-
fight, they will naturally obferve many new Oc-
currences likely to arife from- this Coalition of
Mankind, and their living together in Crowds.
Perhaps the Age in which they live has not
produced an Inftance of one Man's killing an-
other ; yet from the Knov/ledge of their own
Frame, and their Power of doing Hurt, they
conceive this as a pofiible Cafe, and are willing
to provide againft it. Thus all the Ideas that
enter
enter into the 'Complex one of Murder, arc
brought together and united into one Concep-
tion, before the Action itfelf really exifts. It
is not however thought neceflary to take into
Confideration the Age of the Ferfon ; the chief
Thing in View being to prevent the putting an
End to another's Life unjuftly, whether old or
young ; and therefore the Penalty equally af-
fects both Cafes. But when they come to con-
fider the Relation in which the Perfon killed
may ftand to the Murderer, here there appears
a manifeft Difference ; as it adds to the Crime
when committed upon a Benefactor, and ren-
ders it particularly heinous in the Cafe of a
Father. This laft, therefore, is made to con-
flitute a diftinct Species of Adtion, and has a
peculiar Punifhment allotted to it. Thus we
fee how Men, according to their different Man-
ner of Life, and the Relations they ftand in to
one another, are naturally led to form feveral
Collections of fimple Ideas, preferably to others,
as forefeeing they may have frequent Occafion
to take Notice of fuch precife Combinations.
And becaufe it would be tedious in Converfa-
tion, every time thefe complex Notions occur j
to enumerate all the Ideas of which they con-
fift j therefore, for the- Sake of Eafe and Dif-
patch, they give them particular Names, and
thereby render the Cornpofitions fixed and per-
uianenU-
XVII..
( 65 )
XVII. THAT it is in this Man- ~,
The NcceJJity
ner we come by our complex Ideas, of mutual in-
i i i i- tfcourft. and
which multiply upon us according Mensparti-
as the Exigencies of Society require, cular
_ r . * f i i rw -f i Life, a great
or our Purfuits, Method or Lire, and Source ofcom-
difFerent Aims, throw Occafions in
our Way of combining fuch and fuch Percep-
tions together, might be eafily made appear by
a fhort View of the Combinations themfelves.
Human Ac-lions, as occurring moft frequently,
and affording large Matter of Converfation, De-
bate, and Enquiry among Men, have been very
nicely modified, and diftinguiftied into Clafles,
according to the feveral Circumftances moft
likely to attend them. In like manner the Arts
and Sciences, in proportion as they are culti-
vated, leading us into many compound Views
of Things, which otherwife would never offer
themfelves to the Confideration of the Mind ;
the complex Ideas of this Sort, with the Names
by which they are exprefled, are, we find, the
Work of fuch particular Nations^ where thefe
Arts and Sciences have chiefly flouriflied. The,
Greekiy for inftance, excelled in Learning and
polite Knowledge ; hence many of the Terms
belonging to Rhetorick, Poetry, Philofophy,.
Phyfick, &V. come originally from their Lan-
guage. Modern Fortification has received its
greateft Improvements among the French j and,
accordingly
( 66 )
accordingly the Ideas and Terms of the Art arc
moftly derived from Writers of that Nation. In
Italy^ Architecture, Mufick, and Painting, have
been the great Exercife of the Men of Genius ;
it is therefore among them that we find the fe-
veral complex Notions belonging to thefe Parts
of Study, as well as the Names by which they are
exprefledj nor can we difcourfe accurately and
minutely of the above-mentioned Arts, without
having recourfe to the Language of that Cli-
mate. And if we dcfcend into the particular
Callings and Profeffions of Men, they have all
their peculiar Collections of Ideas, diftinguifhed
by their feveral Names, and hardly known but
to fuch as are converfant in that Manner of Life.
Thus Calcination^ Cobobation y Filtration, &c. are
Words ftanding for complex Ideas frequently
framed in the Minds of Chymifts, and therefore
familiar to Men of that Employment. Yet as
thefe, and fuch like Combinations, feldom oc-
cur in common Life, the Generality of Man-
kind, we fee, are in a great Meafure unac-
quainted with them.
Htr.ie d\ffertnt XVIII. I MIGHT purfue thefe
pM&lZ'Z/t- Speculations farther, and fhcw how
rent centner, the feveral Fafhions, Cuftoms, and
and Words in .
ene Larguage Manners or one Natjon, leading
35T* them to form man y com P lex N -
in anoibtr. tions. which come not fo naturally
in
( 6; )
in the Way of another ; different Sets of Ideas
prevail in different Countries, and of courfe have
Names appropriated to them in one Language,
to which there are no Words that anfwer in an-
other. The Procedure and Forms of our Courts
of Juftice have introduced many Terms into
the Englijh Law, which ftand for Collections of
Ideas framed among no other People. Nor
tvould it be pofiible to render thefe Terms by
any fingle Words of another Language; becaufe,
where the Ideas themfelves prevail not, there are
no Names provided to exprefs them. In this
Cafe, therefore, it becomes necefTary to ufe Cir-
cumlocutions, and enumerate the feveral Ideas
comprehended in the Collection, if we would
fo exprefs ourfelves as to be underftood in the
Language of other Nations. Nay, even among
the fame People, the Change of Cuftoms and
Opinions frequently brings new Sets of Ideas,'
which of courfe muft be diftinguifhed by parti-
cular Names ; while, at the fame Time, the No-
tions of former Ages grow into Difufe, and the
Words anfwering them are wholly laid afide, or
employed in a Signification different from what
they had before.
XIX. THUS Languages are in a m WJ tbe
perpetual Flux, and by Degrees vary Caufe that
r \ r i i T^ Lanvuav'.i
fo much from their original Frame, are in * fer >.
as to become unintelligible even to f etual flu *'
the Defcendants of thofe who fpeak them. If
we
( 68 )
we run back into the Ages of Chivalry in Eng-
land* when Tilts and Tournaments were in
Fafhion, how many complex Ideas, peculiar
to that Mode of Life, fhall we find familiar
among the Men of thofe Times, which are now
little known or attended to \ On the contrary,
the Improvements in Arts and Sciences that
have fmce taken place, have led us into innu-
merable Views of Things to which our Fore-
fathers were perfect Strangers. But I fhall not
pufh thefe Reflections any farther, believing that
what has been faid will be fufficient to fhew
the Origin and Progrefs of our compound Ideas,
and how the Mind is directed in the Choice of
the Combinations it makes. We therefore pro-
ceed to the Confideration of abftract Ideas t
which make the Subject of the following Sec-
tion.
SECT. II.
Of dbftraft or Univerfal Ideas.
I. T TAV1NG difpatched what
General Ideal I i ... , f .,
firmed by tbc JL JL was neceflary to be laid,
" 1 "^ concerning our compound Ideas,
confidered merely as they are Com-
binations of the Underftanding, it is now Time
to explain how we come by our general No-
tions, which ferve to reprefent to us a Multitude
of
( 69 )
of Individuals, and are the Standards by which
we rank Things into Sorts. And this, as we
have before intimated, is done by the Abftrac-
tion of the Mind ; which Aft may be extended
to all our Ideas, whether fimple, compound, or
of Subftances. If, for inftance, we fix our
Attention on any particular Colour, as Scarlet,
we can leave out the Confideration of all prefent
Circumftances, as the Subject in which it in-
heres, the Time and Place of feeing it, fcff. and
retaining only the Impreflion itfelf, make it a
Reprefentative of that Quality or Appearance,
wherever we chance to meet with it. It is thus
that abftract and univerfal Ideas are framed ; for
the Mind regarding only the Scarlet Colour,
which one Day it obferves perhaps in a Piece of
Cloth, another in a Picture, and a third in the
Rainbow ; the Appearance is conceived to be
the fame in all thefe Objects, and therefore is
called by the fame Name.
II. BUT to enter a little more AiitbePtr-
clofely into this Matter, and fhew r^'V^'
J U nderflandtng
that thefe our general Conceptions particular,
are the mere Creatures of the Understanding, it
may not be amifs to take Notice, that all our
Perceptions of Things, whether we derive them
from Senfation or Reflection, are of their own
Nature particular, and reprefent to us fingle
determinate Objects. When we fee a Horfe, for
inftance.
( 70 )
inftance, in the Fields, our Idea is that of an In-
dividual. If we hear a Sound, it is fomething
particular, and different from what we hear at
any other Time. Every Perception of the Mind
is diftinct from every other Perception ; nay,
and every Idea brought into View by the Ima-
gination, as when we frame the Image of a
Lion landing before us, is iiill Angular, and
reprefents a fingle Object.
. Ill, BUT when we come to take
tbt'sftcitire- a View of thefe feveral Particulars,
prtftntiiubat we re adily obferve among; fome of
H common to ' '
d:fer<nt jndl- them a Refcmblancej and framing
to ourfelves an Idea of thofe Things,-
in which any of them are found to agree, we
thereby get a general Notion, applicable to
many Individuals. Thus Horfes are found to
refemble one another in Shape, Vcice, and
Structure of Parts. The Idea which takes in
only the Particulars of this Refemblance, ex-
cluding what is peculiar to each fingle Animal,
becomes of courfe common to all Cic- ures of
that Kind, and is therefore the Reprefemative of
a whole Clafs of Beings. Accordingly jhe Name
of that general Idea is given to every Animal
in which that Shape, Voice, and Structure is
found j for the Word Horfe, implying only
thefe Particulars, muft belong to al] Creatures
wherein they exift. This is the firft Step or
Gradation
'Gradation in the forming of abftra& Notions,
when the Mind confines itfelf to the Confide-
ration of individuals, and frames an Idea that
comprehends fuch only under it. The Rank
or Clafs of Things anfwering to this Idea, is
called Species in the Language of the Schools.
So a Horfe is a certain Species of Animals, an
Oak is a Species of Trees, and a Square is a Specif s
of four-fided Figures.
IV. WHEN we have thus learnt
1 T i i i o i "' Idea of
to rank Individuals into sorts and the Genus re-
Claffes, according to the Refem- ?' '/""' vbat
is common tt
blance found among them, the Mind fwerel Spe-
proceeds next to confider the Species
themfelves, and often in thefe too obferves a
certain Likenefs. Whereupon, throwing out all
thofe Particulars wherein the feveral Species
are found to difagree, and retaining only fuch
as are common to them all, we thereby frame a
itill more general Idea, comprehending under it
a Variety of different Species. Thus a Sparrow,
a Hawk, an Eagle, &c. are diftincl Specks of
Birds, which have each their peculiar Shape and
Make. They neverthelefs referable one another,
in being covered with Feathers, and provided
with Wings that bear them through the Air.
Out of thefe Particulars we form a new Idea,
including all the common Properties of the fea-
thered Kind j and appropriating to it the Name
4 Bird,
( 7* )
Bird, mark by that Word another Clafs of
Things, of a higher Order than any of the
former. This fuperior Divifion, which extends
to feveral Species at once, is called in the Schools
the Genus, and is the fecond Step the Mind takes
in advancing to univerfal Notions.
V. AND thus have I given a fhort,
n, Mind may
advance by but 1 hope intelligible Account, of
Jri^lf "-" the Bufmefs of Genera and Species,
/ing from Par- about which fo much has been faid
titulars to Ge- . . . . .
rt.'s. in the Wntmgsof Logicians. Species,
in Stridtnefs and Propriety of Speech, is fuch a
Rank or Clafs of Things, as comprehends under
it only individuals ; Genus advances ftill higher,
and takes in a Variety of diftinft Species. It is
however to be obferved, that the Mind, in rifmg
from Particulars to Generals, does not confine
itfelf to one or two Gradations, but may carry
its Views through the whole Extent of Things,
until at length it arrive at an Idea embracing the
univerfal Compafs of Nature. For when we
have ranked Things into Sorts, and reduced thefe
again to the higher Order or Genus, thefe Genera
are ftill found to refemble one another in fome
Particulars j which being collected into one Idea,
form a new and more comprehenfive Divifion of
Things. Thus Bird is a Genus, embracing all
the Varieties of the feathered Kind. Fijb im-
plies the feveral Species of living Creatures
which
( 73 y
which inhabit the Waters. >yad)-uptd and Infcft
are alfo univerfal Ideas, that take in many infe-
rior Diftributions and Clafles. Yet all thefe dif-
ferent Orders of Being, have this in common ;
that they are provided with organical Bodies,
fitted for the Purpofes of Life and fpontaneous
Motion. An Idea therefore comprehending only
thefe laft Particulars, will equally belong to all
the Divifions before enumerated, and the Word
Animal^ by which it is exprefled, becomes a ge-
neral Name for the feveral Creatures endued with
Life, Senfe, and fpontaneous Motion. If we are
for carrying our Views ftill farther, and framing
a yet more univerfal Notion, we can caft our
Eyes upon both the animate and inanimate Parts
of Nature j wherein we find this mutual Cor*
refpondence, that they exift, and continue in
Being. This laft Idea therefore of Being in ge-
neral, comprehends under it all the Varieties of
Things, and may be univerfally applied to what-
ever has either Life or Exiftence ; fo that in re~
fpe& of' the prefent Frame of Nature, it is the
higheft and moft univerfal Idea we have.
VI. IN this Series of Notions,
. - , i rx Whence many
nnng one above another in the Ue- i^ttrmtdiM
gree of Univerfality ; that Divifion,
which comprehends under it feveral Genus
Genera, is called in the Schools the lowtjl S * ec!es '
higher Genus ; which Denomination continues,
until we arrive at the laft Advance of the Under.
ihnding,
( 74 )
(landing, when being come to the moft general
of all Ideas, that admits not of a fuperior, it is
diftinguifhed by the Name of the Genus genera-
lijjin.um. In like manner, the feveral Genera com-
prehended under a higher Genus^ are in refpecl of
it confidered as Species ; and as thefe two laft
have Species under them, the inferior Divifions
are for Diftinclion's fake termed lower Species.
Thus the Progreflion continues, and when we
come to the loweft Subdivifion of all, compre-
hending only Individuals, which, as I have before
intimated, conftitures the proper Species, this
the Schools denominate the Species fpecialijjima.
All that lie between it and the higheft Dittribu-
tion of things, are the intermediate Genera and
Species which are termed each in their 7'urn,
Gtints gtntralfUS) or Species fpecialior, according as
we confider them in the afcending or defcending
Scale of our Ideas ; or, to fpeak in the Language
of Logicians, according to their Afcent or De-
fcent in Linea pradicamentali. I Ihould not have
entered fo far into thefe verbal Difquifitions, had
not the Terms here explained, been fuch as fre-
quently occur in the Writings of Philofophers ;
infomuch that without fome Knowledge of them,
we muft often be at a Lofs, in the Profecu-
tion of thefe Studies. Befides, it is both cu-
rious and ufeful, to fee the gradual Progrefs of
the Mind, in its Advances from particular to ge-
neral Conceptions ; to obferve it ranging its
Ideas
( 75 )
Ideas into Clafles, and eftablifllinga juft and re^-
gular Subordination in its Views and Notices of
Things. This is the flior teft Way to Knowledge,
and affords the beft Means of preferring the
Order and due Connexion of our Thoughts, fo
as to make them fubfervient to the Increafe of
Science, For when we fee how Things com^
prehend, or are comprehended in one another,
we are able to difcover the mutual Dependence
of all the feveral Branches of Knowledge, which
leads us into the true and natural Method of
conducting our Understandings in the Search
of Truth.
VII. FROM what has been faid it
is evident, that general Ideas are JjSfiJf
the Creatures and Inventions of the eftbtUndtr-
Underftanding. Nature, it is true,
in the Production of Things, makes many of
them alike j but it is the Mind alone, that col-
lefts the Particulars in which they agree, into
one Idea, arid fets it up as a Reprefentative of
many Individuals. And now I think we may ven-
ture upon that much agitated Queflion, Where
do the Genera and Species of Things exift ? To
which I anfwer, in the Mind. Univtrfality be-
longs not to Things themfelves, it being appa-
rent, that they are all particular in their Exif-
tence. However, as they often have many Pro-
perties in common, the Underftanding, by uni-
ting thefe into one Conception, obtains a ge-
E 2 neral
( 7* )
ireral Idea, under which it ranks all the feveral
Objedls wherein thefe Properties are found.
So far indeed we muft allow, that the particular
Combination of Properties, which conftitutes
the Genus or Species, exifts in all the Indivi-
duals referred to that Genus or Species; but
then it is in Conjunction with other Properties,
by which thefe Individuals are diftinguiflied
from one another. Thus the Collection of fim-
ple Ideas, fignified by the Word Bird, is to be
found for Inftance in a Hawk> or any other fingle
Animal, to which we apply that general Name j
but the Notion itfelf, abftracled from all the
Particulars to which it belongs, has evidently
no Exiftence out of the Underftanding. There
is not a Being in Nature that can be called a
Bird in general, or that does not neceflarily im-
ply, in the very Conception of it, feveral fmiple
Ideas, befides thofe marked by that Word. For
the Name in this Cafe fignifies no more than an
Animal covered with Feathers, and provided with
Wings, without Regard either to Shape, Bulk,
or the particular Time and Place of its Exiftence.
Thefe laft Confiderations however are infbpara-
ble from the Reality of Things, and therefore
Hiuft be added to the general Idea, before we can
conceive any Thing conformable to it a&ualljr
brought into Being.
VIII. HENCE
( 77 1
VIII. HENCE we fee at once, c a */yw*-
what fort of an Exigence general part they ex\Jf
tnly in tot
Natures have. Confidered apart, and Mind, im in
by themfelves, they are wholly the JgSS
Workmanfhip of the Underftand- Idtas \ntbe
... i T ' i T Individual*
ing, and derive their Being and Re- comprehended
ality from it j but viewed in con- UKdlrtbem '
jun&ion with other Ideas that co-exift with them
in the feveral Objects of Nature, they are to be
found in the Individuals to which they refer j and
therefore according to this way of Conception,
may be faid to have an Exiftence in them. Thus
fo long as the Ideas anfwering to the Words Man
or Tree, continue general and undetermined, they
have no real Objects anfwering them in Nature ;
nor can the Collections of fimple Ideas, marked
by thefe Names, while all others are fuppofed ex-
cluded, exift any where out of the Underftand-
ing. Neverthelefs, as all the fimple Ideas in-
cluded in the general Notioa of Man, are to be
found in every particular Man j and all thofe im-
plied in the Notion of a Tree, in every particular
Tree; hence the general Nature of Man, exifts
in every individual Man, as does the general Na-
ture of a Tree, in every individual Tree.
IX. ONE Thing ftill remains to Difference f
be obferved, with regard to thefe our UwMfi-
atred at con*-
general Ideas ; that though many of pound and as
them are evidently Combinations of univt ^ ah
different fimple Ideas, and according to that
E 3 Way
( 7* )
Way of confidering them, are included in the
firft Divifion of our complex Conceptions,
thofe namely framed by the Compofitiqn of the
Mind j yet we are carefully to diftinguifli be-
tween an Idea as it is compound, and as it is uni-
yerfal. In the firft Cafe, the Mind chiefly con-
fiders the feveral Ideas that are combined toge-
ther; or, in other Words, all the Attributes, Qua-
lities, or Parts, that are contained in any Idea.
Thus the Idea of a Bird, includes Life, Senfe,
fpontaneous Motion, a Covering of Feathers,
Wings, &(. none of which can be left out with-
out deflroying the very Nature of the Idea, and
making it fomething quite different from what it
was before. This Way of confidering Things
according to the Number of their Parts and Pro-
perties, is called by Logicians the Comprehenfton
of an Idea. But the Univerfality of our Notions
implies quite another Turn of Thinking; in as
much as it fixes the Regard of the Mind, upon
the Subjects to which our Ideas extend, or the
Individuals and Species comprehended under
them. In this Senfe the Ideas anfwering to the
Word Bird, takes in the feveral Species of the fea-
thered Creation, the Hawk, the Eagle, Sparrnv,
Lark, and innumerable others, to all which it
may with equal Propriety be applied. And here
it is remarkable, that the Idea lofes nothing of
its Force or Comprehenfion, by being reftricled to
a particular Kind. When I fay the Bird of Jove,
though
( 79 )
though in this Cafe the Idea is reftrained to the
Eagle alone, it (till remains as diftindt, and in-
cludes as many fimple Ideas in its Compofition,
as when before it was extended to all the diffe-
rent Tribes of feathered Animals.
X. WE fee therefore that our The Compre-
compound Ideas, may continue the
fame in refpect of their Attributes,
or the Number of Parts, and yet vary confidera-
bly in the Degree of Univerfality. The gene-
ral Idea of Man is the fame, whether applied
to the whole human Race, or thofe of any parti-
cular Nation. When I affirm, for Inftance, of
Mankind in general, that their Knowledge falls
fhort of Perfection, and afterwards make the like
Obfervation of the Men of the prefent Age ; in
both Cafes, the Word Man ftands for one and
the fame Collection of fimple Ideas ; but in re-
fpect of the Individuals to which it is applied,
there is a great and manifeft Difference. That
is, the Term, Man, denotes one invariable com-
pound Idea ; which notwithftanding, confider-
ed as a general Notion, may be contracted or
enlarged at Pleafure. And as in the former Cafe
the feveral Parts of the compound Idea is called
its Comprehenfion ; fo in the latter, the Indivi*
duals to which the univerfal Idea is applied, is
called its Extenfion. I might add many more
Obfervations on this Subject, but choofe rather
4 to
to ftop here, having faid enough to explain the
Difference between compound and abftradl
Ideas, and (hew the Reafon of my ranging them
under diiiin& Heads.
SECT. III.
Of our Ideas of Relations*
I. T COME now to the third and
JJtai of Rt-
latiom txct,d- JL laft Divifion of thofe Ideas
which I confider as the Creatures
and Workmanfhip of the Underftanding ; fuch
namely as arife, from the comparing of Things
one with another. For the Mind in its Views,
is not tied to fingle Obje&s ; but can examine
their References and Refpe&s, in regard to
others, brought under Confideration at the
fame time. And when it does fo, and thence
derives new Notices of Things, the Ideas thus
got are called Relations, and make, I am apt
to think, the largeft Clafs of all our Percep-
tions. For every fingle Object will admit of
almoft innumerable Comparifons with others,
and in this Senfe may become a very plentiful
Source of Ideas to the Underftanding. Thus if
We compare one Thing with another in refpeft
of
of Bulky we get the Ideas of greater, lefs, or
Equality; if in refpe& of Time, of older and
younger; and fo for other Relations, which we
can purfue at pleafure, almoft without End j
whence it is eafy to conceive, how very exten*
live this Tribe of our Perceptions muil be.
II. I SHALL not pretend to trace
out thefe Ideas particularly, nor in-
deed fo much as to enumerate thei r to particular
f 1 r\- -r t_ v. Cemparifons
ieveral Divmons j it being enough iy t be
to obferve, that here, as well as in
ctes of Life.
the other kinds of our complex
Ideas, we bound ourfelves for the moft part to
fuch Comparifons, as the Exigencies of Society,
the Wants of Life, and the different Profeffions
of Men, render necefiary j and are more or lefs
accurate in tracing out the Relations of Things,
according to the Degree of Importance they ap-
pear to have in thefe Refpe&s. The Relations
of Men one to another, arifing either from the
Ties of Blood, their feveral Ranks and Places
in the Community, or a mutual Intercourfe of
good Offices, being of great Weight and Con-
cern in the Commerce of Life, have in a parti-
cular Manner engaged our Attention, and are
therefore very minutely defcribed. For the fame
Reafon, Men have found it neceflary, to deter-
mine as exactly as poflible, the various Depen-
dence of Things, as their Happinefs is nearly
5 conne&ed
( 8* )
conne&ed with this Knowledge. When we
confider Objects merely in refpect of Exiftence,
as either giving or receiving it, we come by
the Ideas of Caufe and EffeR ': Nor need I men-
tion, how much the Welfare of Mankind de-
pends upon an extenfive View of Things, as
theyftand connected in this Relation ; it being
evident, that the feveral Schemes and Purpofes
of Life, are all conduced upon a previous Sup-
pofition, that certain known Caufes, will have
their ufual regular Effects, and fuch and fuch
Actions, be attended with fuch and fuch Confe-
quences.
III. BUT there are other Rela-
felations of . r i i i i /* i L/-I
Creator and tlOHS of thlS kllld, belldeS thole that
Creature, &e. re gard merely Exiftence ; as when
we alfo take into the Account, the additional
Gifts of a Capacity for Happinefs, and the
Means of attaining it j which conftitutes the Re-
lation of Creator and - Creature* in the more
folemn Acceptation of thefe Words. Again,
when we confider the great Author of our Be-
ing, not only as the Creator of the Univerfe, but
alfo as preferving and holding it together, and
prefiding over the prefent Frame of Things with
uncontrouled Dominion; he then appears un-
der the Notion of a moral Governor^ to whom
we are accountable for our Actions, and the
Ufe we make of thofe Powers and Faculties we
derive
( 83 )
derive from him. Now as it is of the higheft
Confequence for Men, not to be unacquainted
with thefe, and fuch like Relations ; hence we
find, that the wifeft Nations, and fuch as beft
underftood the true Application of the Powers of
the Mind, have always made it their chief Study
to regulate and afcertain thefe Ideas, and trace
them in all their Confequences. And thus we
may in fome meafure perceive, how the Mind
proceeds in comparing its Ideas together, and
by what Views it is chiefly governed, in fram-
ing the complex Notions of this Clafs, by which
it reprefents the various Habitudes of Things.
I fhall only add upon this Subjeft, thefe two
Obfervations.
IV. FIRST, that our Ideas of
Relations, are for the moft part very SMW
clear and diftincl. For the compar- cle < tr **& A/-
ing of things together, being a vo-
luntary A& of the Mind, we cannot but fuppofe
that it muft be acquainted with its own Views in
the Comparifon ; and of courfe have a clear
Conception of the Foundation of that Relation,,
if fets itfelf to enquire into. Thus the Relation
of Caufe and Effect, implying only that one
thing produces, or is produced by another,
which Notions are always diftin&ly fettled in
the Underftanding before it goes about to make-
the Comparifon j it is evident, that the Idea re-
E 6 prefenting
preferring this mutual Refpecfc of Obje&s, will
be nolefs clear, than are the Notions themfelves
upon which the Relation is founded. And
what is ftill more remarkable of the Ideas of
this Clafs ; they ceafe not to be diftindt, even
where the Subjects compared are but very imper-
fectly known. For I can well enough conceive
that one thing has produced another, and that
therefore they ftand related as Caufe and Effect,
though my Ideas of the things themfelves may
perhaps be very obfcure, and come far fhort of
xeprefenting their real Nature and Properties. I
doubt not but it will be readily owned, that our
Idea of the Univerfe, confidered as comprehend-
ing the whole Frame of created Things, is very
inadequate ; and I think it is ftill more apparent,
that our Notion of the Supreme Being comes
not up to the Excellence and Perfection of his
Nature. Yet we very well underftand what is
meant, by calling God the Author of the World ;
and though we comprehend not the Manner of
his producing it, find no Difficulty in framing
the Ideas, the relative Words Creator and Crea-
ture ftand for.
V. I HAVE yet another Obferva-
Jdeas cfRe!a- . . . . .
Hens among tlOtt tO make Upon thlS bubjeCT ;
the mtf im. and j t j s that Qur J deas of Re j a _
fottant Con-
<ct>thi / the tions are among the moft impor-
tant Conceptions of the Under-
ftanding,
( 85 )
landing, and afford the largeft Field for the
Exercife and Improvement of human Know-
ledge. Moft of our Enquiries regard relative
Ideas, and are fet on foot with a View to invef-
tigate the mutual Habitudes of Things. The
Mathematician has taken Quantity for his Pro-
vince, and teaches us how to compare Magnitudes
of different Figures and Dimenfions, in order to
judge with Certainty of their relative proper-
ties. The Philofopher attaches himfelf to the
Chain of Caufes and Effe&s, and endeavours to
trace out the various Dependence of Things
confidered in this Light. In fine, whither do
all our Refearches tend, but by means of cer-
tain known Properties and Relations, to find
out others that ftand fome how connected with
them ? As for the Importance of thefe Concep-
tions, no one can call that in queftion, who
reflects j that from our Relations to our Creator
and one another, arife all the Duties of Morality
and Religion j and that the Correfpondence of
the feveral Objects of Nature, to the Organs of
the Body, and Faculties of the Mind, is that
by which alone we can judge, of what will
procure us Happinefs or Mifery. Whence it is
evident, that without an exact Knowledge of
thefe Relations, we muft wander on in Life
with great Uncertainty, and may often plunge
into Calamities and Misfortunes, by thofe very
Purfuits,
( 86 )
Purfuits, from which we expected nothing but
Joy and Pleafure.
VI. THUS have I gone through
Recapitulation. . , i T\- -r e TJ
the leveral JJwuons of our Ideas*
which I have endeavoured to reprefent in fuch
a Manner as their vaft Extent may moft eafily
appear, and the Conduct of the Mind in framing
them be diftinctly apprehended. I might eafily
run into other Diftinctions, by confidering them
as clear or olfcure 9 adequate or inadequate, true
orfalfe. But the Limits of this Tract will not
allow my entering more fully into the Subject,
and I think it the lefs needful, becaufe the very
Names are'almoft fufficient to convey a Notion
of thefe feveral Kinds of Ideas into the Mind.
But as the Divifion explained above feems to be
of great Importance, towards fettling in the
Underftanding a juft View of the Progrefs of
human Knowledge, and the Steps by which it
advances from one Degree of Improvement to
another, I fhall here run over it again in as few
Words as poffible, that the whole Procefs may
been feen at once. Our Ideas are all derived into
the Underftanding, either by Senfation or Re-
flection. This however is obfervable, that one
and the fame Object often excites a Variety of
Perceptions at once, which are neverthelefs rea-
dily diftinguifhed by the Mind, and appear each
under a Form peculiar to itfelf. Thefe confti-
tute
tute our primary and original Notices, and are
eafily known from all others, in as much as they
are intirely void of Plurality, and cannot be di-
vided into two or more different Ideas. They
are alfo the Materials out of which the others
are formed, and are therefore by Way of Dif-
tindion called fimple Ideas. But the Mind,
though it has no Power over thefe, either to
fafhion or deftroy them, can yet combine them
in an infinite Number of Ways ; and from their
various Combinations refult all our complex
Ideas, which are of two principal Kinds. Firft,
fuch as are derived from without, and reprefent
thofe Combinations of fimple Ideas, that have a
real Exiftence in Nature. Of this Sort are all
our Ideas of Subftances. Secondly, the Con-
ceptions formed by the Mind itfelf, arbitrarily
uniting and putting together its Ideas. And as
this makes by far the largeft Clafs, and compre-
hends all thofe Ideas which may be properly
termed our own, as being the real Workmanfhip
of the Underftanding ; fo they fall very naturally
under three diftinc~l Heads. For either the Mind
combines feveral fimple Ideas together, in order
to form them into one Conception, in which the
Number and Quality of the Ideas united, are
principally confidered ; and thus it is we come
by all our compound Notions : or it fixes upon
any of its Ideas, whether fimple, compound, or
of
( 88 )
of Subftances, and leaving out the Circumftanees
of Time, Place, real Exiftence, and whatever
renders it particular, confiders the Appearance
alone, and makes that a Reprefentative of all of
the Kind; whence our abjlraft and univerfal
Ideas are derived : or, laftly, it compares Things-
one with another, examines their mutual Con-
nections, and thereby furnifhes itfelf with a new
Set of Notions, known by the Name of Relations,
which, as has been already remarked, make by
no means the leaft important Clafs of our Per-
ceptions. This Divifion of our Ideas, as it feems
to be the moft natural, and truly to reprefent the
Manner in which they are introduced into the
Mind, fo I believe it will be found to compre-
hend them in all their Varieties. I fhall there-
fore now proceed to offer fome Obfervations-
upon Language, as being the great Inftrument,
by which we are enabled to make our Ideas and
Perceptions known to others.
CHAP. V.
Of Words conjidered as the Signs of our Ideas.
Word* fumijb I. "\ T 7"E have fcen how the Miner
tb.Mt.mcf yy comestobefirftfurnifhed
recording our
ewn Thoughts, with Ideas, and by what Methods
it contrives to diverfify and enlarge its Stock 5,
let
( 89 )
let us now confider the Means of making
known our Thoughts to others, that we may
not only underfland how Knowledge is ac-
quired, but alfo in what Manner it may be com-
municated with the greateil Certainty and Ad-
vantage. For our Ideas, though manifold and
various, are neverthelefs all within our own
Breafts, invifible to others, nor can of them-
felves be made appear. But God defigning us
for Society, and to have a Fellowfhip with thofe
of our Kind, has provided us with Organs fitted
to frame articulate Sounds, and given us alfo a
Capacity of ufing thofe Sounds, as Signs of in-
ternal Conceptions. Hence fpring Words and
Languages ; for having once pitched upon any
Sound to ftand as the Mark of an Idea in the
Mind, Cuftom, by Degrees eftablifhes fuch a
Connection between them, that the Appearance
of the Idea in the Underftanding always brings
to our Remembrance the Sound or Name by
which it is exprefled j as in like manner the
hearing of the Sound never fails to excite the
Idea for which it is made to ftand. And thus
it is eafy to conceive, how a Man may record
his own Thoughts, and bring them again into
View, in any fucceeding Period of Life. For
this Connection being once fettled, as the fame
Sounds will always ferve to excite the fame Ideas ;
if he can but contrive to regifter his Words, in
the Order and Difpofition in which the prefent
Train
( 90 )
Train of his Thoughts prefents them to has
Imagination ; it is evident he will be able to re-
call thefe Thoughts at Pleafure, and that too in
the very Manner of their firft Appearance. Ac-
cordingly we find, that the Inventions of Writ-
ing and Painting, by enabling us to fix and per-
petuate fuch perifhable things as Sounds, have
alfo furnifhed us with the Means of giving a
kind of Permanency to the Tranfaclions of the
Mind, infomuch that they may be in the fame
Manner fubjecled to our Review, as any the
other abiding Objects of Nature.
II. BUT befides the Ability of re-
And of tbt .. ,_,,
vutuai Cim- cording our own Thoughts, there is
wiumcaticn of tn i s f art her Advantage in the Ufe of
Kncivlcdgt to. ii 11
jrom om Ma external oigns, that they enable us
to another. to communicate our Sentiments to
others, and alfo receive Information of what
pafles in their Breafts. For any Number of
Men, having agreed to eftablifh the fame Sounds
as Signs of the fame Ideas, it is apparent that
the Repetition of thefe Sounds muft excite the
like Perceptions in each, and create a perfect
Correfpondence of Thoughts. When, for in-
flance, any Train of Ideas fucceed one another
in my Mind, if the Names by which I am wont
to exprefs them, have been annexed by thofe
with whom I converfe, to the very fame Set of
Ideas, nothing is more evident than that by re-
peating thofe Names according to the Tenor of
rn/
my prefent Conceptions, I fhall raife in their
Minds the fame Courfe of Thought as has taken
Pofleffion of my own. Hence, by barely attend-
ing to what pafles within themfelves, they will
alfo become acquainted with the Ideas in my
Underftandie'g, and have them in a manner laid
before their View. So that we here clearly per-
ceive, how a Man may communicate his Senti-
ments, Knowledge, and Difcoveries to others,
if the Language in which he converfes, be ex-
tenfive enough to mark all the Ideas and Tranf-
a&ions of his Mind. But as this is not always
the Cafe, and Men are often obliged to invent
Terms of their own, to exprefs new Views and
Conceptions of Things j it may be afked, how in
thefe Circumftances we can become acquainted
with the Thoughts of another, when he makes
ufe of Words to which we have never annexed
any Ideas, and that of courfe can raife no Per-
ceptions in our Minds. Now in order to unveil
this Myftery, and give fome little Infight into the
Foundation, Growth, and Improvement of Lan-
guage, the following Obfervations'will, I am apt
to think, be found of confiderable Moment.
III. FIRST, that no Word can be
A /r i r<- c T i !! Simple Ideal
to any Man the Sign of an Idea, till can i, ot b eca9 .
that Idea comes to have a real Ex- v '!' d . ',"'" tb *
Mind by
iftence in his Mind. For Names #Wi, or *
being only fo far intelligible, as they e J crt f tu
denote known internal Conceptions, where they
have
( 92 )
have none fuch to anfwer them, there they are
plainly Sounds without Signification, and of
courfe convey no Inftruclion or Knowledge,
But no fooner are the Ideas to which they be-
long raifed in the Underftanding, than finding
it eafy to connect them with the eftablifhed
Names, we can join in any Agreement of this
Kind made by others, and thereby enjoy the
Benefit of their Difcoveries. The firft thing
therefore to be confidered is, how thefe Ideas
may be conveyed into the Mind ; that being
there, we may learn to connect them with their
appropriated Sounds, -and fo become capable
of underftanding others, when they make ufe
of thefe Sounds in laying open and communU
eating their Thoughts. Now to comprehend
this diftin&ly, it will be neceflary to call to
mind, the before-mentioned Divifion of our
Ideas into fimple and complex. And firft, as
for our fimple Ideas, it has been already ob-
ferved, that they can find no Admiflion into
the Mind, but by the two original Fountains
of Knowledge, Senfation and Reflexion. If
therefore any of thefe have as yet no Being in
the Underftanding it is impoflible by Words
or a Defcription to excite them there. A Man
who had never felt the Impreflion of Heat^
could not be brought to comprehend that Sen-
fation, by any thing we might fay to explain it.
If we would really produce the Idea in him, it
nuift
( 93 )
tnuft be by applying the proper Object to his
Senies, and bringing him within the Influence
of a hot Body. When this is done, and Expe-
rience has taught him the Perception to which
Men have annexed the Name Heat, it then be-
comes to him the Sign of that Idea, and he
thenceforth underftands the Meaning of a Term,
which before, all the Words in the World
would not have been fufficient to convey into
his Mind. The Cafe is the fame in refpect of
Light and Colours. A Man born blind, and
thereby deprived of the only Conveyance for
the Ideas of this Clafs, can never be brought
to underftand the Names by which they are ex-
prefled. The Reafon is plain : they ftand for
Ideas that have no Exiftence in his Mind ; and
as the Organ appropriated to their Reception is
wanting, all other Contrivances are vain, nor
can they by any Force of Defcription be raifed
in his Imagination. But it is quite otherwise
in our complex Notions. For thefe being no
more than certain Combinations of fimple Ideas
put together in various Forms j if the original
Ideas out of which thefe Collections are made,
have already got Admiffion into the Underftand-
ing, and the Names ferving to exprefs them arc
known ; it will be eafy, by enumerating the
leveral Ideas concerned in the Compofition, and
marking the Order and Manner in which they
arc
( 94 )
are united, to raife any complex Conception in
the Mind. Thus the Idea anfwering to the
Word Rainbow, may be readily excited in the
Imagination of another, who has never feen the
Appearance itfelf, by barely defcribing the Fi-
gure, Largenefs, Pofition, and Order of Co-
lours ; if we fuppofe thefe feveral fimple Ideas,
with their Names, fufficiently known to him.
<rb< Namn ,f IV ' AND this naturally leads me
com/ilex Idtat to a fecond Obfervation upon this
definaklt, tbofe -,..,-. . . TTT , n ,
of fmpu idea* Subject, namely : that Words itand-
*"" ing for complex Ideas are all defin-
able, but thofe by which we denote fimple Ideas
are not. For the Perceptions of this latter Clafs,
having no other Entrance into the Mind, than
by Senfation or Reflection j can only be got by
Experience from the feveral Objects of Nature,
proper to produce thofe Perceptions in us.
Words indeed may very well ferve to remind us
of them, if they have already found Admiflion
into the Underftanding, and their Connection
with the eftablifhed Names is known j but they
can never give them their original Being and
Exiftence there. And hence it is, that when
any one aflcs the Meaning of a Word denoting
a fimple Idea, we pretend not to explain it to
him by a Definition, well knowing that to be
impoflible ; but fuppofing him already acquaint-
ed with the Idea, and only ignorant of the Name
12 b/
.. ( 95 )
by which it is called, we either mention it to him
by fome other Name, with which we prefume he
knows its Connexion, or appeal to the Object
where the Idea itfelf is found. Thus, was any
one to afk the Meaning of the Word white, we
fliould tell him it flood for the fame Idea as ]
a/bus in Latln^ or blanc in French j or if we
thought him a Stranger to thefe Languages,
might appeal to an Object producing the Idea,
by faying it denoted the Colour we obferve in
Snow or Milk. But this is by no Means a Defi-
nition of the Word, exciting a new Idea in his
Underftanding ; but merely a Contrivance to
remind him of a known Idea, and teach him its
Connection with the eftablifhed Name. For if
the Idea after which he enquires, has never yet ]
been raifed in his Mind ; as fuppofe one who had
feen no other colours than black and white, fhould
afk the Meaning of the Wordfcar/et j it is eafy
to perceive, that it would be no more poflible
to make him comprehend it by Words or a De-
finition, than to difcourfe the fame Perception
into the Imagination of a Man born blind. The
only Method in this Cafe is, to prefent fome
Object, by looking at which the Perception it-
felf many be excited, and thus he will learn both
the Name and the Idea together.
V. SHOULD any one's Curiofity Exf>eriettfeattJ
now prompt him to enquire, how it 0&***t*
comes]
( 96 )
comes to pafs, that Men ao;ree in their
;T;::;V Names f the fim P le "> f ^s
fimpit Ideai. they cannot view the Perceptions in
one another's Minds, nor make known thefe
Perceptions by Words to others ; I anfwer, that
the Effect here mentioned is produced by Expe-
rience and Obfervation. Thus finding, for in-
france, that the Name Heatj is annexed to that
Impreffion which Men feel when they approach
the Fire, I make it alfo the Sign of the Idea ex-
cited in me by fuch an Approach, nor have any
doubt but it denotes the fame Perception in my
Mind as in theirs. For we are naturally led to
imagine, that the fame Objects operate alike upon
the Organs of the human Body, and produce an
Uniformity of Senfations. No Man fancies,
that the Idea raifed in him by the Tafte of
Stigar^ and which he calls Sweetnefs y differs
from that excited in another by the like Means ;
or that Wormwood^ to whofe Relifh he has
given the Epithet Bitter , produces in others
the Senfation which he denotes by the Word
Sweet. Prefuming therefore upon this Confor-
mity of Perceptions, when they arife from the
fame Objects, we eafily agree as to the Names
of our fimple Ideas j and if at any time, by a
more narrow Scrutiny into Things, new Ideas of
this Clafs come in our Way, which we choofe to
exprefs by Terms of our own Invention j thefe
x Names
( 97 )
Names are explained not by a Definition, but
by referring to the Obje&s, whence the Ideas
themfelves may be obtained.
VI. BEING in this Manner ftr-
nifhed with Ample Ideas, and the ***.
Names by which they are exprefled, />/'* idea by
the Meaning of Terms that frand w f/-/c^"ri- '
for complex Ideas is eafily got ; be- vaac '* Na "
J ture.
caufe the Ideas themfelves anfwer-
ing to thefe Terms, may 'be conveyed into the
Mind by Definitions. For our complex Notions,
as was already obferved, are only certain Combi-
nations of fimple Ideas. . When therefore thefe
are enumerated, and the Manner in which they
are united into one Conception explained, no-
thing more .is wanting to raife that Conception
in the Understanding ; and thus the Term de-
noting it comes of courfe to be underftood. And
here it is worth while to refledl a little upon the
wife Contrivance of Nature, in thus furnifhing
us with the very apteft means of communicating
our Thoughts. For were it not fo ordered, that
we could thus convey our complex Ideas from
one to another by Definitions, it would in many
Cafes be impoflible to make them known at all.
This is apparent in thofe Ideas which are the
proper Work of the Mind. For as they exift
only in the Underftanding, and have no real
Objects in Nature, in Conformity to which they
F arc
( 98 )
are framed ; if we could not make them known
by a Defcription, they muft lie for ever hid
within our own Breafts, and be confined to the
narrow Acquaintance of a fingle Mind. All the
fine Scenes, that rife from time to time in the
Poet's Fancy, and by his lively Painting, give
fuch Entertainment to his Readers } were he de-
ftitute of this Faculty, of laying them open to
the View of others by Words and Defcriptions ;
could not extend their Influence beyond his own
Imagination, or give Joy to any but the original
Inventor.
VII. THERE is this farther Ad-
of gnat vantage in the Ability we enjoy, of
il to- . J '*_
rds the Im- communicating our complex No-
tions b 7 Definitions ; that as thefe
make by far the Jargefl Clafs of our
Ideas, and moft frequently occur in the Progrefs
and Improvement of Knowledge ; fo they are by
this means imparted with the greateft Readinefs,
than which nothing could tend more to the In-
creafe and fpreading of Science. For a Definition
is foon perufed, and if the Terms of it are well
underftood, the Idea itfelf finds an eafy Admif-
iion into the Mind. Whereas in fimple Percep-
tions, where we are referred to the Objecls pro-
ducing them, if thefe cannot be come at, as is
fometimes the Cafe, the Names by which they
are exprefled muft remain empty Sounds. But
new Ideas of this Clafs occurring very rarely in
the
( 99 )
the Sciences, they feldom create any great Ob-
ftru&ion ; it is otherwife with our complex No-
tions, for every Step we take, leading us into
new Combinations and Views of Things, it be-
comes neceffary to explain thefe to others, before
they can be made acquainted with our Difcove-
ries. And as the manner of Definitions is eafy,
requiring no Apparatus but that of Words, which
are always ready, and at hand j hence we can
with the lefs Difficulty, remove fuch Obftacles,
as might arife from Terms of our own Inven-
tion, when they are made to ftand for new com-
plex Ideas, fuggefled to the Mind by fome pre-
fent Train of thinking. And thus at laft we are
let into the Myftery hinted at in the Beginning of
this Chapter, viz. how we may become ac-
quainted with the Thoughts of another, when
he makes ufe of Words to which we have as yet
joined no Ideas. The Anfwer is obvious, from
what has been already faid. If the Terms de-
note fimple Perceptions, he muft refer us to thofe
Objedls of Nature, whence the Perceptions them-
felves are to be obtained ; but if they ftand for
complex Ideas, their Meaning may be explained
by a Definition. As for the Names of fimple
Ideas, I fhall here dtfmifs them ; it being fufficient
to take Notice, that our Knowledge this Way
can be extended only by Experience and Obfer-
vation. But the Theory of Definitions making a
F 2 material
material Part of Logiclc, and being indeed of
great Importance towards the Improvement of
human Knowledge, it will be necefiary to lay it
a little more open to the View of the Reader.
VIII. COMPLEX Ideas are, as has
Kirn and Re- Deen already faid, no other than fim-
foiution ef our pl e Ideas put together in various
Cample* Ideal. r> LI
Forms. i>ut then it is to be ob-
ferved, that in making thefe Collections, the Mind
is not always tied down to the immediate View
of the fimple Perceptions out of which they are
framed. For if we fuppofe the Underftanding
already furnifhed with a confiderable Stock of
compound Notions, thefe again maybe made the
conftituent Parts of others ftill more compound-
ed, infomuch that the new Idea thence arifing
may be termed a Combination of complex Con-
ceptions. Thus the Idea annexed to the Word
Animal^ includes many Perceptions under it, as
Life, Scnfe, fpontaneous Motion, C5"r. In like
manner, by the Term rational, we denote a Va-
riety of fimple Ideas. If now combining thefe
two Conceptions together, we form the ftill more
complex Notion of a rational Animal j the Idea
thus got is truly a Collection of compound NQ-
tices. In a Word, the fame Thing happens here
as in Numbers, which we may confider not only
as various Collections of Units, thefe being in-
deed their original -and conftituent Parts 5 but alfo
as
C ioi J
as fometimes compofed of other lefler Numbers,
which all put together make up the refpeftive
Sums. Now in tracing any very large Number,
when for the Eafe of the Mind we confider it at
firft as compofed of various others ftill lefTer : if
we next take thefe lefler Parts to Pieces, and pur-
fue them continually until we arrive at the Units
out of which they are compofed j we thereby to-
tally unravel the Collection, and being able to
pufh our Refearches no farther, reft fatisfied in
the View thus offered to the Underftanding. Juft
fo it is in the Examination of our complex Ideas.
For when any very compounded Notion comes
under the Infpeclion of the Mind in order to be
traced to its firft Principles ; we begin with re-
fblving it into other Ideas lefs complicated ; and
taking thefe again to Pieces one by one, ftill go
on with the Search, until we have broken the
whole into our firft and fimple Perceptions, be-
yond which the Purfuit cannot poflibly be carried.
And this is the Reafon why I have all along
called our fimple Ideas the Foundation and
Ground-work of human Knowledge j becaufe in
unravelling the Conceptions of the Mind, we find
ourfelves at length bounded by thefe Ideas, which
are indeed the laft Refort of the Underftanding.
IX. FROM what has been faid it rte Namn f
will be eafy to conceive, how in de- /"/"' J' / "
may be cenji-
fining a Term, ftanding for any very dtred at tbt
F 3 complex
complex Idea, other Terms may be
EitnttHtirj . .
P*n*fLan- introduced, that alfo denote com-
pound Ideas, though of an inferior
Glafs. For the firft Idea being refolvable into
others lefs complicated ; the Definition which
enumerates thefe component Ideas muft confift
of the Names by which they are exprefied. And
if it fo happen, that the Ideas of this fecond
Clafs are alfo unknown, their Terms too ought
to be ftill farther defined. In this manner may a
Series of Definitions be carried on until we ar-
rive at the Names of fimple Ideas, which not
being definable, the Analyfis muft neceffarily
ceafe. And thus we fee, that as our fimple Ideas
are the Materials and Foundation of Know-.
ledge, fo the Names of fimple Ideas may be
confidered as the Elementary Parts of Language,
beyond which we cannot trace the Meaning and
Signification of Words. When we come to
them, we fuppofe the Ideas they ftand for alrea-
dy known ; or if they are not, Experience alone
muft be confulted, and not Definitions or Ex-
plications. And here it is well worth our No-
tice, that as the Names of thefe our original
Conceptions, conftitute the primary and funda-
mental Articles of Speech, upon which the
whole Superftru&ure of human Language is
built, fo they are of all others the lead doubtful
and uncertain in their Signification. Becaufe
{landing
landing each for one fimple Perception, not pre-
carioufly excited in the Mind, but the Effect of
certain Powers in Things, fitted to produce that
Senfation in us ; there is no Danger of Error or
Miftake. He that once knows Sweetnefs to be
the Name of the Tafte received from Sugar,
Wlntenefs of the Colour in Snow or Milk, and
Heat of the Senfation produced by approaching
the Fire, will not be apt to mifapply thofe Words,
or annex them to Perceptions of a different Kind.
And as the Names of complex Ideas may all be
refolved into thefe primitive Terms, it is apparent
that we are fufficiently provided with the Means
of communicating our Thoughts one to another j
and that the Miftakes fo frequently complained of
on this Head, are wholly owing to ourfelves, in
not fufficiently defining the Terms we ufe, or
perhaps not connecting them with clear and de-
terminate Ideas.
CHAP. VI.
i i
Of Definition, and itsfeveral Kinds.
I. TTAVING laid thefe Foun- The Variety of
rl dations, {hewn what Words 2JL
are, and what are not definable, tbt -various
i in* r r t AtpllCttltn
and taught the Manner or relolv- tfw ar dt.
ing our Notions, as well as Language itfelf,
F 4 into
into its firfl and original Principles ; we now
proceed to explain a little more particularly the
Nature of a Definition, and the feveral Kinds
made ufe of according to the different Views
Men have in communicating their Thoughts one
to another. Definitions are intended to make
known the Meaning of Words franding for com-
plex Ideas j and were we always careful to form
thofe Ideas exactly in our Minds, and copy our
Definitions from that Appearance, much of the
Confufton and Obfcurity complained of in Lan-
guages might be prevented. But unhappily for
us, we are by no means ileady in the Application
of Names, referring them fometimes to one
thing, fometimes to another ; which often creates
great uncertainty in their Signification, and
pbliges us to give a different Turn to our Defini-
tions, according to the different Reference of
the Terms defined. In order therefore to render
this whole Matter as clear and obvious as poffi-
ble, we fhall firft confider to what it is that
Names, in the Ufe of Language, are moft com-
monly applied ; and then from the Variety of
this Application, endeavour to account for the
feveral Methods of defining, mentioned in the
Writings of Logicians.
II. WORDS then have manifeftly a
Words have *
a threefold threefold Reference. Firft and more
wr "</" immediately, they denote the Ideas
tijt ffetbtrs, j n ^e Mind of him who ufes them ;
and
( 105 )
and this is their true and proper Sig-
. , f . and tie real
mhcation. When a Man Ipeaks, it Being cf
is that he may be underftood j and the '*""'
Words he employs to convey his Thoughts, are
fuch as by Ufe he has learnt to connect with the
Ideas then prefent to his Mind. But becaufe
thofe with whom we converfe, are alfo fuppofed
to know the Meaning of the Terms we ufe,
hence Secondly, we confider our Words as
Signs likewife of the Ideas in their Minds ; and
this is the Foundation of what is called Propriety
in Language, when Men take Care to affix
fuch Notions to their Words, as are commonly
applied to them by thofe of moft Underftanding
in the Country where they live. The Third and
laft Reference of Words is to Things them-
felves, For many of our Ideas are taken from the
feveral Objects of Nature, wherewith we are fur-
rounded ; and being confidered as Copies of
Things really exifting, the Words by which
they are exprefled, are often transferred from,
the Ideas themfelves, _to fignify thofe Obje&s
which they are fuppofed to reprefent. Thus the
Word Sun y not only denotes the Idea excited
in the Mind by that Sound, but is alfo frequent-
ly made to ftand for the luminous Body itfelf,
which inhabits the Center of this our Planetary
Syftem. Now according to this threefold Ap-
plication of Names, their Definitions, and the
Manner of explaining them, muft be various ;
FS for
{ 106 )
for it is one Thing to unfold the Ideas in a Man's
own Mind, another to defer! be them as they
are fuppofed to make their Appearance in the
Minds of others ; and laftly, it is fomething
ftill different, to draw Images or Pictures, that
fhall carry in them a Conformity to the Being and
Reality of Things. But we fhall treat of each
in Order.
III. FIRST then, when we con-
Defnitiant of rj _ , c . f T
tke Name "der Words, as bignte of the Ideas in
teach only tbt t h e Mind of him who ufes them : a
Connefttcn of
ear Wordt and Definition is nothing elfe, but fuch v'
SSSflZlm an Explication of the Meaning of
trtry. ar) y Term, as that the complex Idea
annexed to it by the Speaker, may be excited in
the Underftanding of him with whom he con-
verfes. And this is plainly no more than teach-
ing the Connection of our Words and Ideas, that
others may underftand the Senfe of our Expref-
fions, and know diftin&ly what Notions we affix
to the Terms we ufe. When we fay, for in-
ftance, that by the Word Square we mean a Fi-
gure bounded by four equal Sides, joined toge-
ther at right Angles ; what is this but a Decla-
ration, that the Idea of a quadrilateral, equila-
teral, rectangular Figure, is that which in Dif-
courfe or Writing we connect with the Term
Square? This is that Kind of Definition, which
Logicians call the Definition of the Name ; be-
caufe it difcovers the Meaning of the Words or
Names
Names we make ufe of, by fhewing the Ideas for
which they ftand. Now as Sounds are of them-
felves indifferent to fignify any Ideas, hence it
is plain, that the Definitions of Names are arbi-
trary, every Man having a Liberty to affix what
Notions he pleafes to his Words. But the Con-
venience of Communication making it neceflary
for Men fpeaking the fame Language to agree as
nearly as pofllble in the Signification of Sounds,
a Conformity has accordingly been ftudied.
Neverthelefs we find that Differences will from
time to time creep in, which muft create great
Confufion in Men's Difcourfes and Reafonings,
if they are not careful to define their Terms, that
their Signification may be kept fixed and fteady,
and lie always open to the View of the Mind.
The Writings of the Mathematicians are a cleaf
Proof, how much the Advancement of human
Knowledge depends upon a right Ufe of Defini-
tions. For as by means of them they every where
preferve the fame determined Signification to
their Words, hence there is little Difpute as to
the Meaning of their Expreffions, almoft all
Men understanding them in the fame Senfe.
And thus it happens, that fuch as apply their
Thoughts this Way, having perfectly the fame
Views of Things, readily comprehend the Dif-
coveries already made, and are thereby enabled
with joint Labour, and an exa<l Conformity of-
E 6 Notions,,
Notions, to carry on the Improvement of this
Branch of Knowledge. And if Men in other
Parts of Learning, were alike careful to fix the
Meaning of their Terms, the Progrefs of Science
muft be greatly furthered, and all thofe verbal
Difputes, that now fo much interrupt the Courfe
of our Improvement, might be prevented.
IV. THIS then ought to be our
Definition of
the Name not firft Care, when we enter upon a
? J i*Dt- Defign of illuftrating any particular
fnitiotis. Branch of Study ; to afcertain ouv
Ideas, and mark the Names by which they are
exprefled. And altho' Definitions of Words are
indeed arbitrary, (for a Man may affix what Ideas
he pleafes to his Terms, nor can any one conteft
this Liberty with him,) yet it will be proper to
conform as near as poffible to common Accepta-
tion, that thereby our Thoughts may find a
more eafy and ready Entrance into the Minds
/. of others. If it fhould now be afked, what are
the Rules of a good Definition; I anfwer, that as
in Definitions of the Name, we aim at no more
than teaching the Connection of Words and
Ideas ; every Contrivance, by which we are
enabled to excite the Idea annexed to any Word
in the Mind of another, will ferve the Purpofe
of a Definition. Now the Ideas we join with
our Words are of two kinds : either fuch as ^e
have reafon to believe are already in the Minds
of others, though perhaps they know not the
Names by which they are called ; or fuch as
being new and of our own Formation, can be
no otherwife made known than by a Defcription.
In the firft Cafe, there is no Neceflity for lay-
ing open the Idea itfelf, becaufe being already
known, any Contrivance to remind us of it is
fufficient. When we fay, for inftance, that a
Clock is an Inftrument by which pve meafure the
Hours of the Day j it is plain, that the Idea an-
fwering to the Word Clock, is not here unfold-
ed ; but we being before-hand fuppofed to have
an Idea of this Inftrument, are only taught by
what Name it is called. Now in this Senfe,
the Names of even flmple Ideas may be defined.
For by faying that tWite is the Colour we ob-
ferve in Snow or Milk, Heat the Senfation pro-
duced by approaching the Fire, we fufficiently
make known what Ideas we connect with the
Terms IFhite and Heat, which is the true Pur-
pofe of a Definition of the Name. Hence it ap-
pears, that many of thofe Explanations of
Words, which Logicians call Definitions of
the Name, are not Definitions in a true and pro-
per Senfe, that is, fuch Defcriptions of Ideas,
as would ferve to excite them in the Mind of
another, even fuppofing him before wholly un-
acquainted with them, but merely Contrivances
to remind us of known Ideas, and teach us the
Names by which they are called.
V. BUT
( iro )
, V ' BlJT where the
ttey coincide with our Words, are new and of
fnitita If t'be our own Formation, there they are
Wing. to be laid open by a Defcription..
Becaufe being fuppofed unknown to others, we
xnuft firft raife them in their Minds, before they
ean learn to conned them with any particular
Names. And here it is, that the Definition of
the Name coincides with what Logicians call the
Definition of the. Thing^ as in either Cafe we pro-
ceed by unfolding the Idea itfelf for which the
Term defined tands.. And indeed this alone is
what conftitutes a Definition in. the true and
proper Senfe of the Word, as will appear more
fully afterwards, when we come to confider the
Terms we ufe, as referred to the real Objects
of Nature. We fhall therefore poftpone this
Confideration of the Definition of the Name,
till we come to treat of the Definition of the
Thing, when it will more naturally fall, in our
way. It may not however be amifs to obferve,
that when we fay the Definitions of the Name
are arbitrary, we mean not that the Defcriptions
of Ideas are fo too. For every Idea having a
peculiar Appearance of its own, by which it is-
diftinguifhed from all others, nothing is more
evident, than that the Defcription muft be fuch
as to exhibit that precife Conception. But then
the Connection of any Idea, with the Name by
which, it is exprefied, being, as we have faid,-
wholly.
( III ) . -
wholly arbitrary, the confidering the Defcrlp-
tion of that Idea as the Definition of that par-
ticular Name muft be fo to. So that although
Definitions confidered as Defcriptions of our
Ideas, are fteady and invariable, yet the Applica-
tion of them to particular Sounds, (which is all
that we underftand by the Definition of the
Name) is wholly a Work of our own free Choice*.
VI. BUT Secondly, befides con- Definition of
rt' txr j i cv c Wordt accord-
fidenng Words as the Signs of our ing t!>lhe(om ,
own Ideas, we are alfo very apt on mon u f e f
Language not
many Uccahons, to refer them to arbitrary.
the Ideas in the Minds of other Men. Now to
define a Term in this View, is to inveftigate its
Meaning or Acceptation, according to the com-
mon Ufe of Speech. Here then it is plain that
Definitions are not arbitrary. For although in.
regarding Words as the Marks of our own Ideas,,,
we may give them what Meaning we pleafe ; yet
when we confider them in reference to the
Thoughts of others, they have a fixed and fteady
Signification j namely,, that which Cuftom and?
the Propriety of Language has afligned them.
The Words Ability ;and Genius, may by. any Man
be made to ftand for one and the fame Idea in his
own Mind, and if he takes care to advertife us
of this, he is at liberty to ufe them promifcuoufly.
But if the common Courfe of Language hath
confined the Word Genius to exprefs the natural.
Strength and Talents of the Mind, and the
Word
C
Word Ability to denote thofe which are acquired,
whoever pretends to explain the proper Accep-
tation of thefe Terms, is bound to take notice
of this Difference. As Propriety of Speech
makes our Language intelligible, and gives our
Thoughts a ready Entrance into the Minds of
others, it well deferves our Application and Care.
The beft way to acquire it is from the Writings
and Difcourfes of thofe who feem to have had the
cleareft Notions, and to have applied their Terms
\vith the exateft Choice and Fitnefs.
, VII. WE come now to the third
Definition! of
the Thing re- and laft Species of Definition, that
M namely, which confiders Words as
referred to Things themfelves. And
here it is plain we are not at liberty to feign and
fafhion our Explications at pleafure, but being
tied down to the real Objects of Nature, muil
ftudy a Conformity to Things themfelves. When
we define for inftance the Sun y confidered as that
Being who poflefTes the Center of our Syftem,
and diffufes Heat and Light to the Planets around
him ; it is not enough that we give an Account
of the Idea, anfwering to that Word in our Minds.
We muft further take care, that the Idea itfelf
carries in it a real. Conformity to the Object it is
fuppofed to reprefent. And hence it is, that all
Definitions of this kind, when juftly made, are
in reality Pictures or Reprefentations, taken from
* the
the Being and Exiftence of Things. For they arc
intended to exprefs their Nature and Properties,
fo as to diftinguifh them from all others, and
exhibit them clearly to the View of the Mind.
'Tis for this Reafon that Logicians call them De-
finitions of Things^ becaufe they are fuppofed to
refer, not fo much to the Ideas in the Under-
ft and ing, as to the Things themfelves repre-
fented by thofe Ideas.
VIII. AND this alfo lets us into
Ground tftbf
the (jround of that Diftmction fo Dijtmaion
univerfally received, between Defini- b %""*l f
tions of the Name and of the Thing, the Name and
The firft are arbitrary, and not lia- f tbe<rbin &-
ble to Debate or Contradiction. The fecond are
Propofitions capable of Proof and Illuftration,
and which may therefore be contefted. The Rea-
fon is obvious. Definitions of the Name ferve
only to mark what Ideas we connect with our
Words. And as Sounds are of themfelves in-
different to fignify any Ideas, we are intirely at
liberty to affix to them what Notions we pleafe.
But it is otherwife in the Definition of the Thing.
For here our Words ferving to denote particular
Beings in Nature, cannot be the Signs of any
Ideas at pleafure, but of fuch only as carry in
them a Conformity to the feveral Objects to
which the Words refer. A Man may ufe the
Term Square to exprefs that Idea, which others
denote
denote by the Word Triangle, and define it ac-
cordingly. In this Cafe indeed he recedes from
the common Forms of Speech, but his Definition
cannot be charged with Falfehood, He tells us
that by a Square he means a three-fided Figure,
and who can difpute the Truth of this, if he
really all along ufes the Word in that Senfe ? I
would only obferve, that by changing thus the
Meaning of Words, we cHhnge not Things
themfelves, or their Relations and Habitudes one
towards another. Thefe are at all Times the
fame and invariable, nor have any Dependence
upon the Fancy and Caprice of Men. It is
true the Properties of the Triangle may after
this Definition, be affirmed of the Square ; but
as in either Cafe, the Idea to which thefe Proper-
ties belong, is the fame, the Propofitions only
expreifing our Judgments, and not our Judg-
ments themfelves, fuffer a feeming Variation.
jffrevhut IX. BUT where Words are made
Convtetion it- to denote particular Objects, previ-
tvicen Namu r . .
tnd Things, ous to any Definitions given, there-
Tit'ray "EX-'' arbitrary Explications cannot have
fixations, place. For in this Cafe* we are not
put upon explaining what Ideas we conned with-
eur Words, but a Connection being already fup-
pofed between the Name and the Thing fignified^
our Bufinefs is to unfold that Idea by which the
Object itfelf is moft clearly aad diftin<31y repre-v
8
fented. Thus the Word Gold denotes that Me-
tal which is of higheft Value among Men, and
goes fartheft in the way of Commerce. This -
Connection being once fettled, we are no longer
left to arbitrary Definitions, but muft defcribe it
by fuch Properties as are really to be found in it,
and will beft ferve to diftinguifh it when it comes
in our Way ; as by faying it is a SubftanceyelloiV)
very heavy, malleable ^ fufible^ &c.
X. FROM what has been faid it j^ Matlt-
appears. that in the Language of ">*t>cat Dtfi-
rr DO nttiont bavt
Logicians, Definitions of the Thing bun accounted
refpeft only Subflances and Beings
that have a real Exiftence in Nature,
ferving to defcribe them by their Properties
and Attributes. And this I doubt not is the
Reafon, that the Definitions of the Mathema-
ticians are not confidered as Definitions of the
Thing, but of the Name j becaufe the Ideas
therein defcribed, are the mere Creatures of the
Underftanding, and not fuppofed to be copied
from Patterns exifting without us. A Circle, a
Triangle, a Square, &c. fuch as Mathematicians
conceive them, are no where to be found in Na-
ture that we know of. Hence it might juftly be
accounted abfurd, to call our Definitions of thefe^
Definitions of the Thing, when they ferve not to
defcribe any real Objects of Nature, but merely
to unfold the Conceptions of the Mind. And
yet
( 1x6 )
yet if we look into the Matter narrowly, we
fhall find that the Rules followed in thefe 1> fi-
nitions are preciftly the fame with thofe which
Logicians have laid down for the Definition of
the Thing. All the feveral Species of Figures
are defcribed by their Properties, fome of which
are common to different Ranks, others peculiar
to the Tribe defined. The common Properties
conftitute what Logicians call the Genus, and
thofe that are peculiar the Difference. Now the
Genus and Difference make up the Logical Defini-
tion of the Thing, as will be more clearly under-
flood from what follows.
XI. I AM therefore apt to think,
t h at Mathematical Definitions, as
on of they are of the fame general Form
with tne Definitions of Subftances,
ot to be ac- anc ] f u bje6t to the fame Rules, have
teunttder- . J
titrary. been improperly conndered as mere
Definitions of the Name, in which we are left
wholly to arbitrary Explications. For however
we may change the Name of one Figure for ano-
ther in Difcourfe or Writing, ufmg the Term
Square to denote a Triangle, or the Word Triangle
to exprefs a Square^ it is certain the Ideas them-
felves are invariable, and no lefs capable of be-
ing diftinguifhed by their Properties, than the
feveral Species of Subftances. Thus if we fup-
pofe
pofe the Word Square to denote that Species of
Figures, whofe Sides feverally fubtend Quadrants
of a circumfcribed Circle, we ihali find ourfelves
equally fhut out from arbitrary Explications, as
in the Definition of the Names of Subftances.
For as this happens in no Figures but thofe
which are bounded by four equal Sides joined
together at right Angles ; it follows evidently,
that the true and proper Definition of a Square^
is that which exhibits the precife Idea here men-
tioned, and no other, to the Mind. And thus
it appears, that the common Divifion of Defini-
tions, into thofe of the Name and Thing, is not
fuificiendy calculated to give us right Apprehen-
fions, as to what is and what is not arbitrary in
the Explication of Words. It may not therefore
be improper, if we here endeavour to clear up
this Matter a little, and free it from thofe Ob-
fcurities in which it has hitherto been involved.
To this end we fhall premife the following Ob**
fervations.
XII. i. FIRST, that whatever Lo-
. . i T^ DtSnttttns
gicians may pretend about the De- pnperijjptek-
finition of the Thing, it is yet cer- '"* ."^ rt ~
. S ar " **"*'
tain that none of our Definitions, but merely oar
when purfued to their Source, regard
immediately Things themfelves, but merely the
Ideas in our own Minds. This I doubt not will
appear a Paradox to many, who will be apt to
enquire,
( II* )
enquire, whether the Definition of Gold, be not
taken from that Metal, independent of the vari-
ous Conceptions of Men about it. To this I
anfwer, that indeed in framing our Idea of Gold,
we regard chiefly the Thing itfelf, uniting in
our Conception fuch Properties as are moft con-
fpicuous, and ferve beft to diftinguifh it from
other Metals, to which it may bear any Refem-
blance. But as it is by this Idea alone that Gold
is known to us, fo in defcribing it to others, we
aim at nothing more than to transfer the fame
Conception into their Minds. Now this can no-
otherwife be done, but by enumerating the feve-
ral Properties out of which our own complex
Notion is formed. And indeed it were in the
higheft Degree abfurd to imagine, that Men in
explaining Things to others, fliould make ufe
of any Marks or Characters but thole by which
they are known to themfelves. Hence it comes
to pafs, that all our Definitions, are in Fact no-
thing elfe but Tranfcripts of the Ideas in our
Minds. Where thefe are imperfect, the Defi-
nitions muft be fo too ; where they are juft and
adequate, the Copies taken from them, if drawn
out with Accuracy and Care, cannot fail to ex-
hibit the Object defcribed. And this will very
well ferve to account for that great Diverfity of
Definitions we often meet with, even of one
and the fame Object. Becaufe Men, in Con-
fequence
fequence of their different Purfuits and Appli-
cations, falling often into different Views of
Things, muft needs vary no lefs in their Defi-
nitions than in the Ideas themfelves from which
thefe Definitions are copied. He whofe Obfer-
vation goes no farther than the more obvious
Qualities of Gold, will content himfelf with
defcribing it by its Colour, Weight and per-
haps Malleability and Fufibility. On the other
hand a Goldfmith, having enquired farther into
the Nature of that Metal, and finding feveral
other Properties that equally belong to it, will
be apt to take thefe alfo into his complex Idea,
and accordingly introduce them in a Definition,
Hence his Defcription will add to the former,
Fixednefs, and Solubility in Aqua Regia, &c.
And fo in Proportion, as Men's various Purfuits
lead them into a more accurate Examination
of things, their Explications will take a different
Turn, fuitable to the Ideas they have framed
within themfelves.
XIII. 2. THIS then being evi- D ; fllnalon be _
dent, that our Definitions refpeft not tween the Dt '
_,. . i. / i i i T i fait ion of the
1 hings themlelves, but the Ideas in tJameand
our own Minds; I would in the next Tb ^ t f' 7 '/'*
and to be rt-
Place obferve, that the Diftin&ion of jeHed.
them into thofe of the Name and Thing, is al-
together ufelefs, and tends rather to miflead us
than give right Apprehenfions of the Subject in
hand. For thus Men are apt to fancy, that many
of
( 120 )
of their Definitions are expreffive of the real Ef-
fence of Things, whereas they are in truth no
more than Tranfcripts of their own Ideas. And
as it fometimes falls out that thefe Ideas are not
collected with fufficient Care, from the Objects
they reprefent j we find by Experience, that a
miftaken Idea never fails to occafion a Miftake
alfo in the Definition. But this could not happen
were our Definitions copied from Things them-
felves : becaufe their Eflences being immutable
and always the fame, the Definition would in
this Cafe ferve to correct the Idea, and might be
confidered as a Standard, by which to judge
whether the Idea was rightly framed. I deny
not that Words are often transferred from our
Ideas to fignify the Objects which thefe Ideas re-
prefent ; as when we talk of the Sun, the Earth,
Men, and other Animals. But then let it be ob-
ferved, that as thefe Objects are only known to
us by the Ideas of them in our Minds ; fo in de-
fcribing them to others, all we aim at is, diftindtly
to lay open our Conceptions about them. Hence
it appears, that what Logicians call a Definition of
the Thing, is in Truth no more than an unfold-
ing of the Idea, by which that Thing is repre-
fented to the Underftanding. But now in Ma-
thematical Definitions, and indeed all others
whatfoever, this alfo is our whole Aim and Intent,
to exhibit and lay open thofe Ideas, of which the
Words we ufe art the Signs. And thus it hap-
pen*,
( III )
pens, that in innumerable Inftances, what Lo-
gicians call the Definition of the Name, is yet
found to coincide with, and 'proceed by the very
fame Rules, as the Definition of the Thing j which
clearly demonftrates the Neceflity of banifhing
this frivolous Diftin&ion, and eftablifhing fome
precife and determinate Notion, expreffive of the
true Nature of a Definition, and comprehending
it in its full Extent.
XIV. NOR will this appear fo dif- Definitions in
ficult a Tafk. if we call to mind that f Ca f' s D *'
Jcnpttons of
Words are in all Cafes the Signs of cur ideas.
our Ideas, and no otherwife fignify Things, than
as theyftand for thofe Ideas by which Things are
reprefented to the Underftanding. By defining
our Words therefore we can mean no more, than
the laying open to the View of others the Ideas
of which thefe Words are the Signs. For thus it
is that the Meaning of our Expreffions come to
be known, and that we find ourfelves capable
of transferring our Thoughts and Conceptions
into the Minds of thofe with, whom we converfe.
Where Words are referred to Things themfelves,
there we explain the Ideas by which thefe things
are reprefented ; where they denote Conceptions
framed by the Mind, there we lay open thefe Con-
ceptions, and endeavour to exhibit them accord-
ing to their real Appearance within our own
Breads. But in both Cafes it is our own Ideas,
G it
it is the Perceptions of our own Minds, either
as taken from things without, or framed by the
Understanding itfelf, that we explicate and un-
fold.
Wot arbitrary, XV. AND thus we have at length
? t'"V"~ fettled the true and genuine Notion
fned to the
of a Definition, comprehending all
At- lts Varieties, from whatever Science
/. taken, or to whatever Object ex-
tended. For from what we have faid it evidently
follows, that a Definition is the unfolding, of fame
Conception of the Mind^ anfwering to the Word or
I'erm made ufe of as the Sign of it. Now as in ex-
hibiting any Idea to another, it is necefTary that
the Defcription be fuch as may excite that precife
Idea in his Mind ; hence it is plain, that Defi-
nitions properly fpeaking are not arbitrary, but
confined to the reprefenting of certain determi-
nate fettled Notions, fuch namely as are annex-
ed by the Speaker or Writer to the Words he
ufes. As neverthelefs it is univerfally allowed,
that the Signification of Words is perfectly vo-
luntary, and not the Effect of any natural and
neceflary Connection, between them and the
Ideas for which they frand, fome may perhaps
wonder why Definitions are not fo too. In order
therefore to unravel this Difficulty, and fhew
diftinclly what is, and what is not arbitrary in
Speech, we muft carefully diftinguifli between
the.
( "3 )
the Connexion of our Words and Ideas, and
the unfolding of the Ideas themfelves.
XVI. FIRST, as to the Connec- ri>e Cwr-
tion of our Words and Ideas, this it '1 *"'"*
' fvordi and
is plain is a purely arbitrary Inftitu- idt&t, a pcr-
tion, When for inftance we have in fatyEpa*'
our Minds, the Idea of any particu- bnjhmtnt.
lar Species of Metals, the calling it by the Name
Gold, is an Effect of the voluntary Choice of Mea
fpealdng the fame Language, and not of any pe-
culiar Aptnefs in that Sound to exprefs that Idea.
Other Nations we find make ufe of different
Sounds, and with the fame Effect. Thus Aurum
denotes that Idea in Lattn^ and Or in French,
And even the Word Gold itfelf, would have as
well ferved to exprefs the Idea of that Metal
which we call Silver, had Cuftom in the Begin-
ning fo eftablifned it.
XVII. BUT although we are thus
...... fbt Defcr'ip.
mtirely at liberty, in connecting any tiom of Idcst
Idea with any Sound, yet it is quite '."' fy *?'
1 * J bounded to toe
otherwife in unfolding the Ideas Rtprefentation
themfelves. For every Idea, having 3^r
a precife Appearance of its own, by *> " wb ' tcb &V
. , . . ,.. . n i arediflin-
Which it is diitinguiihed from every gwjbed among
other Idea ; it is manifeft, that in them f elv "-
laying it open to others, we muft ftudy fuch a
Defcription, as (hall exhibit that peculiar Ap-
pearance. When we have formed to ourfelves
the Idea of a Figure bounded by four equal Sidej
G 2 joined
C
joined together at right Angles, we are at liberty
to exprefs that Idea by any Sound, and may call
it either a Square or a Triangle. But whichever
of thefe Names we ufe, fo long as the Idea is the
fame, the Defcription by which we would fig-
nify it to another, muft be fo too. 1 et it be
called Square or Triangle^ it is ftill a Figure hav-
ing four equal Sides, and all its Angles right
ones. Hence we clearly fee, what is, and what
is not arbitrary in the Ufe of Words. The
eftablifliing any Sound, as the Mark of fome
determinate Idea in the Mind, is the Effect of
free Choice, and a voluntary Combination
among Men. And as different Nations make ufe
of different Sounds, to denote the fame Ideas,
hence proceeds all that Variety of Languages
which we meet with in the World. But when
a Connection between our Ideas and Words is
once fettled, the unfolding of the Idea anfwering
to any Word, which properly conftitutes a
Definition, is by no means an arbitrary thing.
For here, as I have already obferved, we are
bound to exhibit that precife Conception, which
cither the Ufe of Language or our own particular
Choice, hath annexed to the Term we ufe.
Caufcs of tit XVIII. AND thus it appears that
Obfcurity that -r\ r r j i -rx /- .
tat hitherto Definitions, confidered as Defcnp-
ptrpkxtdtbi t j ons of jd eas j n tne j^ind, are fteady
Ibetry of De- ,...,, *
fnitioti, and invariable, being bounded to
the Reprefentation of thofe precife Ideas. But
then
then in the Application of Definitions to particu-
lar Names, we are altogether left to our own free
Choice. Becaufe as the connecting of any Idea
with any Sound, is a perfectly arbitrary Inftitu-
tion ; the applying the Defcription of that Idea,
to that Sound, muft be fo too. When therefore
Logicians tell us, that the Definition of the
Name is arbitrary, they mean no more than this;
that as different Ideas may be connected with
any Term, according to the good Pleafure of him,
that ufes it, in like manner may different De-
fcriptions be applied to that Term, fuitable to
the Ideas fo connected. But this Connection
being fettled, and the Term confidered as the
Sign of fome fixed Idea in the Understanding,
we are no longer left to arbitrary Explications,
but muft ftudy fuch a Defcription as correfponds
^with that precife Idea. Now this alone, accord-
ing to what has been before laid down, ought to
be accounted a Definition. What I am apt to
think has occafioned no fmall Confufion in this
Matter, is j that many Explanations of Words,
where no Idea is unfolded, but merely the Con-
nection between fome Word and Idea afiertedj,
have yet been dignified with the Name of Defi-
nitions. Thus in the Inftance before given, when
we fay that a Clock is an Instrument by which we
meafure Time: this is by fome called a Definition,
And yet it is plain, that we are beforehand fup-
pofed to have an Idea of this Inftrument, and
G 3 only
( 1*6 }
nly taught that the Word Clock^ ferves in com-
mon Language to denote that Idea. By this Rule
all Explications of Words in our Dictionaries
will be Definitions, nay, as was already ob-
ferved, the Names of even fimple Ideas may be
thus defined. White we may fay is the Colour
we obferve in Snow or Milk, Heat the Senfation
produced by approaching the Fire, and fo in
innumerable other Inftances. But thefe, and
all others of the like kind, are by no means De-
finitions, exciting new Ideas in the Underftand-
ing, but merely Contrivances to remind us of
known Ideas, and teach their Connection with
the eftablifhed Names. It is neverthelefs worth
our Notice, that what Logicians call Definitions
of the Name, extend properly no farther than
ihefe Explanations, ferving to mark the Con-r
ne6lion of our Ideas and Words ; and are there-
fore juftly accounted arbitrary, inafmuch as the
Connections themfelves are altogether fo.
Complex ideal XI X. BUT now in Definitions
kne capable p rO perly fo called, we firft confider
/ that Kind * J
/ Description the Term we ufe, as the bign of
* me i nwar d Conception, either an-
Dtfinition. nexed to it by Cuftom, or our own
free Choice j and then the Bufinefs of the Defi-
nition is to unfold and explicate that Idea. As
therefore the whole Art lies, in giving juft and
true Copies of our Ideas ; a Definition is then
faid to be perfect, when it ferves diftinclly to ex-
cite
( "7 )
cite the Idea described in the Mind of another,
even fuppofing him before wholly unacquainted
with it. This Point fettled, let us next enquire
into what thofe Ideas are, which are capable of
being thus unfolded. And in the firft Place it
is evident, that all our fimple Ideas are necefla-
rily excluded. We have feen already, that Ex-
perience alone is to be confulted here, infomuch
that if either the Objects whence they are de-
rived come not in our Way, or the Avenues ap-
pointed by Nature for their Reception are want-
ing, no Defcription is fuificient to convey them
into the Mind. But where the Underftanding
is already fupplied with thefe original and pri-
mitive Conceptions, as they may be united to-
gether in an Infinity of different Forms; fo may
all their feveral Combinations be diftinclly laid
open by enumerating the fimplc Ideas concerned
in the various Collections, and tracing the Order
and Manner in which they are linked one to ano-
ther. Now thefe Combinations of fimple No-
tices conftitute what we call our complex
Notions j whence it is evident that complex
Ideas, and thofe alone, admit of that kind of
Defcription, which goes by the Name of a
Definition.
G 4 XX. THE
( 128 )
XX. THE Bufmefs of Definitions
e Z' y . now I think pretty plain. They
be fid to be are> as we have feen, Pi&ures or
fully unfolded.
Representations of our Ideas ; and
as thefe Reprefentations are then only poflible,
when the Ideas themfolves are complex ; it is
obvious to remark, that Definitions cannot have
place, but where we make ufe of Terms, {land-
ing for fuch complex Ideas. But perhaps the
Reader may ftill expedt, that we fhould enter a
little more particularly into the Nature of a De-
finition, defcribe its Parts, and Ihew by what
Rules it ought to proceed, in order to the Attain-
ment of its proper End. To give therefore what
Satisfaction we are able upon this Point, we muft
again call to mind, that the Defign of a Defi-
nition is, fo to unfold the Idea anfwering to any
Term, as that it may be clearly and diftindly
transferred into the Mind of another. But now
our complex Ideas, which alone are capable of
this kind of Defcription, being, as we have faid,
nothing more than different Combinations of
fimple Ideas ; we then know and comprehend
them perfedl y> when we know the feveral fimple
Ideas of which they confift, and can fo put
them together in our Minds, as is neceflary to-
wards the framing of that peculiar Connection,
which gives every Idea its diftinct and proper
Appearance,
XXI. Two
( '29 )
XXI. Two Things are therefore Two
i . T\ c. *. 17" n. required in a
required in every Definition, tirft, D y e jf nltilH .
that all the original Ideas, out of tnumeratt tbe
. Ideas, and
which the complex one is formed, explain the
be diftinflly enumerated. Second, g
ly, that the Order and Manner of nation.
combining them into one Conception, be clearly
explained. Where a Definition has thefe Re-
quifites, nothing is wanting to its Perfection ;
becaufe every one who reads it, and underftands
the Terms, feeing at once what Ideas he is to
join together, and alfo in what Manner, can at
pleafure form in his own Mind the complex
Conception anfwering to the Term defined.
.Let us, for inftance, fuppofe the Word Square,
to ftand for that Idea, by which we reprefent to
ourfelves a Figure, whofe Sides fubtend Qua-
drants of a circumfcribed Circle. The Parts of
this Idea, are the Sides bounding the Figure.
Thefe muft be four in Number, and all equal
among themfelves, becaufe they are each to
fubtend a fourth Part of the fame Circle. But
befides thefe component Parts, we muft alfo take
Notice of the Manner of putting them together,,
.if we would exhibit the precife Idea, for which
the Word Square here ftands. For four equal
right Lines, any how joined, will not fubtend
Quadrants of a circumfcribed Circle. A Figure
with this Property, muft have its Sides (landing
G 5 alfo
alfo at right Angles. Taking in therefore this
laft Confideration, refpefting the Manner of
combining the Parts, the Idea is fully defcribed,
and the Definition thereby rendered complete*
.For a Figure bounded by four equal Sides, join-
ed together at right Angles, has the Property
required ; and is moreover the only right-lined
Figure to which that Property belongs.
XXII. AND now I imagine it will
J/ow tut are
topioceidto be obvious to every one, in what
*J?6yrtr Manner we ought to proceed, in
Definitions. order to arrive at juft and adequate
Definitions. Firft, we are to take an exacl View
of the Idea to be defcribed, trace it to its origi-
nal Principles, and mark the feveral fun pie Per-
ceptions that enter into the Compofition of it.
Secondly, we are to confider the particular Man-
ner in which thefe elementary Ideas are com-
bined, in order to the forming of that precife
Conception, for which the Term we make ufe
of ftands. When this is done, and the Idea
wholly unravelled, we have nothing more to
do than fairly tranfcribe the Appearance it makes
to our own Minds. Such a Defcription, by dif-
tin&ly exhibiting the Order and Number of our
primitive Conceptions, cannot fail to excite at
the fame Time, in the Mind of every one that
reads it, the complex Idea refulting from them ;
and therefore attains the true and proper End of
a Definition.
CHAP.
CHAP. VII.
Of the Compofition and Refolution cf our
Ideas y and the Rules of Definition thence
arifing.
I. rpHE Rule laid down in the t ttnptu ^
A foregoing Chapter, is ge- ig our Ideas
i i- 11 /vi i /~i / *v e proceed by
neral, extending to all poflible Cafes j a f u ccefflve
and is indeed that to which alone Gradation.
we can have recourfe where any Doubt or Diffi-
culty arifes. It is not however neceflary, that
we fhould pra&ife k in every particular Inftance.
Many of our Ideas are extremely complicated,
infomuch that to enumerate all the fimple Per-
ceptions out of which they are formed, would
be a very troublefome and tedious Work. For
this Reafon, Logicians have eftabliflied certain
compendious Rules of defining, of which it
may not be amifs here to give fome Account.
But in order to the better underftanding of what
follows, it will be neceflary to obferve, that
there is a certain Gradation in the Compofition
of our Ideas. The Mind of Man is very limited
in its Views, and cannot take in a great Num-
ber of Obje&s at once. We are therefore fain to
proceed by Steps, and make our firft Advances
fubfervient to thofe which follow. Thus in
forming our complex Notions, we begin at firft
G6 \vith
with but a few fimple Ideas, fuch as we can
manage with Eafe, and unite them together into
one Conception. When we are provided with a
fufficient Stock of thefe, and have by Habit and
Ufe rendered them familiar to our Minds, they
become the component Parts of other Ideas ftill
more complicated, and form what we may call
a fecond Order of compound Notions. This
Procefs, as is evident, may be continued to any
degree of Compofition we pleafe, mounting from
one Stage to another, and enlarging the Num-
ber of Combinations.
II. BUT now in a Series of this
Hence Ideai of , >
this C'afs lift kind, whoever would acquaint him-
3KtSi felf p erfeai y with the Iaft and hi s h -
*>ance gradu- eft Order of Ideas, finds it much the
flfy through n ... . .- . . .
Wtbtjtvtral moft expeditious Method, to pro-
Crden. cee j gradually through all the inter-
mediate Steps. For was he to take any very com-
pounded Idea to pieces, and without regard to
the feveral Clafles of fimple Perceptions, that
have already been formed into diflinft Combina-
tions, break in at once into its original Princi-
ples, the Number would be fo great as perfe&ly
to confound the Imagination, and overcome the
utmoft Reach and Capacity of the Mind. When
\ve fee a prodigious Multitude of Men, jumbled
together in Crowds, without Order, or any re-
gular Pofition, we find it impoflible to arrive at
an exaft Knowledge of their Number. But if
they
they are formed into feparate Battalions, and fa
ftationed as to fall within the leifurely Survey of
the Eye ; by viewing them fucceflively, and in
Order, we come to an eafy and certain Deter-
mination. It is the fame in our complex Ideas*
When the original Perceptions, out of which
they are framed, are very numerous, it is not
enough that we take a View of them in loofe
and fcattered Bodies. We muft form them into
diftinct Clafies, and unite thefe Clafles in a juft
and orderly Manner, before we can arrive at a
true Knowledge of the compound Notices re-
fulling from them.
III. THIS gradual Progrefs of the
.. , . j -KT Our Defa!tioHI
Mind to its compound Notions, ought to kiep
through a Variety of intermediate ***
* Ideat, and ob~
Steps, plainly points out the manner ferveoiike
of conducting the Definitions by
which thefe Notions are conveyed into the Minds
of others. For as the Series begins with fimple-
and eafy Combinations, and advances through a
Succefiion of different Orders, rifing one above
another in the Degree of Compofition - 3 it is evi-
dent that in a Train of Definitions expreiTIng
thefe Ideas, a like Gradation is to be obferved.
Thus the complex Ideas of the lovveft Order,
can no otherwife be defcribed, than by enume-
rating the fimple Ideas cut of which they are
made, and explaining the manner of their Union,
But then in the fecond, or any fucceeding Or-
der j
( 134 )
der; as they are formed out of thofe gradual Com-
binations, that conftitute the inferior Clafles, it
is not neceiTary in defcribing them, to mention
one by one, all the fimple Ideas of which they
confift. They may be more diftinftly and briefly
unfolded, by enumerating the compound Ideas
of a lower Order, from whofe Union they re-
fult, and which are all fuppofed to be alVeady
known, in Confequence of previous Definitions.
Here then it is, that the Logical Method of de-
fining takes Place ; which that we may the
better underftand, I fhall explain fomewhat more
particularly, the feveral Steps and Gradations of
the Mind, in compounding its Ideas, and thence
deduce that peculiar Form of a Definition, which
Logicians have thought fit to eftabliih.
IV. ALL the Ideas we receive,
from the feveral Obeds of Nature
Mid proceed* t h at furround us, reprefent diftinft
jromfarticular
togenual Individuals. Thefe Individuals,
ideas ' when compared together, are found
in certain Particulars to refemble. Hence, by
collecting the refembling Particulars into one
Conception, we form the Notion of a Species.
And here let it be obferved, that this laft Idea
is lefs complicated than that by which we re-
prefent any of the particular Objects contained
under it. For the Idea of the Species excludes
the Peculiarities of the feveral Individuals, and
retains only fuch Properties as are common to
them
( '35 )
them all. Again, by comparing feveral Species
together, and obferving their Refemblance, we
form the Idea of the Genus ; where in the fame
Manner as before, the Compofition is lefiened,
becaufe we leave out what is peculiar to the fe-
veral Species compared, and retain only the par-
ticulars wherein they agree. It is eafy to con-
ceive the Mind, proceeding thus from one Step
to another, and advancing through its feveral
Clafles of general Notions, until at laft it comes
to the higheft Genus of all, denoted by the
Word Being, where the bare Idea of Exiftence
is only concerned.
V. IN this Procedure we fee the 7te (^ niltft
Mind unravelling a complex Idea oftbtMindm
i . ... _ ,. r> i c impeundinrits
and tracing it in the afcending scale, ideas, as it ad-
from greater to lefs Degrees of Com- ? c " th '' ' tbe
~ t aiferentOrdtn
poution, until it terminates in one / Perception.
fimple Perception. If now we take the Series
the contrary Way, and beginning with the laft
or higheft Genus, carry our View downwards,
thro' all the inferior Genera and Species, quite
to the Individuals j we fhall thereby arrive at a
diftinit Apprehenfion of the Conduct of the
Underftanding in compounding its Ideas. For
in the feveral Clafles of our Perceptions, the
higheft in the Scale, is for the moft Part made
up of but a few fimple Ideas, fuch as the Mind
can take in and furvey with Eafe. This firft
general
( 136 )
general Notion, when branched out into the
different Subdivisions contained under it, has
in every one of them fomething peculiar, by
which they are diftinguifhed among themfelves ;
infomuch that in defcending from the Genus
to the Species, we always fuperadd fome new
Idea, and thereby increafe the Degree of Com-
pofition. Thus the Idea denoted by the Word
Figure^ is of a very general Nature, and com-
pofed of but few fimple Perceptions, as implying
no more than Space every where bounded. But
if we defcend farther, and confider the Boun-
daries of this Space, as that they may be either
Lines or Surfaces, we fall into the feveral Spe-
cies of Figure. For where the Space is bounded
by one or more Surfaces, we give it the Name
of zfolid Figure ; but where the Boundaries are-
.Lines, it is called a plain Figure,
f be Idea of ^I I N this View of Things it is
the Sfteiei evident, that the Species is formed by
formed by fa- * f '
ft,add\r,g tie fuperadding a new Idea to the Genus.
Here for Jnftance, the Genus is
circumfcribcd Space. If now to !
this we fuperadd the Idea of a Circumfcription
ty Line, we frame the Notion of that Species of
Figures which are called plain ; but if we con-
ceive the Circumfcription to be by Surfaces,
we have the Species of fo/id Figures. This fuper-
added Idea is called ti\e fpecifick Difference, not
3 only
( 137 )
nly as It ferves to divide the Species from the
Genus, but becaufe being different in all the fe-
veral Subdiviflons, we thereby alfo diftinguifh
the Species one from another. And as it is like-
wife that Conception, which by being joined to
the general Idea, compleats the Notion of the
Species', hence it is plain that the Genus and
Specifick Difference are to be confidered as the
proper and conftituent Parts of the Species. If
we trace the Progrefs of the Mind ftill farther,
and obferve it advancing thro' the inferior Spe-
cies, we (hall find its manner of proceeding to
be always the fame. For every lower Species
is formed by fuperadding fome new Idea to the
Species next above it; infomuch that in this
. defcending Scale of our Perceptions, the Under-
ftanding pafles thro' different Orders of complex
Notions, which become more and more com-
plicated at every Step it takes. Let us refume
here, for inftance, the Species of plain Figures.
They imply no more than Space bounded by
Lines. But if we take in an additional Confi-
deration of the Nature of thefe Lines, as whe-.
ther they are Right or Curves, we fall into the
Subdivifions of plain Figure, diftinguilhed by
the Names Reftilinear, Curvilinear? and Mlx-
tilinear.
VII. AND here we are to obferve, And in ail the
that tho' plain Figures when con- '"f tri9r s f e ~
cut by fupsr-
fidcred as one of thofe Branches that adding the
come.
( 13* )
come under the Notion of Figure in
Sfttifiek Dif-
fertnce to the general, take the Name of a bpe-
*urefl CM,. cies . yet CO mpared with the ClafTes
of Curvilinear, Re&ilinear, and Mixtilinear,
into which they themfelves may be divided, they
really become a Genus, of which the before-
mentioned Subdivifions conftitute the feveral
Species. Thefe Species, in the fame manner as
in the Cafe of plain and folid Figures, confift
of the Genus and fpecifick Difference as their
conftituent Parts. For in the Curvilinear Kind,
the Curvity of the Lines bounding the Figure,
makes what is called \hefpecifick Difference ; to
whicn if we join the Genus, which here is plain
Figure, or Space circumfcribed by Lines, we
have all that is necefTary towards completing
the Notion of the Species. We are only to take
Notice, that this laft Subdivifion, having two
Genera above it, viz. plain Figure, and Figure
in general ; the Genus joined with the fpecifick
Difference, in order to conftitute the Species of
Curvilinear*, is that which lies neareft to the
faid Species. It is the Notion of plain Figure,
and not of Figure in general', that joined with
the Idea of Curvity, makes up the complex Con-
ception of Curve-lined Figures. For in this de-
fcending Scale of our Ideas ; Figure in general^
plain Figures^ Curve-lined Figures^ the two firft
are confidered as Genera in refpeit of the third ;
and the fecond in order, or that which (lands
next
( '39 )
next to the third, is called the ntareft Genus.
But now as it is this fecond Idea, which joined
with the Notion of Curvity, forms the Species of
Curve-lined Figures ; it is plain, that the third
or laft Idea in the Series, is made up of the
nearejl Genus cindfpectfici Difference. This Rule
holds invariably, however far the Series is con-
tinued ; becaufe in a Train of Ideas thus fuc-
ceeding one another, all that precede the laft
are conildered as fo many Genera in refpecl: of
that laft, and the laft itfelf is always formed,
by fuperadding the fpecifick Difference to the
Genus next it.
VIII. HERE then we -have an ne idea of
univerfal Defcription, applicable to "* J H ^ td al
r compofcd of
all our Ideas of whatever kind, from the
the higheft Genus to the loweft
Species. For taking them in order /
downwards from the faid general Idea, they
every where confift of the Genus proximum y and
Differentia fpecifica^ as Logicians love to exprefs
themfelves. But when we come to the loweft
Species of all, comprehending under it only In-
dividuals, the fuperadded Idea, by which thefe
Individuals are diftinguifhed one from another,
no longer takes the name of the fpecifick Dif-
ference. For here it ferves not to denote dif-
tindt Species, but merely a Variecy of Indivi-
duals, each of which having a particular exif-
tence of its own, is therefore numerically dif-
feren
( '40 )
ferent from every other of the fame Kind. And
hence it is, that in this laft Cafe, Logicians
chcofe to call the fuperadded Idea by the Name
of the numerical Difference ; infomuch that as
the Idea of a Species, is made up of the nearejl
Genus zndfpecijjcfc Difference^ fo the Idea of an
Individual, confifts of the loweji Species and -
merick Difference. Thus the Circle is a Species
of Curve-lined Figures, and what we call the
loivejl Species^ as comprehending under it only
Individuals. Circles in particular are diftin-
guiftied from one another by the Length and
Pofition of their Diameters. The Length there-
fore and Pofition of the Diameter of a Circle,
is what Logicians call the numerical Difference ;
becaufe thefe being given, the Circle itfelf may
be defcribed, and an Individual thereby con-
flicted.
IX. AND thus we have endea-
Definitttni t , i i n
follow out voured to trace, in the belt manner
e are a bj e t h e p rO ff re f s o f tne
Train, and
faf, tbro" the Mind in compounding its Ideas.
"if ^ begins we fee with the moft gene-
tur compound ra ] Notions, which confifting of but
a few fimple Notices, are eafily
combined and brought together into one Con-
ception. Thence it proceeds to the Species
comprehended under this general Idea, and
thefe are formed by joining together the Genus-
and fpecif.ck Difference, And as it often hap-
pens,
Jpens, that thefe Species may be flill further
fubdivided, and run on in a long Series of con-
tinued Gradations, producing various Orders
of compound Perceptions j fo all thefe feveral
Orders are regularly and fucceffively formed,
fey annexing in every Step, the fpecifick Diffe-
rence to the mareji Genus, When by this Me-
thod of Procedure, we are come to the lowed
Order of all j by joining the Species and numerick
Difference^ we frame the Ideas of Individuals.
And here the Series neceflarily terminates, be-
caufe it is impofiible any farther to bound or
limit our Conceptions. This View of the Com-
pofition of our Ideas, reprefenting their confti-
tuent Parts in every Step of the Progrefllon, na-
turally points out the true and genuine Form of
a Definition, For as Definitions are no more
than Defcriptions of the Ideas for which the
Terms defined ftand ; and as Ideas are then de-
fcribed, when we enumerate diftinftly and in
Order, the Parts of which they confift j it is
plain, that by making our Definitions follow
one another, according to the natural Train of
our Conceptions, they will be fubjecl: to the
fame Rules, and keep pace with the Ideas they
defcribe.
X. As therefore the firft Order of rtt Formcfa
cur compound Notions, or the Ideas Dfiinon
. n . i i i n /- > a '' '^' farioui
that conititute the nigheit Lrenera, Orders of Con-
in, the different Scales of Perception, /"'
arc
are formed, by uniting together a certain Nunr-
ber of finiple Notices j fo the Terms expreffing
thefe Genera, are defined by enumerating the/tmple
Nttices fo combined. And as the Species com-
prehended under any Genus, or the complex
Ideas of the fecond Order, arife from fuper-
adding the fpecifick Difference, to the faid ge-
neral Idea ; fo the Definition of the Names of
the Species is abfolved, in a Detail of the Ideas
ef the fpecifick Difference, connefted with the Term
of the Genus. For the Genus having been before
defined, the Term by which it is exprefled
(lands for a known Idea, and may therefore be
introduced into all fubfequent Definitions, in
the fame manner as the Names of fimple Per-
ceptions. It will now I think be fufficiently
obvious, that the Definitions of all the fuc-
ceeding Orders of compound Notions, will
every where confift of the Term of the nearejl
Genus joined with an Enumeration of the Ideas
that conftitute the fpecijlck Difference ; and that
the Definition of Individuals, unites the Name of
the lowejl Species, with the Terms by which we ex~
prefs the Ideas of the numerick Difference.
Tie Logical XI. Here then we have the true
ofde- anc i proper Form of a Definition, in
f mug perf eft .
in its Kind. all the various Orders of Concep-
tion. This is that Method of Defining, which
is commonly called Logical, and which we fee is
perfect in its kind, inafmuch as it prefects a full
and
( 143 )
*md adequate Defcription of the Idea, for whick
the Term defined ftands. There are ftill two
Things worthy of Obfervation, before we take
leave of this Subject. Firft, that the very Frame
and Contexture of thefe Definitions, points out
the Order in which they ought to follow one
another. For as the Name of the Genus is ad-
mitted into a Defcription, only in confequence
of its having been before defined ; it is evident,
that we muft pafs gradually through all the
different Orders of Conception. Accordingly,
Logicians lay it down as a Rule, that we are
to begin always with the higheft Genus, and
carry on the Series of Definitions regularly,
thro' all the intermediate Genera and Species,
quite down to the Individuals. By this means
our Defcriptions keep pace with our Ideas, and
pafs through the fame fucceflive Gradations ;
infomuch, that the Perufal of them muft excite
thofe Ideas in the Underftanding of another,
in the very Order and Manner in which they
are put -together by the Mind, in its uniform
Advances from fimple to the moft complicated
Notions. Now this is the true and proper End
of Defining, and indeed the higheft Perfection
of that Art.
XII. THERE is yet another . , ^
f And applicable
Thing to be obferved on this Head, to all Words
^.u . *.\- T> wbatfoevir,
namely; that the Form here pre- capable of a
/crjbed, is applicable to all Words De fi n t9 '
2 whatfo-
"whatfoever, capable of a Definition. For as
every Term we ufe, muft denote fome Idea,
either general or particular ; and as all our
complex Notions, relating to both thefe Clafles
of Perception, from the higheft Genus quite
down to the Individuals, come within the Rules
of Defcription here given j it is evident, that
this particular Manner of unfolding an Idea,
may be extended to all the pofiible complex
Conceptions we can connect with our Words.
By the Rules therefore of this Method, Defini-
tions may be applied to all Terms {landing
for complex Ideas ; and as thefe, by what we
have fliewn at large in the two foregoing Chap-
ters, are the only definable Articles of Speech ;
it neceflarily follows, that the Directions here
given are univerfal, extend to all particular In-
itances, and are alike applicable in all Lan-
guages. And thus at length, we have not only
deduced that peculiar Form of a Definition,
which obtains among Logicians, but fliewn it
-alfo to be perfect in its kind, and to take in the
whole Compafs of Language.
THE
( I4S )
THE
ELEMENTS
O f
LOGIC K.
BOOK II.
Of JUDGMENT 0r INTUITION.
CHAP. I.
Of the Grounds of human Judgment.
w:
ed with Ideas, its next Step fpeffi tie Re-
., TIT TJ- i j .1 lations he-
rn the Way to Knowledge is, the lvleen our
comparing thefe Ideas together, in Idtai v>he ' t
thy are \m-
order to judge of their Agreement mediately per-
orDifagreement. In this joint View ttlvabl <'
of our Ideas, if the Relation is fuch, as to be
immediately difcoverable by the bare Infpe&ion
of the Mind j the Judgments thence obtained are
H called
called intuitive, from a Word that denotes to look
at: for in this Cafe, a mere Attention to the
Ideas compared, fuffices to let us fee, how far
they are connected or disjoined. Thus, that the
Whole is greater than any of its Parts, is an intui-
tive Judgment, nothing more being required to
convince us of its Truth, than an Attention
to the Ideas of 'Whole and Part. And this too is
the Reafon, why we call the Ac} of the Mind
forming thefe Judgments, Intuition ; as it is in-
deed no more than an immediate Perception of
the Agreement or Difagreement of any two
Ideas.
Ixperunce ^* ^ UT nere lt IS tO ^ e bfcrved,
anj Ttjiimony tna t our Knowledge of this kind.re-
tbt Ground of _ . T . i i_ T
Judging at to fpects only our Ideas, and the Rela-
faRs. tions between them, and therefore
can ferve only as a Foundation to fuch Reafon-
ings, as arc employed in inveftigating thefe Rela-
tions. Now it fo happens, that many of our
Judgments are converfant about Fa&s, and the
real Exiftence of Things which cannot be traced
by the bare Contemplation of our Ideas. It does
not follow, becaufe I have the Idea of a Circle in
my Mind, that therefore a Figure anfwering to
that Idea, has a real Exiftence in Nature. I can
form to myfelf the Notion of a Centaur, or golden
Mountain, but never imagine on that account,
that either of them exift. What then are the
Grounds of our Judgment in relation to Fah ?
I anfwer,
( '47 )
I anfwer, thefe two : Experience and Tejlimony.
By Experience we are informed of the Exiftence
of the feveial Objects which furround us and
operate upon our Senfes. Tejlimony is of a wider
Extent, and reaches not only to Objects beyond
the prefent Sphere of our Obfervation, but alfo
to Facts and Tranfactions, which being now
paft, and having no longer any Exiftence, could
not without this Conveyance, have fallen under
our Cognizance.
III. HERE then we have three ^^ Foun _
Foundations of human Judgment, dathnt /-
from which the whole Syftem of our w?,,",'Vizf~
Knowledge may with Eafe and Ad- l ;
\ T" the Ground of
vantage be deduced, run Intuition, f
which refpefts our Ideas themfelves,
and their Relations, and is the Foundation of
that Species of Reafoning, which we call.De-
monflration. For whatever is deduced from our
intuitive Perceptions, by a clear and connected
Series of Proofs, is faid to be demonftrated, and
produces abfolute Certainty in the Mind. Hence
the Knowledge obtained in this manner, is what
we properly term Science ; becaufe in every Step
of the Procedure, it carries its own Evidence
along with it, and leaves no room for Doubt or
Hefitation. And what is highly worthy of No-
tice; as the Truths of this Clafs exprefs the Re-
lations between our Ideas, and the fame Rela-
tions muft ever and invariably fubfift between the
H 2 fame
fame Ideas, our Deductions in the way of Sci-
ence, conftitute what we call eternal, necefTary,
and immutable Truths. If it be true that the
Whole is equal to all its Parts, it muft be fo un-
changeably ; becaufe the Relations of Equality
being attached to the Ideas themfelves, muft ever
intervene where the fame Ideas are compared.
Of this Nature are all the Truths of natural Re-
ligion, Morality and Mathematics j and in ge-
neral whatever may be gathered from the bare
View and Confideration of our Ideas.
a. Exptrinc, IV ' THE fecond Ground of hu-
rt; Ground of man' Judgment is Experience : from
far Know-
ledge of ibe which we infer the Exiftence of thofe
S^inia'f Ob J eas that Around us, and fall
SoJiet. under the immediate Notice of our
Senfes. When we fee the Sun, or caft our Eyes
towards a Building, we not only have Ideas of
thefe Objects within ourfelves, but afcribe to
them a real Exiftence out of the Mind. It is alfo
by the Information of the Senfes that we judge
of the Qualities of Bodies j as when we fay that
Snow is white, Fire hot, or Steel hard. For as
we are wholly unacquainted with the internal
Structure and Conftitution of the Bodies that
produce thefe Senfations in us, nay, and are un-
able to trace any Connection between that Struc-
ture and the Senfations themfelves, it is evident,
that we build our Judgments altogether upon
Obfcrvation, afcribing to Bodies fuch Qualities
as
( H9 )
as are anfwerable to the Perceptions they excite
in us. But this is not the only Advantage de-
rived from Experience, for to that too are we
indebted for all our Knowledge regarding the
Co-exiftence of fenfible Qualities in Objects,
and the Operations of Bodies one upon another.
Ivory, for inftance, is hard and elaftic ; this
we know by Experience, and indeed by that
alone. For being altogether Strangers to the
true Nature both of Elafticity and Hardnefs,
we cannot by the bare Contemplation of our
Ideas determine how far the one neceflarily
implies the other, or whether there may not be
a Repugnance between them. But when we
obferve them to exift both in the fame Objecl,
we are then aflureu from Experience, that they
iire not incompatible j and when we alfo find,
that a Stone is hard and not elaftic, and that
Air though elaftieis not hard, we alfo conclude
upon the fame Foundation, that the Ideas are
not neceflarily conjoined, but may exift fepa-
rately in different Objects. In like manner with
regard to the Operations of Bodies one upon
another, it is evident that our Knowledge this
Way is all derived from Obfervation. Aqua Re-
gia diflblves Gold, as has been found by frequent
Trial, nor is there any other Way of arriving at
the Difcovery. Naturalifts may tell us if they
pleafe, that the Parts of dqua Regia are of a
H 3 Texture
Texture apt to infmuate between the Corpufcles
of Gold, and thereby loofen and (hake them
afunder. If this is a true Account of the Matter,
I believe it will notwithftanding be allowed, that
our Conje&ure in regard to the Conformation
of thefe Bodies is deduced from the Experiment,
and not the Experiment from the Conjecture. It
was not from any previous Knowledge of the in-
timate Structure of Aqua Regla and Gold^ and the
Aptnefs of their Parts to a<3: or be acted upon,
that we came by the Conclufion above mentioned.
The internal Cohftitution of Bodies is in a man-
ner wholly unknown to us ; and could we even
furmount this Difficulty, yet as the Separation of
the Parts of Gold implies fomething like an ac-
tive Force in the Menflruum^ and we are unable
to conceive how it comes to be poflefled of this
Activity; the Effect muft be owned to be alto-
gether beyond our Comprehenfion. But when
repeated Trials had once confirmed it, infomuch
that it was admitted as an eftabliflied Truth in
Natural Knowledge, it was then eafy for Men
to fpin out Theories of their own Invention, and
contrive fuch a Structure of Parts both for Gold
and Aqua Regia, as would beft ferve to explain
the Phenomenon, upon the Principles of that
Syftem of Philofophy they had adopted. I might
eafily (hew from innumerable other Inftances,
how much our Knowledge of the mutual Ac-
tion
tion of Bodies depends, upon Obfervation. The
Bite of a Viper will kill. Plants are fome falu-
tary, others noxious. Fire diflblves one Body,
and hardens another. Thefe are Truths gene-
rally known, nor is it lefs evident, that we owe
their Difcovery wholly to Experience.
V. AND hence it is eafy to ac- .,
rr py many
count for what to fome Writers has /<// /-
n i i tioni owe their
appeared a very great Paradox j that Birtb ta
many of the moft important Inven- Chance.
tions in human Life have taken their Rife from
Chance, and inftead of coming out of the Schools
of Philofophers, are for the moft part afcribed
to Men of no Figure in the Commonwealth of
Learning. Sowing, Planting, the Ufe of the
Compafs, and fuch like, are not Deductions of
human Reafon, but Difcoveries which owe their
Birth to Obfervation and Trial. No wonder
therefore, if thefe Inventions derived their Be-
ginning from fuch as being engaged in the ac-
tive and bufy Scenes of Life, were more in the
Way of thofe Experiments which lead to Difco-
veries of this Nature. And here, as the parti-
cular Callings and Profeflions of Men, and oft-
times Chance, has a great Afcendant, it need not
feem ftrange, if fome of the moft ufeful Arts in
Society appear to haye had an Original purely
cafual.
H 4 VI. FROM
( 152 )
VI. FROM what has been faid it
Natural . . .
is evident, that as Intuition is the
Foundation of what we call fdenti-
wbicb it reft fi ca l Knowledge, fo is Experience
*f>tly termed J f ,
Exferimentai or natural. V or this laft being
PMoftbj. who]ly taken up wjth the objeds
of Senfe, or thofe Bodies that conftitute the natu-
ral World : and their Properties, as far as we can
difcover them, being to be traced only by a long
and painful Series of Obfervations ; it is appa-
rent, that in order to improve this Branch of
Knowledge, we muft betake ourfelves to the
Method of Trial and Experiment. Accordingly
we find, that while this was neglected, little
Advance was made in the Philofophy of Nature ;
whereas a contrary Proceeding has inriched the
prefent Age with many valuable Difcoveries j
infomuch that Natural Knowledge, in Allufion
to the Foundation on which it {rands, has been
very aptly called Experimental Philofophy.
Tbotigb much VII. BUT though Experience is
/ -rr
we ma term l ^ e ' mrnet ^' ate
depends an Foundation of Natural Knowledge,
Ttflimeny, yet r _ t T-
Exferiirceii yet with refpect to particular rer-
tbi ultimate fo j ts i n fl uence j s ver y narrow
Foundation of
it. and confined. The Bodies that fur-
round us are numerous, many of them lie at a
great Diftance, and fome quite beyond our
Reach. Life too is fhort, and fo crouded with
Cares,
( '53 )
Cares, that but little Time is left for any fingle
Man to employ himfelf in unfolding the Myf-
teries of Nature. Hence it is necefTary to ad-
mit many Things upon the Teftimony of others,
which by this means becomes 'the Foundation
of a great Part of our Knowledge of Body. No
Man doubts of the Power of Aqua Regia to dif-
folve Gold, though perhaps he never himfelf
made the Experiment. In thefe therefore, and
fuch like Cafes, we judge of the Facts and Ope-
rations of Nature, upon the mere Ground of
Teftimony. However, as we can always have
recourfe to Experience where any Doubt or
Scruple arifes, this is juftly confideredas the true
Foundation of Natural Philofophy ; being indeed
the ultimate Support upon which our Aflent refts,
and whereto we appeal, when the higheft Degree
of Evidence is required.
VJII. BUT there are many Facts 3 . r t fti m y,
that will not allow of an Appeal to t ^.^ rot " l , d /
r Hijtoncal
the Senfes, and in this Cafe Tefti- Knowledge.
mony is the true and only Foundation of our
Judgments. AH human Actions-, of whatever
Kind, when considered as already part, are of tht*
Nature here defcribed ; becaufe having now no
longer any Exiftence, both the Facts themfelves,.
and the Circumftances attending them, can be
known only from the Relations of fuch as had
fufficient Opportunities of arriving at the Truth.
Tejtimony therefore is juftly accounted a third
H 5 Ground
( '54 )
Ground of human Judgment; and as from the
other two we have deduced fdentijical and natural
Knowledge, fo may we from this derive htftori-
cal- t by which I would be underftood to mean,
not merely a Knowledge of the civil Tranfadions
of States and Kingdoms, but of all Fac"ls whatfo-
ever, where Teftimony is the ultimate Founda-
tion of our Belief.
IX. BEFORE I conclude this Chap-
Tbeficor.d .
of ter, it will be neccflary to obferve ;
the Mind, that tho , the fecond Operation o f t h e
commonly ex-
tended btyond Mind, properly fpeaking, extends
not beyond intuitive Perceptions,
yet Logicians have not confined themfelves to fo
flri& a View of it j but calling it by the Name
Judgment, thereby denote all Ah of the Mind,
where only two- Ideas are compared, without the
immediate Interpofition of a third. For when the
Mind joins or feparates two Ideas tho' perhaps
this is done in confequence of a Train of pre-
vious Reafoning, yet if the Underftanding pro-
ceeds upon eftablifhed Notions, without attend-
ing to that Train of Reafoning, its Determina-
tions are ilill confidered as A&s of Judgment.
Thus, that God created the Univerfe, that Men are
accountable for their Attions^ are frequently men-
tioned by Logicians, as Inftances of the Mind
judging. And yet it is apparent, that thefe Judg-
ments are by no means of the Kind we call in-
g tuitive j
C 155 )
tuitive ; nay, that it requires much Exercife of
the Reafoning Faculty, before a Man can trace
their Connection with the Perceptions of that
Name. I could in the fame manner eafily fliew,
that even our Judgments of Experience and Tef-
timony, when purfued to their Source, derive all
their Power of Perfuafion, from being linked
with intuitive Truths. But I fhall wave this
Enquiry for the prefent, as being of a Nature
too fubtile for a Work of this kind. The Re-
mark itfelf however was needful, as well to illuf-
trate the proper Diftin&ion between the Powers
of the Underibnding, as to explain the Reafon,
why in this Part of Logick, we extend the fe-
cond Operation of the Mind beyond thofe Li-
mits, that in Striclnefs of Speech belong to it.
Let us now proceed to confider a Jittle more par-
ticularly the Nature and Variety of thefe our
Judgments.
CHAP. I
Of Affirmative and Negative
I. "\ T 7" H I L E the comparing
VV ofourldeasisconfidered S
merely as an AcT: of the Mind, af- f a Pnpofi-
f . ,. , .... tion explaintd*
fembhng them together, and joining
H6 or
( 156 )
or disjoining them according to the Refult of its
Perceptions, we call it Judgment ; but when our
Judgments are put into Words, they then bear
the N ame of Proportions. A Proportion there-
fore is a Sentence expreffing fome Judgment of
the Mind, whereby two or more Ideas are affirm-
ed to agree or difagree. Now as our Judgments
include at leaft two Ideas, one of which is affirm-
ed or denied of the other, fo muft a Proportion
have Terms anfwering to thefe Ideas. The
Idea of which we affirm or deny, and of courfe
the Term exprefling that Idea, is called the Sub-
jeff of the Propofition. The Idea affirmed or
denied, as alfo the Term anfwering it, is called
the Predicate. Thus in the Propofition, God is
omnipotent: God is the Subject, it being of him
that we affirm Omnipotence j and omnipotent is
the Predicate, becaufe we affirm the Idea, ex-
preffed by that Word, to belong to God.
, H- BUT as in Propofltiom, Ideas
arc either joined or disjoined ; it is
not enough to have Terms expreffing thofe Ideas,
unlefs we have alfo fome Words to denote their
Agreement or Difagreement. That Word in
a Propofition, which connects two Ideas together,
is called the Copula; and if a negative Particle be
annexed, we thereby underftand that the Ideas
are disjoined. The Subftantive Verb is common-
ly made ufe of for the Copula, as in the above-
men-
( 157 )
mentioned Propofition God is omnipotent ; where
it reprefents the Copula, and fignifies the Agree-
meht of the Ideas of God and Omnipotence* But
if we mean to feparate two Ideas j then, befides
the Subftantive Verb, we muft alfo life fome
Particle of Negation, to exprefs this Repug-
nance. The Propofition, Man is not perfect ;
may ferve as an Example of this kind, where
the Notion of Perfeflion, being removed from
the Idea of Man, the negative Particle not is in-
ferted after the Copula, to fignify the Difagree-
ment between the Subjedl and Predicate.
III. EVERY Propofition necefla-
rily confifts of thefe three Parts, fgg^,
but then it is alike needful that pn/ed by a
they be all feverally exprefled in
Words ; becaufe the Copula is often included
in the Term of the Predicate, as when we fay,
be Jtts ; which imports the fame as he is fitting.
In the Latin Language, a fingle Word has often
the Force of a whole Sentence. Thus ambulat
is the fame, as tile eft ambulans ; amo, as ego fum
amans ; and fo in innumerable other Inftances ;
by which it appears, that we are not fo much
to regard the Number of Words in a Sentence,
as the Ideas they reprefent, and the Manner in
which they are put together. For whenever
two Ideas are joined or disjoined in an Expref-
fion, though of but a fingle Word, it is evi-
dent that we have a Subject, Predicate, and
Copula,
( 158 )
Copula, and of confequence a complete Pro-
pofition.
IV. WHEN the Mind joins two
jQfK' motive T , 1 1 ,. or
*d negttnii Ideas, we call it an affirmative
Propojitttnt. Judgment j when it feparates them,
a negative j and as any two Ideas compared to-
gether, muft necefTarily either agree or not
agree, it is evident, that all our Judgments fall
under thefe two Divifions. Hence, likewife,
the Propofitions expreffing thefe Judgments,
are all either affirmative or negative. An af-
firmative Proportion connects the Predicate
with the Subject, as a Stone is heavy ; a nega-
tive Propofition feparates them, as God is not
the Author of Evil. Affirmation therefore is the
fame as joining two Ideas together, and this
is done by means of the Copula. Negation on
the contrary marks a Repugnance between the
Ideas compared, in which Cafe a negative Par-
ticle muft be called in, to fhew that the Con-
nection included in the Copula does not tak
place.
Wben the ne- V. AND hence we fee the Reafon
J??" of the Rule commonly laid down
Idtai. by Logicians ; that in all negative
Propofitions, the Negation ought to affect the
Copula. For as the Copula, when placed by
itfelf, between the Subject and the Predicate,
manifestly binds them together j it is evident,
that in order to render a Proportion ne-
gative,
( 159 )
gative, the Particle of Negation muft enter it in
fuch Manner, as to deftroy this Union. In a
Word, then only are two Ideas disjoined in a
Propofition, when the negative Particle may be
fo referred to the Copula, as to break the Affir-
mation included in if, and undo that Connec-
tion it would otherwife eftablifh. When we fay,
for Inftance, No Man is per f eft ; take away the
Negation, and the Copula of itfelf plainly unites
the Ideas in the Propofition. But as this is the
very Reverfe of what is intended, a negative
Mark is added, to fhew that this Union does
not here take place. The Negation, therefore,
by deftroying the Effect of the Copula, changes
the very Nature of the Propofition, infomuch
that inftead of binding two Ideas together, it de-
notes their Separation. On the contrary, in
this Sentence ; The Man who departs not from an
upright Behaviour, is beloved of God : the Predi-
cate, beloved of God) is evidently affirmed of the
Subject, an upright Man, fo that notwithftand-
ing the negative Particle, the Propofition is ftill
affirmative. The Reafon is plain j the Nega-
tion here affects not the Copula, but making
properly a Part of the Subject, ferves with other
Terms in the Sentence, to form one complex
Idea, of which the Predicate, beloved of God, is
directly affirmed. This perhaps to fome may
appear a mere Logical Refinement, contrived to
juftify
( 160 )
juftify the Scholaftic Rule for diflinguifliing be-
tween affirmative and negative Propofidons.
But if it be confidered, that this Diftinftion is
of great Importance in Reafoning, and cannot
in many Cafes be made with Certainty but by
means of this Criterion here given, the Reader
will fee fufficient Reafon for my taking fo much
Pains to iiluftrate it.
Hw * Co fu ia VI - PERHAPS it may ftill appear
tomes to be a Myftery, how a Copula can be faid
Part of a nt- , r> e r r
gative Pnpo- to be a rart of a negative Propou-
J lMn ' tion, whofe proper Bufinefs it is to
disjoin Ideas. This Difficulty however will
vanifh, if we call to mind, that every Judgment
implies a direct Affirmation, and that this Affir-
mation alone makes the true Copula in a Propo-
fition. But as our Affirmations are of two kinds,
viz. either of Agreement or of Difagreement,
between the Ideas compared; hence there is alfo
a twofold Expreffion of our Judgments. In the
Cafe of Agreement, the Copula alone fuffices,
becaufe it is the proper Mark whereby we de-
note an Identity or Conjunction of Ideas. But
where Perceptions difagree, there we muft call
in a negative Particle ; and this gives us to un-
derftand that the Affirmation implied in the
Copiua, is not of any Connection between the
Subject and Predicate, but of their mutual Op-
pofition and Repugnance.
CHAP.
CHAP. III.
Of Univerfal and Particular Proportions.
I. / I AH E next confiderable Divi- u; v ^ og O f
JL fion of Propofitions, is into P't>f"'"> KI
i /~\ T i ""* iint-vtrjal
univerfal and particular. Our Ideas, and fanicu-
according to what has been already lar '
obferved in the firft Part, are all fingular as they
enter the Mind, and reprefent individual Ob-
jects. But as by Abftra&ion we can render
them univerfal, fo as to comprehend a whole
Clafs of Things, and fometimes feveral Clafles
at once ; hence the Terms expreffing thefe
Ideas muft be in like manner univerfal. If
therefore we fuppofe any general Term to be-
come the Subject of a Propofition, it is evident,
that whatever is affirmed of the abftrat Idea
belonging to that Term, may be affirmed of all
the Individuals to which that Idea extends.
Thus when we fay, Men are mortal } we confi-
der Mortality, not as confined to one or any
Number of particular Men, but as what may
be affirmed without Reftriction of the whole
Species By this means the Propofition becomes
as general as the Idea which makes the Subject
of it, and indeed derives its Univerfality intirely
from that Idea, being more or lefs fo, according
as this may be extended to more or fewer Indi-
viduals.
viduals. But it is further to be obfcrved of" thefo
general Terms, that they fometimes enter a Pro-
pofition in their full Latitude, as in the Ex-
ample given above; and fometimes appear with
a Mark of Limitation. In this laft Cafe we are
given to underftand, that the Predicate agrees
not to the whole univerfal Idea, but only to a
Part of it ; as in the Propofition, Some Men art
wife: for here Wifdom is not affirmed of every
particular Man, but reftrained to a few of the
human Species.
II. Now from this different Ap-
Propofitiont
vniverfai pearance of the general Idea, that
J t fihfc'^,"b'- conftitutes the Subject of any Judg-
es a Mark of m ent, arifes the Divifion of Propo-
Xe/lriflieH.
fitions into univerfal and particular,
An univerfal Propofition is that, wherein the
Subjedl is Ibme general Term, taken in its full
Latitude, infomuch that the Predicate agrees to
all the Individuals comprehended under it, if it
denotes a proper Species ; and to all the feveral
Species and their Individuals, if it marks an Idea
of a higher Order. The Words, a//, every y
no, none, &c. are the proper Signs of this Uni-
verfality j and as they feldom fail to accompany
general Truths, fo they are the moft obvious
Criterion whereby to diflinguifh them. All Ani-
mals have a Power of beginning Motion. This is
an univerfal Propofition ; as we know from the
Word all t prefixed to the Subject Animal, which
denotes
( 163 )
denotes that it muft be taken in its full Extent.
Hence the Power of beginning Motion may be
affirmed of all the feveral Species of Animals; as
of Birds, Quadrupeds, Infe&s, Fifties, &c. and
of all the Individuals of which thefe different
dalles confift, as of this Hawk, that Horfe, and
fo for others.
III. A particular Propofition has Propofitknt
in like manner fome general Term t ar ' icul f r
ivbtrefome
for its Subject, but with a Mark of uaiverfai Sub-
-r 111 i t i f ff appeart
Limitation added, to denote, that \ hk a Mark
the Predicate agrees only to fome of f Limitation.
the Individuals comprehended under a Species,
or to one or more of the Species belonging to
any Gennc, and not to the whole univerfal Idea.
Thus, Some Stones are heavier than Iron ; Some
Men have an uncommon Share of Prudence. In the
laft of thefe Propofitions, the Subje&fome Men t
implies only a certain Number of Individuals,
comprehended under a fmgle Species. In the
former, where the Subject is a Genus, that ex-
tends to a great Variety of diftincl Chfks,fome
Stones may not only imply any Number of par-
ticular Stones, but alfo feveral whole Species
of Stones ; inafmuch as there may be not a few,
with the Property there defcribed. Hence we
fee, that a Propofition does not ceafe to be par-
ticular, by the Predicate's agreeing to a whole
Species, unlefs that Species, fmgly and dif-
tinflly corifidered, makes alfo the Subject of
which
which we affirm or deny. For if it belongs to
feme Genus, that has other Species under it,
to which the Predicate does not agree ; it is plain,
that where this Genus is that of which we affirm
or deny, the Predicate agreeing only to a Part of
it, and not to the whole general Idea, conilitutes
the Propofition particular.
dfurtindin- IV. HERE then we have a fure
f.lnkhCrit*. and infallible Mark, whereby to dif-
nwwbertby to '
dtfir.guift) be- tinguifti between univerfal and par-
fWt n un'f'tr- > T r TITL i.
fat^ndfartku- ticular Propoutions. Where the
l Prtftftitns. Predicate agrees to all the Indivi-
duals comprehended under the Notion of the
Subject, there the Propofition is univerfal j where
it belongs only to lome of them, or to fome of
the Species of the general Idea, there the Pro-
pofitioii is particular. This Criterion is of eafy
Application, and much fafer than to depend upon
the common Signs of <?//, every, forne^ none t
&c. becaufe thtfe being different in different
Languages, and often varying in their Signifi-
cation, are very apt in many Cafes to miflcad
the Judgment. Thus if we fay, All the Soldiers
when drawn up^ formed a Square of a hundred
Men a Side : it is evident, that the Predicate
cannot be affirmed of the feveral Individuals,
but of the whole collective Idea of the Subject ;
whence by the Rule given above, the Propofition
is not univerfal. It is true, Logicians lay down
many Obfei vations, to enable us to diftinguifti
aright
aright on this Head ; but if the Criterion here
given be duly attended to, it will be of more real
Service to us than an hundred Rules. For it is
infallible, and may be applied with Eafe j whereas
the Directions which we meet with in Treatifes
of Logick, being drawn for the moft Part from
the Analogy of Language, and common Forms
of Speech, are not only burdenfome to the Me-
mory, but often very doubtful and uncertain in
their Application.
V. THERE is ftill one Species of singular Pro.
Proportions that remains to be de- ftf'' ** -
tamed under
Icnbed ; and which the more deferves the Head of
our Notice, as it is not yet agreed a- Particulars.
mong Logicians, to which of the two Clafles
mentioned above, they ought to be referred. I
mean fingular Propositions j or thofe where the
Subject is an Individual. Of this Nature are the
following : Sir Ifaac Newton was the Inventor of
Fluxions j This Book contains many ufeful Truths,
What occafions fome Difficulty, as to the proper
Rank of thefe Propofitions, is ; that the Subject
being taken according to the whole of its Exten-
fion, they fometimes have the fame Effect in Rea-
foning, as Univerfals. But if it be confidered,
that they are in Truth the moft limited kind of
particular Propofitions, and that no Proportion,
can with any Propriety be called univerfal, but
where the Subject is fome univerfal Idea ; we
ihall not be long in determining to which Clafs
they
( 166 )
they ought to be referred. When we fay, Some
Books contain ufeful Truths ; the Propofition is
particular, becaufe the general Term appears
with a Mark of Reftri&ion. If therefore we fay,
This Book contains ufeful Truths ; it is evident
that the Propofition muft be ftill more particu-
lar, as the Limitation implied in the Word this,
isof_a more confined Nature, than in the for-
mer Cafe. I know there are Inftances, where
fmgular Propofitions have the fame Effect in
Reafoning, as Univerfals; yet is not this, by
reafon of any proper Univerfality, belonging to
them ; but becaufe the Conclufion in fuch Cafes
being always fmgular, may be proved by a mid-
dle Term which is alfo fmgular ; as I could ea-
fily demonftrate, were this a proper Place for
entering into a Difcuffion of that Nature.
Tb, fourfold VI - WE fee therefore, that all
DivifioH of Propofitions are either affirmative or
Proto/itlens. . .......
negative ; nor is it lels evident, that
in both Cafes, they may be universal or particular.
Hence arifes that celebrated fourfold Divifion
of them, into univerfal Affirmative^ and univer-
fal Negative ; particular Affirmative^ and parti'
cular Negative; which comprehends indeed all
their Varieties. The Ufe of this Method of dif-
tinguifhing them will appear more fully after-
wards, when we come to treat of Reafoning and
Syllogifm.
CHAP.
CHAP. IV.
Of Abjolute and Conditional Proportions.
I. nr^H E Objects about which we
J _ f DijtinSion f
JL are chiefly converfant in this Qua/iiits into
World, are all of a Nature liable to *
Change. What may be affirmed of
them at one time, cannot often at another; and
it makes no fmall Part of our Knowledge to dif-
tinguifh rightly thefe Variations, and' trace the
Reafons upon which they depend. For it is ob-
fervable, that amidft all the Viciflitudes of Na-
ture, fome things remain conftant and inva-
riable ; nor are even the Changes to which we
fee others liable, effected, but in confequence of
uniform and fteady Laws, which when known,
are fufficient to direct us in our Judgments about
them. Hence Philofophers, in diftinguifhing the
Objects of our Perception into various ClafTes,
have been very careful to note, that fome Pro-
perties belong effentially to the general Idea, fo
as not to be feparable from it but by deftroying
its very Nature ; while others are only acciden-
tal, and may be affirmed or denied of it, in dif-
ferent Circumftances. Thus, Solidity, a yellow
Colour, and great Weight, are confidered as
eflential Qualities of Gold j but whether it fhall
exift as an uniform conjoined Mafs, is not alike
necefTary.
( 168 )
jiece/Tary. We fee that by a proper Menftruum,
it may be reduced to a fine Powder ; and that
intenfe Heat will bring it into a State of Fufion.
II. Now from this Diverfity in
Hence a tor.Ji- *
dtrabu Diver- the feveral Qualities of Things,
ar ^ es a confiderablc Difference as
to the Manner of our judging about
them. For in the firft Place, all fuch Proper-
ties, as are infeparable from Obje&s, when
confidercd as belonging to any Genus or Spe-
cies, are affirmed abfofutely and without Re-
ferve of that general Idea. Thus we fay ; Gold
ts very weighty ; A Stone is hard', Animals have
a Power of Self-Motion. But in the Cafe of
mutable or accidental Qualities, as they depend
upon fome other Confideration, diftincl: from
the general Idea j that alfo muft be taken into
the Account, in order to form an accurate Judg-
ment. Should we affirm, for inftance, of fome
Stones, that they are very fufceptible of a rolling
Motion; the Propofition, while it remains in this
general Form, cannot with any Advantage be
introduced into our Reafonings. An Aptnefs
to receive that Mode of Motion flows from the
Figure of the Stone j which, as it may vary in-
finitely, our Judgment then only becomes ap-
plicable and determinate, when the particular
Figure of which Volubility is a Confequence,
is alfo taken into the Account. Let us then bring
in
C ^9 )
in this other Confideration, and the Proportion
will run as follows : Stones of afpherical Form are
eafily put into a rolling Motion. Here we fee the
Condition upon which the Predicate is affirmed,
and therefore know in what particular Cafes the
Propofition may be applied.
III. THIS Confideration of Pro- jv b - icb g - tvet
pofitions, refpe&ing the Manner in "/" " ihe '**
* . . Dtvijkn f
which the Predicate is affirmed of the Profofnions
SubjeS, gives rife to the Divifion of % %%
them into abfolute and conditional, /
Abfolute Propofitions are thofe, wherein we affirm
fome Property infeparable from the Idea of the
Subject, and which therefore belongs to it in all
poflible Cafes ; as, God is infinitely wife : Virtue
tends to the ultimate Happinefs of Man. But where
the Predicate is not neceflarily connected with
the Idea of the Subject, unlefs upon fome Con-
fideration diftint from that Idea, there the Pro-
pofition is called conditional. The Reafon of the
Name is- taken from the Suppofition annexed,
v/hich is of the Nature of a Condition, and may
be exprefled as fuch. Thus ; If a Stone is expofcd
to the Rays of the Su>i 9 it ivill contrail fome Degree
sf Heat. If a River runs in a very declining Chan-
nel-t its Rapidity will conflantly increafe.
IV. THERE is not any thing of
greater Importance in Philofophy, 2jJJ' g f ir "
than a due Attention to this Divi- tbit Divijion^
r ,. ,, r . f r at it rendtrt
iion or Propofitions. If we are care-
I ful
Proponent ful never to affirm Things abfolute-
dtttiminatt. ]y ? k u t -where the Ideas are infcpa^
rably conjoined ; and if in our other Judgments,
we diftin&ly mark the Conditions, which deter-
mine the Predicate to belong to the Subject ;
we fhall be the lefs liable to miftake, in applying
general Truths to the particular Concerns of
human Life. It is owing to the exact Obfervance
of this Rule, that Mathematicians have been fo
happy in their Difcovcrics ; and that what they
demonstrate of Magnitude in general, may be ap-
plied with Eafe in all obvious Occurrences.
V. THE Truth of it is, particu-
^ Propofitions are then known to be
Particulars tt true, when we can trace their Con-
nection with Unive; fuls ; and it is ac-
cordingly the great Bufmefs of Science, to find
out general Truths, that may be applied with
Safety in all obvious Infhnces. Now the great
Advantage arifing from determining with Care
the Conditions upon which one Idea may be
affirmed or denied of another, is this ; that there-
by particular Propofitions really become univer-
fal, may be introduced with Certainty into our
Reafonings, and ferve as Standards to conduct
and regulate our Judgments. To illuftrate this
by a familiar Inftance : If we fay, Some Water
aJts very forcibly > the Propofition is particular:
and as the Conditions on which this forcible
Action depends are not mentioned, it is as yet
uncertain
C 171 )
uncertain in what Cafes it may be applied. Let
us then fupply thefe Conditions, and the'Propo-
fition will run thus : Water conveyed infufficient
Quantity along a Jleep Defcent afts very forcibly.
Here we have an univerfal Judgment, inafmuch
as the Predicate forcible Aftion^ may be afcribed to
all Water under the Circumftances mentioned.
Nor is it lefs evident, that the Propofition in
this new Form, is of eafy Application ; and in
fact we find, that Men do apply it in Inftances
where the forcible Action of Water is required j
as in Corn-Mills, and many other Works of Art.
Thus we fee, in what manner we are to proceed,
in order to arrive at univerfal Truths, which is
the great End and Aim of Science. And indeed,
would Men take the fame Care, duly to exprefs
the Conditions on which they affirm and deny,
as Mathematicians do, in thofe Theorems which
they term hypothetical, I doubt not, but we
might be able to deduce many Truths, in other
Parts of Philofophy, with no lefs Clearnefs,
Force, and Perfpicuity, than has hitherto been
thought peculiar to the Science of Quantity.
I 2 CHAP.
CHAP. V.
Of Simple and Compound Propofitions.
I. "FTlTHERTO we have treated
p'r^poKt'tani J^ JL of Propofitions, where only
ititofimpu two Ideas are compared together.
and compound. f . ,
Thefe are in the general called fwi~
pie ; becaufe having but one Subject and one Pre-
dicate, they are the Effect of a fimple Judgment
that admits of no Subdivifion. But if it fo hap-
pens, that feveral Ideas offer themfelves to our
Thoughts at once, whereby we are led to affirm
the fame thing of different Objects, or different
things of the fame Object ; the Propofitions cx-
prefling thefe Judgments are called co?npound :
becaufe they may be refolved into as many
others as there are Subjects or Predicates in
the whole complex Determination of the Mind.
Thus : God is infinitely wife, and infinitely power-
ful Here there are two Predicates, infinite Wtf-
dom and infinite Powar^ both affirmed of the fame
Subject ; and accordingly, the Propofition may
be refolved into two others, affirming thefe Pre-
dicates feverally. In like manner in the Propo-
fition, Neither Kings nor People are exempt from
Death ; the Predicate is denied of both Subjects,
and may therefore be feparated from them, in
diftinct Propofitions. Nor is it kfs evident, that
if
( '73 )
if a complex Judgment confifts of feveral Sub-
jects and Predicates, it may be refolved into as
many fimple Propofitions as are the Number
of different Ideas compared together. Riches,
and Honours are apt to elate the Mind and increafs
the Number of our Defires. In this Judgment
there are two Subjects and two Predicates, and
it is at the fame time apparent, that it may be
refolved into four difrincl: Propofitions. Riches
are apt to elate the Mind. Riches are apt to increafe
the Number of our Defires. And fo of Honours.
II. LOGICIANS have divided thefe n e proptr
compound Propofitions into a great Nottonc f*
rr /-, rr compound Pro*.
many different Clafies ; but in my fofr,on afrtr-
Opinion, not with a due Regard """"*
to their proper Definition. Thus Conditional*}
Caufals, Relatives, &c. are mentioned as fo many
diftinct Species of this Kind, though in fact they
are no more than fimple Propofitions. To give
an Inftanceofa Conditional : If a Stone is expofed
to the Rays of the Sun, it will contraft fome Degree
of Hfat. Here we have but one Subject and one"
Predicate ; for the complex Expreflion, A Stone
expofed to the Rays of ths Sun, conftitutes the
proper Subject of this Propofition, and is no
more than one determinate Idea. The fame
Thing happens in Caufals. Rehoboam was ;;-
happy, b<caiife h? followed evil Counfel. I deny not
that there is here an Appearance of two Propo-
I 3 fitions
( 174 )
fitions arifmg from the Complexity of the Ex-
preflion j but when we come to confidcr the
Matter more nearly, it is evident that we have
but a fingle Subject and Predicate. The Purfuit
cf evil Counftl brought Mifery upon Rehoboam.
It is not enough therefore to render aPropofition
compound, that the Subject and Predicate are
complex Notions, requiring fometimes a whole
Sentence to exprefs them : for in this Cafe, the
Comparifon is {till confined to two Ideas, and
conftitutes what we call a fimple Judgment.
But where there are feveral Subjects or Predi-
cates, or both, as the Affirmation or Negation
nuiy be alike extended to them all, the Propo-
fition expreffing fuch a Judgment is truly a
Collection of as many fimple ones as there arc
different Ideas compared. Confining ourfelves
therefore, to this more ftricT: and juft Notion of
compound Propofitions, they are all reducible to*
two Kinds, viz. Copulatives and Disjunctives.
Compound III. A Copulative Propofition is,
P e - t l f fc"p u . where the Subjefls and Predicates
la:ivt, ' are fo linked together, that they may
be all feverally affirmed or denied one of another,
Of this Nature are the Examples of compound
Propofitions given above. Riches and Honours are
apt to elate the Mlnd^ and inircafe the Number of
our Deftres. Neither Kings nor People are exempt
from Death. In the firfl of thefe, the two Predi-
cates
catcs may be affirmed feverally of each Subject,
whence we have four diftincSl Propofitions. The
other furnifhes an Example of the Negative Kind,
where the fame Predicate being disjoined from
both Subjects, may be alfo denied of them in
Separate Propofitions.
IV. THE other Species of com- Or phjunc-
pound Propofitions are thofe called ''*"
Disjunctives ; in which, comparing feveral Pre-
dickies with the fame Subject, we affirm that one
of them necefTarily belongs to it, but leave the
particular Predicate undetermined. If any one,
for example, fays : This World either exijh ofit-
felf-> or is the Work of fame all-wife and powerful
Caufe ; it is evident that one of the two Predi-
cates mud belong to the World ; but as the Pro-
pofition determines not which, it is therefore of
the kind we call Disjunctive. Such too are the
following : The Sun either moves round the Earth ,
or is the Center about which the Earth revolves.
Friendjhip finds Men equal^ or makes them fo. It
is the Nature of all Propofitions of this Clafs,
fuppofmg them to be exact in Point of Form ;
that u.;on determining the particular Predicate,
the'relt are of courfe to be removed ; or if all
the Predicates but one are removed, 'that one
ncceflarily takes place. Thus in the Example
given above ; if we allow the World to be the
Work of fome wife and powerful Caufe, we o/
courfe. deny it to be felf-exiftent, or if we deny
1 4 it
It to be felf-exifienr, we muft neceflarily adnut
that it was produced by fome wife and jwwerful
Caufe. Now this particular Manner of linking
the Predicates together, fo that the eftablifhing
one difplaces all the reft ; or the excluding all
but one neceflarily eftablifhes that one ; cannot
otherwife be effected than by means of disjunc-
tive Particles. And hence it is that Propofitions
of this Clafs take their Names from thefe Par-
ticles, which make fo neceflary a Part of them,
and indeed conftitute their very Nature, con-
fidered as a diftindl Species. But I (hall referve
what farther might be faid on this Head till
I come to treat of Reafoning, where the great
Ufe and Importance of disjunctive Propofitions
will better appear.
CHAP. VI.
Of the Divifion of 'Propofitions into Self-
evident and Dcwonftrable.
oftbit I. A S we are foon to enter
/A. upon the third Part of
Logick, which treats of Reafoning, and as the
Art of Reafoning lies in deducing Propofitions
whofe Truth does not immediately appear, from
others more known j it will be proper before we
proceed
proceed any farther, to examine a little the dif-
ferent Degrees of Evidence that accompany our
Judgments ; that we may be the better able to
diftinguifh, in what Cafes we ought to have re-
courfe to Reafoning, and what thofe Propofi-
tions are, upon which, as a fure and unerring
Foundation, we may venture to build the Truth
of others.
II. WHEN any Propofition is of- Prtfojilhat
fered to the View of the Mind, if the divided into
T- v- i tr J (elf -evident
Terms in which it is expreiled are J a ^ d emon -
underftood ; upon comparing the ft rable -
Ideas together, the Agreement or Difagreement
afTerted is either immediately perceived, or found
to lie beyond the prefent Reach of the Under-
ftanding. In the firft Cafe the PropofiUon is faid
to be felf- evident, and admits not of any Proof,
becaufe a bare Attention to the Ideas themfelves
produces full Conviction and Certainty ; nor is
it pofllble to call in any thing more evident, by
way of Confirmation. But where the Connec-
tion or Repugnance comes not fo readily under
the Infpeclion of the Mind, there we muft have
recourfe to Reafoning ; and if by a clear Series
of Proofs we can make out the Truth propofed,
infomuch that Self-evidence fhall accompany
every Step of the Procedure, we are then able
to demonftrate what we affert, and the Propo-
fition itfdf is faid to be demwjlrable* When we
I 5 affirm,
affirm, for inftance, that it is itnpojfible for the
fame thing to be and not to be ; whoever under-
frands the Terms made ufe of, perceives at firft
Glance the Truth of what is aflerted ; nor can
he by any Efforts bring himfdf to believe the
contrary. The Propofition therefore \sfelf- evi-
dent^ and fuch, that it is impoffible by Reafon-
ing to make it plainer ; becaufe there is no Truth
more obvious, or better known, from which as
a Confcquence it may be deduced. , But if we
fay, This World had a Beginning ; the Afiertion
is indeed equally true, but (bines not forth with
the fame Degree of Evidence. We find great
Difficulty in conceiving how the World could
be made out of nothing ; and are not brought to
a free and full Confenr, until by Reafoning we
arrive at a clear View of the Abfurdity involved
in the contrary Suppofition. Hence this Propofi-
tion is of the kind we call demonjlrable, inafmuch
as its Truth is not immediately perceived by the
Mind, but yet may be made appear by means of
others more known and obvious, whence it fol-
lows as an unavoidable Confequence.
, , ,. III. FROM what has been faid it
N by ttefecor.a
Operation of appears, that Reafoning is employ -
'corfJdivboiiy ed only about demonftrable Propo-
10 ir.sui:i;n. fitions, and that our intuitive and
felf-evident Perceptions, are the ultimate Foun-
dation on which it refts, And now we fee
clearly
( 179 )
clearly the Reafon, why in the Diftinclion of
the Powers of the Underftanding, as explained
in the Introduction to this Treatife, the feconcl
Operation of the Mind was confined wholly to
intuitive A6h. Our firft Step in the Way to
Knowledge, is to furnifh ourfdves with Ideas.
\Vhen thefe are obtained, we next fet ourfelves
to compare them together, in order to judge
of their Agreement or Difagreement. If the
Relations we are in queft of lie immediately
open to the View of the Mind, the Judgments
expreffing them are felf-evident ; and the At
of the Mind forming thefe Judgments is what
we call Intuition. But if upon comparing our
Ideas together, we cannot readily and at once
trace their Relation, it then becomes necefl'ary
to employ Search and Examination, and call
in the AfTiftance of felf-evident Truths, which
is what we properly term Reafoning. Every
Judgment therefore that is not intuitive, being
gained by an Exercife of the Reafoning Faculty,
neceffarily belongs to the third Operation of the
Mind, and ought to be referred to it in a juft
Divifion of the Powers of the Underftanding.
And indeed it is with this View chiefly, that we
have diftinguifhed Pronofitions into felf-evident
and demonftrable. Under the firil Head are
comprehended all our intuitive Judgments, that
is, all belonging to the fecond Operation of the
I 6 Mind.
Mind. Demonftrable Proportions are the pro-
per Province of the Reafoning Faculty, and
conftitute by far the moft confiderable Part of
human Knowledge. Indeed Renfon extends alfo
to Matters of Experience and Tcftimony, where
the Proofs adduced are not of the kind called
Demonftration. But I am here only confider-
ing the Powers of the Mind as employed in
tracing the Relations between its own Ideas, in
which View of Things every true Propofition is
cemonftrable ; tho' very often we find ourfelves
incapable of difcovering and applying thofe in-
termediate Ideas upon which the Demonftration
depends.
IV. DEMONSTRABLE Propofi-
r'{'tiTttyrft tions therefore, belonging properly
Printifht of to t h e t hj r a Operation of the Mind,
I {hall for the prefent difmifs them,
and return to the Confederation of felf-evident
Truths. Thefe, as I have already obferved,
furnifh the firft Principles of Reafoning ; and
it is certain, that if in our Refeaiches, we em-
ploy only fuch Principles as have this Charac-
ter of Self-evidence, and apply them according
to the Rules to be afterwards explained, we
fhall be in no Danger of Error, in advancing
from one Difeovery to another. For this I may
appeal to the Writings of the Mathematicians,
which
which being conducted by the exprefs Model
here mentioned, are an inconteftible Proof of the
Firmnefs and Stability of human Knowledge,
when built upon fo fure a Foundation. For
not only have the Propofitions of this Science
flood the Teft of Ages, but are found attended
with that invincible Evidence, as forces the
Affent of all who duly confider the Proofs upon
which they are eftablifhed. Since then Mathe-
maticians are univerfally allowed to have hit
upon the right Method of arriving at Truths ;
fince they have been the happieft in the Choice,
as well as Application of their Principles ; it
may not be amifs to explain here the Divifion
they have given of felf-evident Propofitions j
that by treading in their Steps, we may learn
fomething of that Juftnefs and Solidity of
Reafoning for which they are fo defervedly
efteemed.
V. FIRST then it is to be ob-
Dtpnitions a
ferved, that they have been very great Help to
careful in afcertaining their Ideas, %". %'
and fixing the Signification of their Knowledge.
Terms. For this Purpofe they begin with De-
finitions, in which the Meaning of their Words
is fo diftin&ly explained, that they cannot fail
to excite in the Mind of an attentive Reader
the very fame Ideas as are annexed to them by
the Writer. And indeed I am apt to think
that
( 182 )
that the Clearnefs and irrefiftible Evidence of
Mathematical Knowledge, is owing to nothing
fo much as this Care in laying the Foundation.
Where the Relation between any two Ideas is
accurately and juftly traced, it will not be dif-
ficult for anothfcr to comprehend that Relation,
if in fetting himfelf to difcover it, he brings the
very fame Ideas into Comparifon. But if, on
the contrary, he affixes to his Words Ideas dif-
ferent from thofe that were in the Mind of him
who firft advanced the Demonftration ; it is evi-
dent, that as the fame Ideas are not compared,
the fame Relation cannot fubfift, infomuch that
a Propofition will be rejected as falfe, which,
had the Terms been rightly underftood, muft
have appeared unexceptionably true. A Square,
for inftance, is a Figure bounded by four equal
right Lines, joined together at right Angles.
Here the Nature of the Angles makes no lefs a
Part of the Idea, than the Equality of the Sides ;
and many Properties demonftrated of the Square
flow from its being a rectangular Figure. If
therefore we fuppofe a Man who has formed a
partial Notion of a Square, comprehending only
the Equality of its Sides, without regard to the
Angles, reading feme Demonftration that im-
plies alfo this latter Confideration ; it is plain
he would rejec~t it as not univerfally true, inaf-
inuch as it could not be applied where the Sides
were
were joined together at unequal Angles. For
this laft Figure anfwering (till to his Idea of
a Square, would be yet found without the
Property afligned to it in the Propofition. But
if he comes afterwards to correct his Notion,
and render his Idea complete, he will then rea-
dily own the Truth and Juftnefs of the De-
monft ration.
VI. WE fee therefore, that no- Matbtmai ,
thing contributes fo much to the "** ty bs-
T i f-< r i "" ; ' n S to'nb
Improvement and Certainty of hu- them, frocure
man Knowledge, as the having de- a ready R e -
_ ctpnn to the
terminate Ideas, and keeping them Truths tbty
{ready and invariable in all our ad " vance -
Difcourfes and Reafonings about them. And
on this Account it is, that Mathematicians, as
was before obferved, always begin by defining
their Terms, and diftin&ly unfolding the No-
tions they are intended to exprefs. Hence fuch
as apply themfelves to thefe Studies, having
exactly the fame Views of Things, and bring-
ing always the very fame Ideas into Comparifon,
readily difcern the Relations between them,
when clearly and diftin&ly reprefented. Nor
is there any more natural and obvious Reafon
for the univerfal Reception given to Mathema-
tical Truths, and for that Harmony and Cor-
refpondence of Sentiments which makes the
diftinguifliing Character of the Literati of this
Clafs.
VII. WHE*
ntepaiii/bini VI1 - W HEN they have taken this
tf Principles fi r fl. step, and made known the
tbt ftcond Step *
in Matbem'iti- Ideas whole Relations they intend
te) their next
lay down fome felf-evident 1 ruths, which may
ferve as a Foundation for their future Reafon-
ings. And here indeed they proceed with re-
markable Circumfpection, admitting no Prin-
ciples but what flow immediately from their
Definitions, and neceflarily force themfelves
upon a Mind in any Degree attentive to its
? Perceptions. Thus a Circle is a Figure formed
by a Right Line, moving round fome fixed
Point in the fame Plane. The fixed Point round
which the Line is /uppofed to move, and where
one of its Extremities terminates, is called the
Center of the Circle. The other Extremity,
which is conceived to be carried round, until
it returns to the Point whence it firft fet out,
defer ibes a Curve running into itfelf, and termed
the Circumference. All Right Lines drawn from
the Center to the Circumference are called
Radii. From thefe Definitions compared, Geo-
metricians derive this felf-evident Truth, that
the Radii of the fame Circle are all equal one to
another. I call it felf-evident, becaufe nothing
more is required, to lay it open to the imme-
diate Perception of the Mind, than an Attention
to the Ideas compared. For from the very Ge-
nefis of a Circle it is plain, that the Circum-
ference
icrence is every where diftant from the Center,
by the exadr. Length of the defcribing Line ;
and that the feveral Radii are in Truth nothing
more, than one and the fame Line varioufly
pofited within the Figure. This fhort Defcrip-
tion will, I hope, ferve to give fome little In-
fight into the Manner of deducing Mathemati-
cal Principles, as well as into the Nature of that
Evidence which accompanies them.
VIII. AND now I proceed to ob-
f L ^ 11 r> r Propofitient
ferve, that in all Proportions we d ^\ d j edini9
either affirm or deny fome Property St e ' ulat ' me
r i TI i /T i Vi i andpra&ical.
of the Idea that conftitutes the Sub-
ject of our Judgment, or we maintain that
fomething may be done or effected. The firil
Sort are called fyeculatlve Proportions, as in
the Example mentioned above, the Radii of the
fame Circle are all equal one to another. The
others are called practical, for a Reafon too ob-
vious to be mentioned ; thus, that a Right Line
may be drawn from one Point to another, is a prac-
tical Propofition ; inafmuch as it exprefles that
fomething may be done.
IX. FROM this twofold Confi-
. c T, r . /- , Hence Mai be-
deration of Propofitions anfes the ma ,; C a, Pri-
twofold Divifion of Mathematical "ff" <<&'-
guijeta into
Principles, into Axioms and Pojiu- Axioms and
lates. By an Axiom they umlerftand
any felf- evident fpcculative Truth : as, that the
Whole is greater than its Parts: That Things equal
to
f 186 )
to one ar.d the fdir.eThing, are equal to one another.
But a felf-evident practical Propofition is what
they cajl a Pojhdate. Such are thofc of Euclid - t
that a finiie Right Line may be continued direEily
forwards : That a Circle may be dcfcribed about
any Center with any Dijiance. And here we arc
to obferve, that as in an Axlom^ the Agreement
or Difagreement between the Subject and Pre-
dicate muft come under the immediate Infpec-
tion of the Mind ; fo in a Pojlitlate, not only
the Poffibility of the Thing afterted mud be
evident at firft View, but alfo the Manner in
which it may be effected. But where this Man-
ner is not of itfelf apparent, the Propofition
comes under the Notion of the demonftrable
kind, and is treated as fuch by the Geometrical
Writers. Thus, to draw a Right Line from ont
Point to another ; is afiumed by Euclid as a Pof-
tu'ate, becaufe the manner of doing it is fo ob-
vious. as to require no previous Teaching.
But then it is not equally evident, how we are
to conjlrucl an equilateral Triangle. For this
Reafon he advances it as a demonftrable Pro-
pofition, lays dowji Rules for the exact Per-
formance, and at the fame time proves that if
thcfe Rules are followed, the Figure will be
juftly defcribed.
A'-.d tetr.in- X. THIS naturally leads me to
^onlnt^"' talce notice > tll2t zsfdf -evident Truth,
1'beortmi and arc diilin^uiflied into different kinds,
Prothms. ..
5 according
according as they are fpcculative or practical ;
(a is it alfo with dcmonjlrable Propofitions. A
demonftrable fpeculative Proportion, is by Ma-
thematicians called a Theorem. Such is the fa-
mous 4jth Proposition of the firft Book of the
Elements, known by the Name of the Pythagorick
Theorem, from its fuppofed Inventor Pythagoras,
"viz. That In every Right-angled Triangle, the
Square defcribed upon the Side fubtending the Right
/ingle, is equal to both the Squares defcribed upon
the Sides containing the Right Jingle. On the
other hand, a demonftrable practical Propofi-
tion is called a Problem ; as where Euclid teaches
us to defcribe a Square upon a given Right Line.
XI. SINCE I am upon this Sub-
1 Lorollanes an
jeer, it may not be amifs to add, obihutDe-
that befides the four Kinds of Pro- JSSfeT
pofitions already mentioned, Mathe- P r ^"'>
maticians have alfo a fifth, known by the Name
of Corollaries. Thefe are ufually fubjoined to
Theorems^ or Problems, and differ from them only
in this ; that they flow from what is there de-
monftrated, in fo obvious a Manner as to dif-
cover their Dependence upon the Proportion
whence they are deduced, almoft as foon as
propofed. Thus Euclid having demonftrated,
that in every Right-lined Triangle, all the three
Singles taken together are equal to two Right Angles ;
adds by way of Corollary, that all the three
C 188 )
Angles of any one Triangle taken together , are equal
to all the three Angles cf any other Triangle taken
together : which is evident at firil Sight ; be-
caufe in all Cafes they are equal to two right
ones, and Things equal to one and the fume
thing, are equal to one another.
XII. THE laft Thing I (hall take
Scbclia ftrvi . i r r>- e i
the Purport notice or in the Practice or the
f Annotate Mathematicians, is what they call
tr a Cunment,
their Scholia. They are indifferently
annexed to Definitions, Proportions, or Corol-
laries ; and anfwer the fame Purpofes as Anno-
tations upon a Claffic Author. For in them
Occafion is taken, to explain whatever may
appear intricate and obfcure in a Train of Rea-
foning ; to anfwer Objections ; to teach the
Application and Ufes of Propofitions j to lay
open the Original and Hiftory of the feveral Dif-
coveries made in the Science ; and in a Word,
to acquaint us with all fuch Particulars as de-
ferve to be known, whether confidered as Points
of Curiofity or Profit.
XIII. THUS we have taken a
Tb:iMtthodof _ ,,. c i r >i
the Matbt.na- ihort View of the io much cele-
ticitnt unrvtr. brated Method of the Mathemati-
/tf/, and a furt
Guide to Ctr- cians ; which to any one who con-
fiders it with a proper Attention,
mud needs appear univerfal, and equally appli-
cable in other Sciences. They begin with De-
finitions.
( 1 89 )
finitions. From thefe they deduce their Axioms
and Poftulates, which ferve as Principles of
Reafoning j and having thus laid a firm Foun-
dation, advance to Theorems and Problems,
eftablifliing all by the ftri&eft Rules of Demon-
ftration. The Corollaries flow naturally and
of themfelves. And if any Particulars are ftill
wanting to illuftrate a Subject, or complete the
Reader's Information j thefe, that the Series of
Reafoning may not be interrupted or broken,
are generally thrown into Scholia. In a Syftem
of Knowledge fo uniform and well connected,
no wonder if we meet with Certainty ; and if
thofe Clouds and DarknefTes, that deface other
Parts of human Science, and bring Difcredit
even upon Reafon itfelf, are here fcattered and
difappear.
XIV. BUT I fhall for the prefent , ,, ...
aelf-e-viifent
wave thefe Reflections, which every Trmbi km-io*
Reader of Underftanding is able to /J, u^ij.
make of himfelf, and return to the ab!t Co<ftion
/", r . r r ic i n bet-Wten the
Confideration of felf-evident Propo- Sutj.-a and
fitions. It will doubtlefs be expeft- *'*<*<'
ed, after what has been here faid of them, that
I fhould eftablifh fome Criteria^ or Marks, by
which they may be diftinguifhed. But 1 frankly
own my Inability in this RefpecT:, as not being
able to conceive any Thing in them more obvi-
ous and ftriking, than that Self-evidence which
. constitutes
) -:
conftitutes their very Nature. All I have there-
fore to obferve on this Head is, that we ouo-ht
* O
to make it our firft Care, to obtain clear and de-
terminate Ideas. When afterwards we come
to compare thefe together, if we perceive be-
tween any of them a neceffary and unavoidable
Connection, infomuch that it is impoffible to
conceive them exifting afunder, without deftroy-
ing the very Ideas compared; we may then
conclude, that the Proportion expre/fing this
Relation is a Principle, and of the Kind we
call felf-evident. In the Example mentioned
above, The Radii of the fame Circle are all equal
between themfehcs, this intuitive Evidence fhines
forth in the cleared Manner ; it being impoflible
for any one who attends to his own Ideas, not
to perceive the Equality here aflerted. For as
the Circumference is every where diftant from
the Center by the exact Length of the defcrib-
ing Line ; the Radii drawn from the Center to
the Circumference, being feverally equal to this
one Line, muft needs alfo be equal among them-
felves. If we fuppofe the Radii unequal, we at
the fame Time fuppofe the Circumference more
diftant from the Center in fome Places than
in others ; from which Suppofition, as it would
exhibit a Figure quite different from a Circle,
we fee there is no feparating the Predicate from
the Subject in this Proportion, without deflroy-
in<r
ing the Idea in relation to which the Compa-
rifon was made. The fame Thing will be found
to hold in all our other intuitive Perceptions,
infomuch that we may eftablifh this as an uni-
verfal Criterion, whereby to judge of and dif-
tinguifh them. I would not, however, be un-
derftood to mean, as if this ready View of the
unavoidable Connection between fome Ideas
was any Thing really different from Self-evidence.
It is indeed nothing more than the Notion of
Self-evidence a little unfolded, and as it were
laid open to the Infpe<5tion of the Mind. In-
tuitive Judgments need no other diftinguifhing
Marks, than that Brightnefs which furrounds
them ; in like Manner as Light difcovers itfelf
by its own Prefence, and the Splendor it uni-
verfally diffufes. But I have faid enough of
felf-evident Propofitions, and fhall therefore now
proceed to thofe of the demonftrable kind ;
which being gained in confequence of Reafon-
ing, naturally leads us to the third Part of Logick,
where this Operation of the Underftanding is
explained,
THE
( 19* )
THE
ELEMENTS
O F
L O G I C K.
BOOK III.
Of REASONING.
CHAP. I.
Of Reafoning in general, and the Parts
of which it confifts.
Remote R,Ia . "* \\ T^ haVC ^ een h W the
"?7 dl ' c *"", V V proceeds in furnifhin? it-
ed by mrans of
ir.:ermtdiau felf with Ideas, and framing intuitive
Perceptions. Let us next enquire
into the manner of difcovering thofe more remote
Relations, which lying at a Diftance from the
Underflanding, are not to be traced but by means
of a higher Exercife of its Powers. It often hap-
pens
C 193 )
pens In comparing Ideas together, that their
Agreement or Difagreement cannot be difcerned
at firft View, efpecially if they are of fuch a Na-
ture, as not to admit of an exa& Application one
to another. When, for inftance, we compare 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 exact Determination ; be-
caufe by reafon of their difagreeing Forms, it is
impoffible fo to put them together, as that their
feveral Parts ftiall 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 fuc-
ceed, all Difficulties vanifh, and the Relation
we are in queft of may be traced with Eafe. Thus
right-lined Figures are all reducible to Squares,
by means of which we can meafure their Areas,
and determine exactly their Agreement or Dif-
agreement in Point of Magnitude.
II. IF now it be afked, how any Tbh Manntr
third Idea can ferve to difcover a Re- jf "T""'"* j'
I rule termid
lation between two others : I an- Rtafoning.
fwer, by being compared feverally with thefe
others ; for fuch a Comparifon enables us to fee
how far the Ideas with which this third is com-
pared, are connected or disjoined between them-
felves. In the Example mentioned above of two
right-lined Figures^ if we compare each of them
K. \r!th
( 194 )
wjth fome Square whofe Area is known, and
find the one exactly equal to it, and the other
lefs by a Square-Inch, we immediately conclude
that the Area of the firft Figure is a Square Inch
greater than that of the fecond. This manner
of determining the Relation between any two
Ideas, by the Invention of fome third with which
they may be compared, is that which we call
Reasoning t and indeed the chief Inftrument, by
which we pulh on our Difcoveries, and enlarge
our Knowledge. The great Art lies, in finding
out fuch intermediate Ideas, as when compared
with the others in the Queftion, will furnifh evi-
dent and known Truths, becaufe, as will after-
wards appear, it is only by means of them, that
we arrive at the Knowledge of what is hidden
and remote.
III. FROM what has been faid it
7 be Partf
'that eonfiitute appears, that every Act of Reafon^
f fie -' j ing neceflarily includes three dif- /
J\QJGnit]g Afid O J
a Syllogijm. tinct Judgments j two, wherein the
Ideas, whofe Relation we want to difcover, are
feverally compared with the middle Idea, and
a third, wherein they are themfelves connected
or disjoined according to the Refult of that Com-
parifon. Now as in the fecond Part of Logick,
our Judgments when put into Words were cal-
led Propofitions, fo here in the third Part, the
Expreflions of our Reafonings are termed Syllo-
gifms. And hence it follows, that as every Act
of
( 195 )
of Reafoning implies three feveral Judgments,
fo every Syllogifm muft include three diftinft
Propofitions. When a Reafoning is thus put
into Words, and appears in Form of a Syllogifm,
the intermediate Idea made ufe of to difcover
the Agreement 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.
IV. BUT as thefe things are beft T ,.
, Inftanct, Matt
illuftrated by Examples ; let us, for and Actount-
inftance, fet ourfelves to enquire,
whether Men are accountable for their Actions. As
the Relation between the Ideas of Man and Ac-
count ablenefs 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
imall Meafure of Reflection is fufficient to in-
form us, that no Creature can be accountable
for his Actions, unlefs we fuppofe him capable
of diftinguifhing the good from the bad ; that
is, unlefs we fuppofe him poflefled of Reafon.
Nor is this alone fufficient. For what would
it avail him to know good from bad Actions, if
he had no Freedom of Choice, nor could avoid
the one, and purfue the other ? Hence it be-
comes neceflary to take in both Confederations
in the prefent Cafe. It is at the fame Time equally
apparent, that wherever there is this Ability of
K 2 diitinguilhing
( 196 )
diftittguifhing good from bad A&ions, and pur-
fuing the one and avoiding the other, there alfo
a Creature is accountable. We have then got a
third Idea, with which Accountablenefi is infepa-
r ably connected, viz, Reafon and Liberty; which
are here to be confidered as making up one com-
plex 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. Hav-
ing thus by means of the intermediate Idea form-
ed two feveral Judgments, viz. that Man is pof-
fejjed of Reafon and Liberty ; and that Reafun and
Liberty imply Acccuntablenefs ; a third obvioufly
and neceffarily follows, viz. that Man is accoun-
table for his dtfions. Here then we have a com-
plete At of Reafoning, in which, according to
what has been already obferved, there are three
diftindt Judgments j two that may be ftiled pre-
vious, inafmuch as they lead to the other, and
arife from comparing the middle Idea with
the two Ideas in the Queflion : the third is a Con-
fequence of thefe previous Acts, and flows from
combining the extreme Ideas between them-
felves. If now we put this Reafoning into Words,
it exhibits what Logicians term a Syllogifm,
and when propofed in due Form, runs thus :
Every Creature pojj'ej/ed of Reafon and Liberty is
accountable for his Aftions.
Man is a Creature poj/ejftd of Reafin and Liberty.
There-
( 197 )
Therefore Man is accountable for his.
V. IN this Syllogifm we may ob- Premife^
ierve, that there are three fcveral JjjJjJ" 1
Propofitions, exprefling the three miiidieTtrm.
Judgments implied in the Act of Reafoning, and
fo difpofed, as to reprefent diftin&ly what pafles
within the Mind, in tracing the more diftant Re-
lations of its Ideas. The two firft Propofitions
anfwer the two previous Judgments in Reafon-
ing, and are called the Premifes^ becaufe they are
placed before the other. The third is termed the
Conclufiori) as being gained in confequence of
what was afTerted in the Premifes. We are alfo
to remember, that the Terms exprefling the
two Ideas whofe Relation we enquire after, as
here Man and Accountablenefs^ are in general cal-
led the Extremes', and that the intermediate Idea,
by means of which the Relation is traced, viz.
A Creature pojjejjed of Reafon and Liberty , takes
the Name of the middle Term. Hence it follows,
that by the Premifes of a Syllogifm, we are al-
ways to underftand the two Propofitions, where
the middle Term is feverally compared with Ex-
tremes ; for thefe conftitute the previous Judg-
ments, whence the Truth we are in queft of
is by Reafoning deduced. The Condujion is that
other Propofition, in which the Extremes them-
felves are joined or feparated, agreeably to what
appears upon the above Comparifon. All this
is evidently feen in the foregoing Syllogifm,
K 3 where
where the two firft Propositions which reprefcnt
the Premifes, and the third' that makes the Con-
clufion, are exactly agreeable to the Definitions
here given.
,. , VI. BEFORE we take leave of
Major and
Mimr Term, this Article, it will be farther nccef-
Mwr "pro- f" ar y to obferve, that as th Conclu-
fo/itio*. f lon i s mac ] e * U p O f the extreme
Terms of the Syllogifm, fo that Extreme, which
ferves as the Predicate of the Conclufion, goes
by the Name of the Majir Term : the other Ex-
treme, which makes the Subject in the fame
Propofition, is called the Minor Term. From
this Diftinction of the Extremes, arifes alfo a
Diftindtion between the Premifes where thefe
Extremes are feverally compared with the mid-
dle Term. That Propofition which compares
the greater Extreme, or the Predicate of the Con-
clufion, with the middle Term, is called the
Major Propofition : the other, wherein the fame
middle Term is compared with the Subject of the
Conclufion, or lefler Extreme, is called the Mi-
nor Propofition. All this is obvious from the Syl-
logifm already given, where the Conclufion is
Man is accountable for his rfttwns.. For here the
Predicate Accountable for his Acliom, being con-
nected with the middle Term in the firft of the
two Premifes ; Every Creature pojjeffed of Reafon
*nd Liberty is accountable for his Aft'ions^ gives
what we call the Major Propofition. In the fe-
cond
( 199 )
cond of the Premifes ; Man is a Creature psjfijf-
ed of Reafon and Liberty ', we find the lefler Ex-
treme, or Subject of the Cpnclufion, viz. fifarr,
connected with the fame middle Term, whence
it is known to be the Minor Proportion, I (hall
only add, that when a Syllogifm is propofed in
due Form, the Major Proportion is always placed
firft, the Minor next, and the Concluiion lair, ac-
cording as we have done in that offered above.
VII. HAVING thus cleared the ~ ;
Judgment and
Way, by explaining iuch Terms, as Propa/itien,
IM i L r c Reifaniaf and
we are likely to have occafion for fyfoif t Jip.
in the Progrefs of this Treatife ; it tUgntpa.
may not be amifs to obferve, that tho' we have;
carefully diftinguimed between the Aft of Reafon-
ing) and a Syllogifm, which is no more than the
Expreffion of it, yet common Language is not
fo critical on this Head ; the Term Reafoning be-
ing promifcuoufly ufed to fignify, either the
Judgments of the Mind as they follow one an-
other in Train, or the Propofitions exprefling
thefe Judgments. Nor need we wonder that it
is fo, inafmuch as our Ideas, and the Terms ap-
propriated to them, are fo connected by Habit and
Ufe, that our Thoughts fall as it were fpontane-
oufly into Language, as faft as they arife in the
Mind j fo that even in our Reafonings within
ourfelves, we are not able wholly to laid afide
Words. But notwithftanding this ftricT: Con-
nection between mental and verbal Reafoning, if
K 4 1 may
( 200 )
I may be allowed that Expreflion, J thought' it
needful here to diftinguifh them, in order to
give a juft Idea of the manner of deducing on*
Truth from another. While the Mind keeps
the Ideas of Things in view, and combines its
Judgments according to the real Evidence at-
tending them, there is no great Danger of Mif-
take in our Reafonings, becaufe we carry our
Conclufions no farther than the Clearnefs of our
Perceptions warrants us. But where we make
ufe of Words, the Cafe is often dtherwife ; no-
thing being more common than to let them pals
y/ithout attending to the Ideas they reprefent 5
infomuch that we frequently combine Expreflions
which upon Examination appear to have no de-
terminate Meaning. Hence it greatly imports
us to diftinguifh between Reafoning and Syllo-
gifm j and to take care that the one be in all
Cafes th true and juft Reprefentation of the
other. However, as I am unwilling to recede
too far from the common forms of Speech, or
to multiply Diftin&ions without Necefiity, I
fhall henceforward confider Propofitions as re-
prefenting the real Judgments of the Mind, and
Syllogifms as the true Copies of our Reafonings ;
which indeed they ought always to be, and un-
doubtedly always will be, to Men who think
juftly, and are defirous of arriving at Truth.
Upon this Suppofition there will be no Danger
in ufing the Words Judgment and Propofnion
promifcuoufly ;
( 201 )
promifcuoufly ; or in confidering Reafoning as
either a Combination of various Judgments, or
of the Proportions exprefiing them; becaufe
being the exacT: Copies one of another, the
Refult will be in all Cafes the fame. Nor is it
a fmalt Advantage that we can thus conform
to common Speech, without confounding our
Ideas, or running into Ambiguity. By this
means we bring ourfelves upon a Level with
other Men, readily apprehend the Meaning of
their ExprefTions, and can with Eafe convey
our own Notions and Sentiments into their
Minds.
VIII. THESE things premifed,
u u D r l**fiKle
we may in the general define Reafon- An of Rea-
ing, to be an Al or Operation of the ^f mujl
Mind^ deducing fame unknown Pro- ^ intuit ivt
r . V , Trutbt.
p^itton^ from other previous ones that
ate evident and known. Tbefe previous Propo-
fitrons, in a fimple Act of Reafoning, are only
two in Number j #nd it is always required that
they be of themfelves apparent to the Under-
ftanding, infomuch that we a/lent to and per-
ceive the Truth of them as foon as propofed. In
the Syllogifm given above, the Premifes are
fuppofed to be felf-evident Truths, otherwife
the Conclufion could not be inferred by a fingle
Acl of Reafoning. If, for inftance, in the Ma-
jor, Every Creature pojjejjed of Reafon and Liber-
ty is accountable for his Ati'ion^ the Connection
K 5 between
( 202 )
between the Subject and Predicate could nof
be perceived by a bare Attention to the Ideas
themfelves ; it is evident, that this Propofition
would no lefs require a Proof, than the Conclu-
fion deduced from it. In this Cafe a new mid-
dle Term muft be fought for, to trace the Con-
nection here fuppofed ; and this of courfe fur-
nifhes another Syllogifm, by which having efta-
blifhed the Propofition in queftion, we are then,
and not before, at liberty to ufe it in any fuc-
ceeding Train of Reafoning. And fhould it fo
happen that in this fecond Eflay, there was ftill
fome previous Propofition whofe Turn did not
appear at firft Sight; we muft then have recourfe
to a third Syllogifm, in order to lay open that
Truth to the Mind ; becaufe fo long as the Pre-
mifes remain uncertain, the Conclufion built
upon them muft be fo too. When by conduct-
ing our Thoughts in this Manner, we at laft
arrive at fome Syllogifm, where the previous
Propofitions are intuitive Truths; the Mind
then refts in full Security, as perceiving that the
feveral Conclufions it has pafled through, ftand
upon the immoveable Foundation of Self-evi-
dence, and when traced to their Source termi-
nate in it.
Rfafon'mg in IX. WE fee therefore, that in or-
t k, tigbtfl der to infer a Conclufion by a fingle
Extrcije oj tt, 1
tr.ty a Coma- A&of Reafoning, the Premifesmuft
be
1O
be intuitive Proportions. Where tension f
they are not, previous Syllogifms are $%#*
required, in which Cafe Reafoning becomes a
complicated Acl, taking in a Variety of fuccefllve
Steps. This frequently happens in tracing the
more remote Relations of our Ideas, where many
middle Terms being called in, the Conclufion
cannot be made out, but in confequence of a
Series of Syllogifms following one another in
Train. But although in this Concatenation of
Propofitions, thofe that form the Premifes of
the laft Syllogifm, are often considerably re-
moved from Self-evidence j yet if we trace the
Reafoning backwards, we fhall find them the
Conclufions of previous Syllogifms, whofe
Premifes approach nearer and nearer to In-
tuition, in proportion as we advance, and
are found at laft to terminate in it. And if
after having thus unravelled a Demonftration,
we take it the contrary way j and obferve
how the Mind, fetting out with intuitive Per-
ceptions, couples them together to form a
Conclufion j how by introducing this Conclu-
fion into another Syllogifm, it ftill advances
one Step farther ; and fo proceeds, making
every new Difcovery fubfervient to its future
Progrefs ; we fhall then perceive clearly, that
Reafoning, in the higheft Exercife of that Fa-
culty, is no more than an orderly Combina-
tion of thofe fimple Acts, which we have al-
K 6 ready
( 204 )
ready fo fully explained. The great Art lies, in
fo adj ufting our Syllogifms one to another, that
the Proportions feverally made ufe of as Premifes,
may be manifeft Confluences of what goes be-
fore. For as by this means, every Conclufion is
deduced from known and eftablifhed Truths, the
*ery laft in the Series, how far foever we carry it,
will have no lefs Certainty attending it, than the
original intuitive Perceptions themfelves, in which
the wkole Chain of Syllogifms takes its Rife.
we fee that
'*''*" c<r - beginning with firft Principles, rifes
tatnty in tvery fc
ftepoftte gradually from one Judgment to
Progrtfo*. another> and connecls them in fuch
Manner, that every Stage of the Progreflion
brings intuitive Certainty along with it. And
now at length we may clearly underftand the
Definition given above of this diftinguifhing
Faculty of the human Mind. Reafon we have
faid is the Ability of deducing unknown Truths
from Principles or Propofitions that are already
known. This evidently appears by the fore-
going Account, where we fee, that no Propo-
fition is admitted into a Syllogifm, to ferve as
one of the previous Judgments on which the
Conclufion refts, unlefs it is itfelf a known and
eftablifhed Truth, whofe Connection with felf-
evident Principles has been already traced.
Stlf-eviJent ^CI. THERE is yet another Obfer-
fmtbt, tbt yation which naturally offers itfelf,
in
in confequence of the above Detail ; ultimate
viz. that all the Knowledge acquired ^-"^
by Reafoning, how far foever we Certainty,
carry our Difcoveries, is ftill built upon our intui-
tive Perceptions. Towards the End of the laft
Part we divided Proportions into felf-evident
and demonftrable, and reprefented thofe of the
felf-evident Kind, as the Foundation on which
the whole Superftru&ure of human Science
refted. This Do&rine is now abundantly con-
firmed by what has been delivered in the prefent
Chapter. We have found that every Difcovery
of human Reafon, is the Confequence of a Train
of Syllogifms, which when traced to their
Source, always terminate in felf-evident Per*
ceptions. When the Mind arrives at thefe pri-
mitive Truths, it purfues not its Enquiries far-
ther, as well knowing, that no Evidence can
exceed that which flows from an immediate
View of the Agreement or Difagreement be-
tween its Ideas. And hence- it is, that in unra-
velling any Part of Knowledge, in order to
come at the Foundation on which it ftands ;
intuitive Truths are always the laft Refort
of the Underftanding, beyond which it aims
not to advance, but poflefles its Notions in
perfect Security, as having now reached the
very Spring and Fountain of all Science and
Certainty.
CHAP-
( 206 )
CHAP. II.
Of the fever al Kinds of Reafcningj and fir ft
of that ly which we determine the Genera
and Species of things.
ig I. *\ TT 7"E have endeavoured in the
t^o. yy f ore g i n g Chapter to give
as diftinft a Notion as poffible of Reafoning,
and of the Manner in which it is conduced.
Let us now enquire a little into the Difcoverics
made by this Faculty, and what thofe Ends are,
which we have principally in View in the Ex-
crcife of it. All the Aims of human Reafon
may in the general be reduced to thefe two :
I. To rank Things under thofe univerfal Ideas
to which they truly belong ; and 2. To afcribc
to them their leveral Attributes and Properties
in confequence of that Diftribution.
The frji Kind H. FIRST, then I fay, that one
regards tie great Aim of human Reafon is, to
Centra and
Species of determine the Genera and Species
Thing,. of Things. We have feen in the
firft Part of this Treatife, how the Mind pro-
ceeds in framing general Ideas. We have alfo
feen in the fecond Part, how by Means of thefe
general Ideas, we come by univerfal Propofi-
tions. Now as in thefe univerfal Proportions,
we affirm fome Property of a Genus or Species,
it
( 207 )
it is plain, that we cannot apply this Property
to particular Objects, till we have firft deter-
mined, whether they are comprehended under
that general Idea, of which the Property is af-
firmed. Thus there are certain Properties be-
longing to all even Numbers, which neverthelefs
cannot be applied to any particular Number,
until we have firft difcovered it to be of the Spe-
cies exprefled by that general Name. Hence
Reafoning begins with referring Things to their
feveral Divifions and ClafTes in the Scale of our
Ideas 3 and as thefe Divifions are all diftinguifhed
by peculiar Names, we hereby learn to apply the
Terms exprefung general Conceptions, to fuch
particular Objects, as come under our immediate
Obfervation.
III. Now in order to arrive at ne Stefl ly
thefe Conclufions, by which the
. rive at Can-
feveral Objects of Perception are ciufons of tint
brought under general Names, two Sort '
Things are manifeftly neceflary. Firft, that we
take a View of the Idea itfelf denoted by that ge-
neral Name, and carefully attend to the diftin-
guifhing Marks which ferve to characterize it.
Secondly, that we compare this Idea with the
Obje6l under Confideration, obferving diligently
wherein they agree or differ. If the Idea is found
to correfpond with the particular Object, we
then without Hefitation apply the general N^me;
but if no fuch Correfpondence intervenes, the
Conclu-
( 208 )
Onclufion muft neceflarily take a contrary
Turn. Let us, for Inftance, take the Number
Eighty and confider by what fteps we are led to
pronounce it an even Number. Firft then we call
to mind the Idea fignified by the Expreflion an
even Number, viz. that it is a Number diviftble
into two equal Parts. We then compare this Idea
with the Number Eight^ and finding them ma-
nifeftly to agree, fee at once the Neceflity of ad-
mitting the Conclufion. Thefe feveral Judg-
ments therefore, transferred into Language, and
reduced to the Form of a Syllogifm, appear thus :
Every Number that may be divided Into two
tqual Parti Is an EVEN Number.
The Number EIGHT may be divided Into two
equal Parts.
Therefore the Number "EiGHT is an EVEN
Number.
IV. I HAVE made Choice of this
Theft Sups al-
iio&yifaiio-uitd, Example, not fo much for the Sake
L/MW**" of the Conclufion, which is obvious
always attend enough, and might have been ob-
tained without all that Parade of
Words j but chiefly becaufe it is of eafy Compre-
henfion, and ferves at the fame time diftinctly to
exhibit the Form of Reafoning by which the
Underftanding conduces itfelf in all Inftances
of this Kind. And here it may be obferved, that
where the general Idea, to which particular Ob-
jects are referred, is very familiar to the Mind,
and
( 209 )
and frequently in View; this Reference, and
the Application of the general Name, feem to
be made without any Apparatus of Reafoning.
When we fee a Horfe in the Fields, or a Dog
in the Street, we readily apply the Name of the
Species ; Habit, and a familiar Acquaintance
with the general Idea, fuggefting it inflantane-
oufly to the Mind. We are not however to ima-
gine on this Account, that the Underftanding
departs from the ufual Rules of juft Thinking.
A frequent Repetition of Acts begets a Habit;
and Habits are attended with a certain Prompt-
nefs of Execution, that prevents our obferving
the feveral Steps and Gradations by which any
Courfe of A3ion is accomplifhed. But in other
Inftances, where we judge not by pre-contra&ed
Habits, as when the general Idea is very com-
plex, or lefs familiar to the Mind; we always
proceed according to the Form of Reafoning
eflablifhed above. A Goldfmith, for Inftance,
who is in doubt as to any Piece of Metal, whe-
ther it be of the Species called Gold; fir ft exa-
mines its Properties, and then comparing them
with the general Idea fignified by that Name,
if he finds a perfect Correfpondence, no longer
hefitates under what Clafs of Metals to rank it.
Now what is this, but following Step by Step
thofe Rules of Reafoning, which we have be-
fore laid down as the Standards, by which to
regulate
( 210 )
regulate our Thoughts in all Conclufions of this
kind?
Tbtgrtat Im- V. NOR let it be imagined, that
r""btf- tb " our Refearches here, becaufe in Ap-
R<ajomng. pearance bounded to the impofmg of
general Names upon particular Objedts, art
therefore trivial and of little Confequence.
Some of the moft confiderable Debates among
Mankind, and fuch too as nearly regard their
Lives, Ifltereft, and Happinefs, turn wholly upon
this Article. Is it not the chief Employment
of our feveral Courts of Judicature, to deter-
mine in particular Inftances, what is Law, Juf-
tice, and Equity? Of what Importance is it in
many Cafes, to decide aright, whether an Action
fliall be termed Murder or Manflaughter? We
fee that no lefs than the Lives and Fortunes of
Men depend often upon thefe Decifions. The
Reafon is plain. Actions when once referred to
a general Idea, draw after them all that may
be affirmed of that Idea ; infomuch that the de-
termining the Species of Actions, is all one with
determining what Proportion of Praife or Dif-
praife, Commendation or Blame, &c. ought to
follow them. For as it is allowed that Murder
deferves Death, by bringing any particular Ac-
tion under the Head of Murder, we of courfe
decide the Punifhment due to it.
VI. BUT
( 211 )
VI. BUT the great Importance Andtbcexaa
f this Branch of Reafoning, and 0'fw" f
L XT n~ n " fttffid h
the Neceffity of Care and Circum- M^b^.afi-
fpech'on, in referring particular Ob- '"""'
jecls to general Ideas, is ftill farther evident from
the Practice of the Mathematicians. Every one
who has read Euclid knows, that he frequently
requires us to draw Lines thro' certain Points,
and according to fuch and fuch Directions.
The Figures thence. refulting are often Squares,
Parallelograms, or Rectangles. Yet Euclid ne-
ver fuppofes this from their bare Appearance,
but always demonftrates it upon the ftridteft
Principles of Geometry. Nor is the Method he
takes in any thing different from that defcribed
above. Thus, for Inftance, having defined a
Square to be a Figure bounded by four equal
Sides, joined together at right Angles - 3 when
fuch a Figure arifes in any Conftruciion previous
to the Demonftration of a Proportion, he yet
never calls it by that Name, until he has fhewn
that the Sides are equal, and all its Angles right
ones. Now this is apparently the fame Form of
Reafoning we have before exhibited, in proving
Eight to be an even Number ; as will be evident
to any one who reduces it into a regular Syl-
logifm. I (hall only add v that when Euclid has
thus determined the Species of any Figure, he.
is then, and not before, at Liberty to afcribe to
it all the Properties already demonftrated of that
Figure,
( 212 )
Figure, and thereby render it fubfervient to the
future Courfe of his Reaftming.
VII. HAVING thus fufficiently
Fixed and in- *
explained the Rules by which we
a re to conduct ourielves, in ranking
particular Obiccls under general
tbii Part of J
Ideas, and fticwn their Conformity
a " d ^ the Plaice and Manner of the
Mathematicians ; it remains only to
obferve, that the true Way of rendering this Part
of Knowledge both eafy and certain, is ; by ha-
bituating ourfelves to clear and determinate
Ideas, and keeping them fteadily annexed to
their refpedlive Names. For as all our Aim is,
to apply general Words aright; if thefe Words
fland for invariable Ideas, that are perfectly
known to the Mind, and can be readily diftin-
guiflied upon Occafion, there will be little
Danger of Miftake or Error in our Reafonings.
Let us fuppofe that by examining any Object,
and carrying our Attention fucceflively from
one Part to another, we have acquainted our-
felves with the feveral Particulars obfervable in
it. If among thefe we find fuch as conflitute
fome general Idea, framed and fettled before-
hand by the Understanding, and diftinguifhed
by a particular Name j the Refemblance thus
known and perceived, neceflarily determines
the Species of the Object, and thereby gives
ft a Right to the Name by which that Species
is called. Thus four equal Sides, joined toge-
ther at right Angles, 'make up the Notion of
a Square. As this is a fixed and invariable Idea,
without which the general Name cannot be
applied, we never call any particular Figure a
Square, until it appears to have thefe feverai
Conditions j and contrarily, wherever a Figure
i-s found with thefe Conditions, it neceflarily
takes the Name of a Square. The fame will be
found to hold in all our other Reafonings of this
Kind ; where nothing can create any Difficulty
but the Want of fettled Ideas. If for inftance
we have not determined within ourfelves, the pie-
cife Notion denoted by the Word Manjlaugh-
ter ; it will be impoflible for us to decide, whe-
ther any particular Action ought to bear that
Name: becaufe however nicely we examine the
Action itfelf, yet being Strangers to the general
Idea with which it is to be compared, we are
utterly unable to judge of their Agreement or
Difagreement. But if we take Care to remove
this Obftacle, and diftinclly trace the two Ideas
under Confideration, all Difficulties vanifti, and
the Refolution becomes both eafy and certain.
VIII. THUS we fee of what Im- gyfueb a
portance it is, towards the Improve- Co ^ dui t Cer-
7 fainty and Di-
ment and Certainty of human
Knowledge, that we accuftom our-
f 214 )
traduced ht felves to clear and determinate Ideas,
ether Parti of
Knowledge at and a fteady Application of Words.
tbtmaticks. Nor is this fo eafy a Tafk as fome may
perhaps be apt to imagine ; it requiring both a
comprehenfive Understanding, and great Com-
mand of Attention, to fettle the precife Bounds
of our Ideas, when they grow to be very com-
plex, and include a Multitude of Particulars.
Nay, and after thefe Limits are duly fixed, there
is a certain Quicknefs of Thought and Extent
of Mind required, towards keeping the feveral
Parts in View, that in comparing our Ideas one
.with another, none of them may be overlooked.
.Yet ought not thefe Difficulties to difcourage us',
tho' great they are not unfurmountable, and the
Advantages ajifing from Succefs will amply re-
compenfe our Toil, The Certainty and eafjr
Application of Mathematical Knowledge is
\vholly owing to the exa& Obfervance of this
Rule. And I am apt to imagine, that if we were
to employ the fame Care about all our other
Ideas, as Mathematicians have done about thofe
of Number and Magnitude, by forming them
into exact Combinations, and diftinguifhing
thefe Combinations by particular Names, in or-
der to keep them fteady and invariable ; we
fhould foon have it in our Power to introduce
Certainty and Demonftration into other Parts of
human Knowledge.
CHAP,
CHAP. III.
Of Reafoning) as it regards the Powers and
Properties of Things, and the Relations of
our general Ideas.
"T T T
VV
I.
great End which Men
have in View in their Reafonings, regard* tt
, i i-r i r Sciences* and
namely ; the difcovenng and af- as k concerm
cribing to Things their feveral Attri- com>non L 'f e '
butes and Properties. And here it will be necef-
fary to diftinguifh between Reafoning, as it re-
gards the Sciences, and as it concerns common
Life. In the Sciences, our Reafon is employed
chiefly about univerfal Truths, it being by them
alone that the Bounds of human Knowledge are
enlarged. Hence the Divifion of Things into
various Clafles, called otherwife Genera and
Species. For thefe univerfal Ideas, being fet up
as the Reprefentatives of many particular Things,
whatever is affirmed of them, may be alfo affirm-
ed of all the Individuals to which they belong.
Murder for Inftance is a general Idea, reprefent-
ing a certain Species of human Actions. Reafon
tells us, that the Puniftiment due to it is Death.
Hence every particular Action coming under the
Notion of Murder, has the Punifhment of Death
allotted
allotted to it. Here then we apply the general
Truth to fome obvious Inftance, and this is what
properly conftitutes the Reafoning of common
Life. For Men, in their ordinary Tranfadtions
and Intercourfe one with another, have for the
moft part to do only with particular Objects.
Our Friends and Relations, their Characters and
Behaviours, the Conftitution of the feveral Bodies
that furround us, and the Ufes to which they
may be applied, are what chiefly engage our At-
tention. In all thefe we reafon about particular
Things ; and the whole Refult of our Reafonin:;
is, the applying the general Truths of the Sci-
ences to the ordinary Tranfadtions of human
Life. When we fee a Viper, we avoid it.
Wherever we have Occafion for the forcible -Ac-
tion of Water, to move a Body that makes con-
fiderable Refinance, we take care to convey it in
fuch a Manner, that it (hall fall upon the Object
with Impetuofity. Now all this happens, in
confcquence of our familiar and ready Applica-
tion of thefe two general Truths : Ibe Bite of a
Viper is mortal : Water falling upon a Body with
Impetuofity t affs very forcibly towards fetting It in
Motion. In like Manner, if we fet ourfelves to
confider any particular Character, in order to
determine the Share of Praife or Difpraife that
belongs to it, our great Concern is, to afcertain
exactly the Proportion of Virtue and Vice. The
Reafon
Reafon is obvious. A juft Determination in all
Cafes of this kind depends intirely upon an Ap-
plication of thefe general Maxims of Morality :
Virtuous Allans deferve Praife : Vicious A ft ions
deferve Blame.
II.- HENCE it appears, that Rea- rte Steps by
foning, as it regards common Life. wA/fAw^ra-
J teed in the Rea-
is no more than the afcribing the fining of -
general Properties of Things to thofe "'" L ' fc '
feveral Objects with which we are immediately
concerned, according as they are found to be of
that particular Divifion or Clafs to which the
Properties belong. The Steps then by which
we proceed are manifeftly thefe. Firft we refer
the Object under Confideration to fome general
Idea or Clafs of Things. We then recollect the
feveral Attributes of that general Idea. And,
laftly, afcribe all thofe Attributes to the prefent
Object. Thus irt confidering the Character of
Sempronius, if we find it to be of the Kind called
Virtuous ; when we at the fame Time reflect, that
a virtuous Character is deferving of Efteem, it
naturally and obvioufly follows, that Sempronius
is fo too. Thefe Thoughts put into a Syllogifm y
in order to exhibit the Form of Reafoning here
required, run thus :
Every virtuous Man is worthy of EJleem.
SEMPRONIUS is a virtuous Man:
Thtrefort SEMPRONIUS is worthy of EJleem.
L III. BY
III. BY this Syllosrifm it appear*,
tffiM . , f ' ' y ,. f
- that before we affirm any Thing of a
jtT ' particular Objeft, that Object muft
jirancbei of be referred to fome general Idea.
Reafoninv one r , c
ufmanoibtr. Sempromusis pronounced worthy of
Efteem, only in Confequence of his
being a virtuous Man, or coming under that ge-
neral Notion. Hence we fee the neceflary Con-
nection of the various Parts of Reafoning, and
the Dependence they have one upon another.
The determining the Genera and Species of
Things is, as we have faid, one Exercife of hu-
man Reafon ; and here we find that this Exer-
cife is the firft in Order, and previous to the
other, which confifts in afcribing to them their
Powers, Properties, and Relations. But when we
have taken this previous Step, and brought par-
ticular Objects under general Names ; as the Pro-
perties we afcribe to them are no other than thole
of the general Idea, it is plain, that in order to a
fuccefsful Progrefs in this Part of Knowledge,
we muft thoroughly .acquaint ourfelves with the
feveral Relations and Attributes of thefe our ge-
neral Ideas. When this is done, the other Part
will be eafy, and require fcarce any Labour of
Thought, as being no more than an Application
of the general Form of Reafoning reprefented in
the foregoing Syllogifm. Now as we have already
fufficiently (hewn, how we are to proceed in de-
termining
tertnining the Genera and Species of Things,
which as we have faid is the previous Step to this
fecond Branch of human Knowledge; all that
is farther wanting to a due Explanation of it is,
to offer fome Confiderations, as to the Manner '
of inveftigating the general Relations of our
Ideas. This is the higheft Exercife of the Pow-
ers of the Underftanding, and that by means
whereof, we arrive at the Difcovery of univerfal
Truths ; infomuch that our Deductions in this
Way conftitute that particular Species of Rea-
foning which we have before faid regards princi-
pally the Sciences,
IV. BUT that we may conduct
our Thoughts with fome Order and required t*
Method, we fliall begin with obferv- makf "S ^
Reajoncr.
ing, that the Relations of our gene-
ral Ideas are of two Kinds. Either fuch as im-
mediately difcover themfelves, upon comparing
the Ideas one with another ; or fuch, as being
more remote and diftant, require Art.and Con-
trivance to bring them into View. The Rela-
tions of the firft Kind, furnifh us with intuitive
and felf-evident Truths : thofe of the fecond are
traced by Reafoning, and a due Application of
intermediate Ideas, It is of this laft Kind that
we are to fpeak here, having difpatched what
was neceflary with regard to the other in the
fecond Part. As therefore in tracing the more
diftant Relations of\ Things, we muil always
L 2 have
( 220 )
have recourfe to intervening Ideas, and are more
or lefs fuccefsful in our Refearches, according to
our Acquaintance with thefe Ideas, and Abi-
lity of applying them ; it is evident, that to
make a good Rcafoner, two Things are princi-
pally required. Fir/t, an extenfive Knowledge
of thofe intermediate Ideas by means of which
Things may be compared one with another. Sc-
fondly^ the Skill and Talent of applying them
happily, in all particular Inftances that come
under Confideration.
F,rfl, an ex- V. FIRST I fay, that in order to
JEJrJjJJ: our fuccefsful Progrefs in Reafoning,
median Ideas, we muft have an extenfive Know-
ledge of thofe intermediate Ideas, by means of
which Things may be compared one with ano-
ther. For as it is not every Idea that will an-
fwer the Purpofe of our Enquiries, but fuch only
as are peculiarly related to the Objects about
which we reafon, fo as by a Comparifon with
them, to furnifh evident and known Truths j
nothing is more apparent, than that the greater
Variety of Conceptions we can call into View,
the more likely we are to find fome among them
that will help us to the Truths here required.
And indeed it is found to hold in Experience,
that in Proportion as we enlarge our View of
Things, and grow acquainted with a Multitude
of different Objects, the Reafoning Faculty ga-
thers Strength. For by extending our Sphere
of
of Knowledge, the Mind acquires a certain
Force and Penetration, as being accuflomed
to examine the feveral Appearances of its Ideas,
and obferve what Light they caft one upon ano-
ther.
VI. AND this I take to be the Rea- TO txceli*
fon, that in order to excel remark- a ^ a " b O f
ably in any one Branch of Learning, Learning we
_. in wft bt i
it is neceflary.to have at leait a gene- nera iac-
ral Acquaintance with the whole f "
,~\ n TM '
Circle of Arts and Sciences. The c\,deofArtt
Truth of it is, all the various Divl- " /5f '-
fions of human Knowledge are very nearly re-
lated among thcmfelves, and in innumerable Tn-
ftances ferve to illuitrate and fet off each other,
And altho' it is not to be denied, that by an ob-
ftinate Application to one Branch of Study, a
Man may make considerable Progrefs, and ac-
quire fo me Degree of Eminence in it; yet his
Views will be always narrow and contracted,
and he will want that rnafterly Difcernment
which not only enables us to purfue our Difco-
veries with Eafe, but alfo in laying them open to
others, to fpread a certain Brightnefs around
them. I would not however here be underftood
to mean, that a general Knowledge alone is fuf-
ficient for all the Purpofes of Reafoning. I only
recommend it as proper to give the Mind a cer-
tain Sagacity and Quicknefs, and qualify it for
L 3 judging
( 222 )
judging aright in the ordinary Occurrences of
Life. But when our Reafoning regards a parti-
cular Science, it is farther necefTary that we
more nearly acquaint ourfelves with whatever
relates to that Science. A general Knowledge
is a good Preparation, and enables us to proceed
with Eafe and Expedition in whatever Branch
of Learning we apply to. But then in the mi-
nute and intricate Queftions of any Science, we
are by no means qualified to reafon with Advan-
tage, until we have perfectly mattered the Science
to which they belong- ft being hence chiefly
tf>?.t -^e are furnifhed with thofe intermediate
Ideas, which lead to a juft and fuccefsful Solu-
tion.
WbyMubt- VII. AND here, as it comes fo
matieians naturally in my Way, I cannot
(onetimes an- __ . .~,
fv>e r rot the avoid taking Notice of an Obferva-
Expttfation t ; on ^t is frequently to be met
tbetr great *
Learning with, and feems to carry in it at
firft Sight fomething very ftrange
and unaccountable. It is in fliort this, that
Mathematician^ even fuch as are allowed to ex-
cel in their own Profeffion, and to have difco^
vered themfelves perfect Matters in the Art of
Reafoning, have not yet been always happy in
treating upon other Subjects ; but rather fallen
fhort, not only of what might naturally have
been expe&ed from them, but of many Writers
much kfs exercifed in the Rules of Argumen-
tation.
( 223 )
tation. This will not appear fo very extraor-
dinary, if we reflect on what has been hinted
above. Maihtmaticks is an engaging Study, and
Men who apply themfelves that Way, fo wholly
plunge into it, that they are for the mod part
but little acquainted with other Branches of
Knowledge. When therefore they quit their
favourite Subject, and enter upon others that
are in a manner new and ftrange to them, no
wonder if they find their Invention at a Stand.
Becaufe however perfect they may be in the Art
of Reafoning, yet wanting here thofe interme-
diate Ideas which are neceflary to furnifli out
a due Train of Proportions, all their Skill and
Ability fails them. For a bare Knowledge of *(
the Rules is not fufficbnt. We muft farther
have Materials whereunto to apply them. And
when thefe are once obtained, then it is that an
able Reafoner difcovers his Superiority, by the
juft Choice he makes, and a certain mafterly
Difpofition, that in every Step of the Procedure
carries Evidence and Conviction along with it.
And hence it is, that fuch Mathematicians as
have of late Years applied themfelves to other
Sciences, and not contented with a fuperficial
Knowledge, endeavoured to reach their inmoft
Recefies ; fuch Mathematicians, I fay, have by
mere Strength of Mind,, and a happy Applica-
tion of Geometrical Reafoning, carried their Dif-
coveries far beyond what was heretofore judged
LA the
( 224 )
the utmoft Limits of human Knowledge. This
is a Truth abundantly known to all who arc
acquainted with the late wonderful Improve-*
ments in Natural Philofophy.
Secondly, ttt VIIl.IcoME now to the fccond
*/// 4>W/-
i*g intermediate 1 hing required, in order to a fuccefs-
f^X? ful Pro f efs in Reafoning, namely ;
IrfaKctt. the Skill and Talent of applying
intermediate Ideas happily in all particular In-
llances that come under Confideration. And
here I {hall not take up much Time in laying
down Rules and Precepts, becaufe I am apt to
think they would do but little Service. Ufe and
Zxercife are the beft Inftru&ors in the prefent
Cafe: and whatever Logicians may boaft, of
being able to form perfect Reafoners by Book
and Rule, yet we find by Experience, that the
Study of their Precepts does not always add any
great Degree of Strength to the Underftanding.
In fliort, 'tis the Habit alone of Reafoning that
makes a Reafoner. And therefore the true Way
to acquire this Talent is, by being much con-
verfant in thofe Sciences where the Art of
Reafoning is allowed to reign in the greateft
Perfection. Hence it was that the Ancients,
who fo well understood the Manner of forming
the Mind, always began with Matbematicks as
the Foundation of their Philofophical Studies.
Here the Underftanding is by Degrees habituat-
ed to Truth, contrails infenfibly a certain Fond-
efs
( s )
nefs for it, ad karns never to yield its AfTent to
any Propofition but where the Evidence is fuf-
ficient to produce full Conviction* For this
Reafon Plato has called Mathematical Demon-
firations the Catharticks or Purgatives of the Soul,
as being the proper Means to cleanfe it from
Error, and reftore that natural Exercife of its
Faculties in which juft Thinking confifts. And
indeed I believe it will be readily allowed, that
no Science furnifhes fo many Inftances of a happy
Choice of intermediate Ideas, and a dexterous
Application of them, for the Difcovery of Truth
and Enlargement of Knowledge.
IX. IF therefore we would form The Study of
.... T T i / T / Mathematical
our Minds to a Habit of Keafoning Dtmonftra-
clofelv and in train,, we cannot take '''"' fg r * a t
f . ' Avail t* tbtt
any more certain Method, than the refpee-.
cxercifing ourfelves in Mathematical
Demonftrations, fo as to contract a kind of Fa-
miliarity with them, " Not that we look upon
" it as neceflary, (to ufe the Words of the great
" Mr. Locke) that all Men fhould be deep
" Mathematicians, but that, having got the
" Way of Reafoning which that Study necefla-
" rily brings the Mind to, they may be able to
" transfer it to other Parts of Knowledge, as
** they fhall have Occafion. For in all forts of
'* Reafoning, every fingle Argument fhould
" be managed as a Mathematical Demonftra-
** tion, the Connection and Dependence of
L 5 ? Idea*
( 226 )
" Ideas fhould be followed, till the Mind is
" brought to the Source on which it bottoms,
" and can trace the Coherence through the
" whole Train of Proofs. It is in the general
" obfervable, that the Faculties of our Souls are
" improved and made ufeful to us juft after the
" fame manner as our Bodies are. Would you
" have a Man write or paint, dance or fence
" well, or perform any other manual Operation,
" dexteroufly and with Eafe ? Let him have ever
" fo much Vigour and Activity, Supplenefs and
*' Addrefs naturally, yet nobody expects this
" from him unlefs he has been ufed to it, and
" has employed Time and Pains in fafliioning
** and forming his Hand, or outward Parts, to
thefe Motions. Juft fo it is in the Mind ;
" would you have a Man reafon well, you mud
" ufe him to it betimes, exercife his Mind in
" obferving the Connection of Ideas, and fol-
" lowing them in train. Nothing does this
" better than Mathematicks ; which therefore
'* I think fhould be taught all thofe, who have
** the Time and Opportunity, not fo much
" to make them Mathematicians, as to make
*' them reafonable Creatures ; for though we
" all call ourfelves fo, becaufe we are born to
* it, if we pleafe ; yet we may truly fay, Na-
" ture gives us but the Seeds of it. We are born
" to be, if we pleafe, rational Creatures ; but
* 'tis Ufe and Exercife only that makes us fo,
"and
f 227 )
* and we are indeed fo, no farther than Induftry, ^
" and Application has carried us." Conduft of
the Under/landing*
X. BUT although the Study of ^ ta if of
Mathematicks be of all others the >'* J*"* 8 ?
en other Ou0-
moir. ufeful to form the Mind and jeffi, as are
i T> 1-/1. r T u L diftlnguifhed-
give it an early Relifh of Truth, yet j / tre j ttg[b
Gus:ht not other Parts of Philofophy a d J^S*
T? L ir fteajni'ig.
to be neglected, tor there alfo we
meet with many Opportunities of exercifing the
Powers of the Underftandingj and the Variety
of Subjects naturally leads- us to obferve all thofe
different Turns of Thinking that are peculiarly
adapted to the feveral Ideas we examine,, and the-
Truths we fearch, after. A Mind thus trained,
acquires a certain Maftery over its own
Thoughts, infomuch that it can range and mo-
del them at pleafure,. and call fuch into View
as befl fuit its prefent Defigns. Now in this,
the whole Art of Reafoning confifts, from a
mong a great Variety of different Ideas to fingle-
out thofe that are moft proper for the BufinefSf
in hand r and to lay them together in fuch Or-r
der, that from plain and eafy Beginnings, byr
gentle Degrees, and a continual Train of evi-:
dent Truths, we may be infenftbly led. on to
fuch Difcoveries, as at our firft fetting out ap-
peared beyond the Reach of the human Under
ftanding. For this purpofe, befides the Study
L 6 oS
( "8 )
of Mathematicks before recommended, we ought
to apply ourfelves diligently to the reading of
fuch Authors as have diftinguilhed themfelves
for Strength of Reafoning, and a juft and ac-
curate Manner of Thinking. For it is obferv-
able, that a Mind exercifed and feafoned to Truth
feldom refts fatisfied in a bare Contempla-
tion of the Arguments offered by others, but
will be frequently eflaying its own Strength, and
purfuing its Difcoveries upon the Plan it is moft
accuftomed to. Thus we infenfibly contract a
Habit of tracing Truth from one Stage to ano-
ther, and of inveftigating thofe general Rela-
tions and Properties which we afterwards af-
cribe to particular Things, according as we find
them comprehended under the abftracl: Ideas to
which the Properties belong. And thus having
particularly fhewn how we are to diftribute the
feveral Objects of Nature under general Ideas^
what Properties we are to afcribe to them in
confequence of that Diftribution, and how to-
trace and inveftigate the Properties themfelves j
I think I have fufficiently explained all that is
neceflary towards a due Conception of Reafon-
ing, and {hall therefore here conclude this
Chapter.
CHAP.
CHAP. IV.
Of the Forms of Syllogifmt.
H 1
tented ourfelves with age- g mtt
neral Notion of Syllogifms, and of
the Parts of which they confift. It is now time
to enter a little more particularly into the Sub-
ject, to examine their various Forms, and to lay
open the Rules of Argumentation proper to each.
In the Syllogifms mentioned in the foregoing
Chapters, we may obferve that the middle Term
is the Subject of the Major Propofition, and the
Predicate of the Minor. This Difpofition, tho'
the moft natural and obvious, is not however
neceflary ; it frequently happening, that the
middle Term is the Subject in both the Premifes,
or the Predicate in both ; and fometimes di-
rectly contrary to its Difpofition in the forego-
ing Chapters, the Predicate in the Major, and
the Subject in the Minor. Hence the Diftindtion
of Syllogifms into various kinds, called Figures
by Logicians. For Figure, according to their
Ufe of the Word, is nothing elfe but the Order
and Difpofition of the middle Term in any Syl-
logifm. And as this Difpofition is we fee four-
fold, fo the Figures of Syllogifms thence arifing
are four in Number. When the middle Term
C
Is the Subject of the Major Proportion, and the
Predicate of the Minor, we have what is called
thej?r/? Figure. If on the other hand, it is the
Predicate of both the Premifes, the Syllogifm is
faid to be in tbe fecond Figure. Again, in the
third FigurejFmj middle Term is the fubjeft of
the two Premifes. And laftly, by making it the
Predicate of the Major, and Subject of the Minor,
we obtain Syllogifms in the fourth Figure.
of U- BUT befides this fourfold Dif-
tinction of Syllogifrns, there is alfo
a farther Subdivifion of them in every Figure,
arifing from the n<antity and Quality as they are
called of the Propofitions. By Quantity we mean
the Confederation of Propofitions as univerfal or
particular, by ghiality as affirmative or negative.
Now as in all the feveral Difpofitions of the mid-
dle Term, the Propofitions of which a Syllogifm
confifts may be either univerfal or particular,
affirmative or negative; the due Determination
of thefe, and fo putting them together as the
Laws of Argumentation require, conftitute what
Logicians call the Moods of Syllogifms. Of
thefe Moods there are a determinate Number to
every Figure, including all the poflible Ways in
which Propofitions differing in Quantity or Dua-
lity can be -combined, according to any Difpofi-
tion of the middle Term, in order to arrive at a
juft Conclufion. The Shortnefs of the prefent
Work
Work will not allow of entering into a more
particular Defcription of thefe feveral Diftinc-
tions and Divifions. I fhall therefore content
myfelf, with referring the Reader to the Port-
Royal Art of thinking^ where he will find the
Moods and Figures of Syllogifms diftinctly ex-
plained, and the Rules proper to each very neatly
demonstrated.
III. THE Divifion of Syllogifms Foundation of
according to Mood and Figure, re- laAH" "
fpefts thofe efpecially, which are
known by the Name of plain fimple Syllogifms j
that is, which are bounded to three Proportions,
all fimple, and where the Extremes and middle
Term is connected, according to the Rules laid
down above. But as the Mind is not tied down
to any one precife Form of Reafoning, but fome-
times makes ufe of more, fometimes of fewer
Premifes, and often takes in compound and con-
ditional Proportions, it may not be amifs to take
notice of the different Forms derived from this
Source, and explain the Rules by which the
Mind conducts itfelf in the ufe of them.
IV. WHEN in any Syllogifm, the Conditional '
Major is a conditional Propofition, Syikg\fmi.
the Syllogifm itfelf is .termed Conditional. Thus:
If there is a God^ he ought to be wor flipped..
But there is a God:
Therefore he ought to be worflipped.
( 232 }
In this Example, the Major or firft Propofifion,
is we fee conditional, and therefore the Syllo-
gifm itfelf is alfo of the kind called by that
Name. And here we are to obferve, that all
conditional Propofitions are made up of two
diftincl Parts; one expreffing the Condition-
upon which the Predicate agrees or difagrees
with the Subject:, as in this now before us, if
there is a God; the other joining or disjoining
the faid Predicate and Subject, as here, he ought
to be worjhipped. The firft of thefe Parts, or that
wlv'-h implies the Condition, is called the An~
tecedent; the fecond r where we j.oin or disjoia
the Predicate and Subject,, has the Name of
the Confequent.
V. THESE Things explained, we
are farther to obferve; that in all
Proportions of thia kind, fuppofmg
them to be exact in point of Form, the Relation
between the Antecedent and Confequent muft
ever be true and real ; that is, the Antecedent
muft always contain fome certain and genuine
Condition,, which neceflarily implies the Con-
fequent : for otherwife, the Propofition itfelf
witt be falfe, and therefore ought not to be ad-
mitted into our Reafonings. Hence it follows,
that when any conditional Propofition is aflumed,
if we admit the Antecedent of that Propofition,
we muft at the feme time neceiTarily admit the
Confe-
( 233 )
Confequent ; but if we reject the Confequent,
we are in like manner bound to rejecl alfo the
Antecedent. For as the Antecedent always ex-
prefles fome Condition which neceflarily im-
plies the Truth of the Confequent ; by admit-
ting the Antecedent we allow of that Condition,
and therefore ought alfo to admit the Confe-
quent. In like manner if it appears that the
Confequent ought to be rejected, the Antece-
dent evidently muft be fo too; becaufe as we
juft now demonftrated, the admitting of the An-
tecedent would neceflarily imply the Admiflion
alfo of the Confequent.
VI. FROM what has been faid it ,
The fwo
appears, that there are two Ways of Af/>di of
arguing in hypothetical Syllogifms, *Jg
which lead to a certain and un-
avoidable Conclufion. For as the Major is
always a conditional Propofition, confiding of
an Antecedent and a Confequent j if the Minor
admits the Antecedent, it is plain that the Con-
clufion muft admit the Confequent. This is
- called arguing from the Admiflion of the Ante-
cedent to the Admiflion of the Confequent, and
onftitutes that Mood or Species of hypothetical
Syllogifms, which is diftinguiflied in the Schools
by the Name of the Modus ponens, inafmuch as
by it the whole conditional Propofition, both
Antecedent and Confequent, is eftablifhed.
Thus:
If God is infinitely wife, and afis with perfitf
Freedom, he does nothing but what is beji.
But God is infinitely wife, and afls with per-
fefl Freedom :
Therefore he does nothing but what is be/I.
Here we fee the Antecedent or firft Part of
the conditional Propofition is eftablifhed in the
Minor, and the Confequent or fecond Part in
the Conclusion ; whence the Syllogifm itfelf is
an Example of the Modus ponens. But if now
we on the contrary fuppofe, that the Minor re-
jects the Confequent, then it is apparent, that
the Conclufion muft alfo rejedl: the Antecedent.
In this Cafe we are faid to argue from the Re-
moval of the Confequent, to the Removal of
the Antecedent, and the particular Mood or
Species of Syllogifms thence arifing is called by
Logicians the Modus tollens j becaufe in it, both
Antecedent and Confequent are rejected or taken
away, as appears by the following Example :
If Gcd were not a Being of infinite Goodnefs r
neither would he canfult the Happinefs of
his Creatures,
But God does confuh the Happinefs of his
Creatures :
Therefore he is a Being of infinite Goodnefe.
Delude VII. THESE two Species take in
the whole Cbfs of ""M" 1 Syl-
logifms, and include all the poflible
Ways of arguing that lead to a legitimate Con-
clufion j
( 235 )
clulion ; becaufe we cannot here proceed by a
contrary Procefs of Reaibning, that is, from
the Removal of the Antecedent to the Removal
of the Confequenr, or from the eftablifhing of
the Confequent to the eftablifhing of the Ante-
cedent. For altho* the Antecedent always ex-
prefles fome real Condition, which once ad-
mitted neceflarily implies the Confequent, yet it
does not follow that there is therefore no other
Condition ; and if fo, then after removing the
Antecedent, the Confequent may fti)l hold, be-
caufe of fome other Determination that infers it.
When we fay : If a Stone is expo fed fome time tit
the Rays of the Sun> it will contra ff a certain De-
gree of Heat j the Propofition is certainly true,
and admitting the Antecedent, we muft alfo ad-
mit the Confequent. But as there are other
Ways by which a Stone may gather Heat, it
will not follow, from the ceafing of the befope-
mentioned Condition, that therefore the Confe-
quent cannot take place. In other Words, we
cannot argue, But the Stone has not been expo fed
to the Rays of the Sun ; therefore neither has it ar.y
Degree of Heat ; inafmuch as there are a great
many other Ways by which Heat might have
been communicated to it. And if we cannot
argue from the Removal of the Antecedent to
the Removal of the Confequent, no more can
we from the Admiffion of the Confequent to the
Admiffion
Admiflion of the Antecedent. Becaufe as the
Confequent may flow from a great Variety of
different Suppofitions, the allowing of it does
not determine the precife Suppofition, but only
that fome one of them muft take place. Thus
in the foregoing Propofttion, If a Stone is ex-
pofed fome time to the Rays of the Sun, it will con-
tra fi a certain Degree of Heat : Admitting the
Confequent, viz. that it has contrasted a certain
Degree of Heat, we are not therefore bound to
admit the Antecedent, that it has been fome time
expofed to the Rays of the Sun j becaufe there are
many other Caufes whence that Heat may have
proceeded. Thefe two ways of arguing there-
fore hold not in conditional Syllogifms. Indeed,
where the Antecedent exprefles the only Condi-
tion on which the Confequent takes place, there
they may be applied with Safety ; becaufe where-
ever that Condition is not, we are fure that
neither can the Confequent be, and fo may ar-
gue from the Removal of the one to the Removal
of the other ; as on the contrary, wherever the
Confequent holds, it is certain that the Condi-
tion muft alfo take place; which ihews, that
by eftablifhing the Confequent, we at the fame
time efbblifii the Antecedent. But as it is a
very particular Cafe, and that happens but fcl-
dom, it cannot be extended into a general Rule,
and therefore affords not any fteady and univer-
fal
( 237 )
fal Ground of Reafoning upon the two foregoing
Suppositions.
VIII. As from the Major's being
... . n ,, . J . . Tbt M.nr.tr
a conditional Propohtion, we obtain O f arguing in
the Species of conditional Syllo-
. . ...
gifms ; fo where it is a disjunctive
Proportion, the Syllogifm to which it belongs is
called disjunctive, as in the following Example :
The World is either f elf- exijlent, or the Work
of fame finite ^ or of fame infinite Being.
But it is not felf-exijlent, nor the Work of a
finite Being :
Therefore it is the Work of an infinite Being.
Now a disjunctive Proportion is that where
of feveral Predicates we affirm one neceflarily
to belong to the Subject, to the Exclufion of
all the reft, but leave that particular one unde-
termined. Hence it follows, that as foon as
we determine the particular Predicate, all the
reft are of courfe to be rejected; or if we rejecl
all the Predicates but one, that one neceflarily
takes place. When therefore in a disjunctive
Syllogifm, the feveral Predicates are enumerated
in the Major ; if the Minor eftablifhes any one
of thefe Predicates, the Conclufion ought to
remove all the reft j or if in the Minor, all the
Predicates but one are removed, the Conclufion
muft necefTarily eftablifh that one. Thus in
the disjunctive Syllogifm given above, the
Major affirms one of three Predicates to belong
to
to the Earth, viz. Self-exiftence, or that it is
the Work of a finite, or that it is the Work of an
infinite Being. Two of thefe Predicates are re-
moved in the Minor , viz. Self-exijlence, and
the Work of a finite Being. Hence the Conclu-
fion neceflarily afcribes to it the third Predicate,
and affirms that it is the Work of an infinite Being.
If now we give the Syllogiihi another Turn,
infomuch that the Minor may eftablifli one of
the Predicates, by affirming the Earth to be
the Production of an infinite Being ; then the
Conclufion muft remove the other two, afTert-
ing it to be neither felf-exijlent^ nor the Work of
a finite Being. Thefe are the Forms of Reafon-
ing in this Species of Syllogifms, the Juftnefs
of which appears at firft Sight ; and that there
can be no other, is evident from the very Nature
of a disjunctive Propofition.
ImperfcEi or I^f. * N tne feveral Kinds of Syl-
logifms hitherto mentioned, we
may obferve, that the Parts are
complete ; that is, the three Propofitions of
which they confift are reprefented in Form.
But it often happens, that fome one of the Pre-
mifes is not only an evident Truth, but alfo fa-
miliar and in the Minds of all Men ; in which
Cafe it is ufually omitted, whereby we have an
imperfect Syllogifm, that feems to be made up of
only two Propofitions. Should we, for inftance,
argue in this manner :
Every
( 239 )
Every Man is mortal ;
Therefore -every King is mortal ;
the Syllogifm appears to be imperfect, as confifr-
ing but of two Propofitions. Yet it is really
complete, only the Minor [Every King is a Man]
is omitted, and left to the Reader to fupply, as
being a Proportion fo familiar and evident, that
it cannot efcape him.
X. THESE feemingly imperfect
p 11 -r ~ 11 j r- 7 Entbymtmct.
byllognms are called knthymemes,
and occur very frequently in Reafoning, efpe-
cially where it makes a Part of common. Con-
verfation. Nay, there is a particular Elegance
in them, becaufe not difplaying the Argument
in all its Parts, they leave fomewhat to the
Exercife and Invention of the Mind. By this
means we are put upon exerting ourfelves, and
feem to (hare in the Difcovery of what is pro-
pofed to us. Now this is the great Secret of
fine Writing, fo to frame and put together our
Thoughts, as to give full Play to the Reader's
Imagination, and draw him infenfibly into our
very Views and Courfe of Reafoning. This
gives a Pleafure not unlike to that which the
Author himfelf feels in compofmg. It befides
fhortens Difcourfe, and adds a certain Force
and Livelinefs to our Arguments, when the
Words in which they are conveyed, favour the
natural Quicknefs of the Mind in its Opera-
tions,
8
lions, and a fingle Expreflion is left to exhibit a
whole Train of Thoughts.
XI. BUT there is another Spe-
Ground of ,
Reajtning in cies of Reafonmg with two Propo-
immeaiatt fitions, which feems to be complete
Conftfutncei.
in itfelf, and where we admit the
Conclufion, without fuppofing any tacit or fup-
prefled Judgment in the Mind, from which it
follows fyllogiflically. This happens between
Propofitions where the Connexion is fuch, that
the Admifiion of the one, neceflarily, and at
the firft fight, implies the Admiflion alfo of the
other. For if it fo falls out, that the Propofi-
tion on which the other depends is felf-evident,
we content ourfelves with barely affirming it,
and infer that other by a direcl: Conclufion.
Thus by admitting an univerfal Propofition, we
are forced alfo to admit of all the particular Pro-
pofitions comprehended under it, this being the
very Condition that conftitutes a Propofition
univerfal. If then that univerfal Propofition
chances to be felf-evident, the particular ones
follow of courfe, without any farther Train of
Reafoning. Whoever allows, for inftance, that
Things equal to one and the fame Thing are equal
to one another^ muft at the fame time allow, that
two Triangle j, each equal to a Square wbofe Side
is three Inches^ are alfo equal between thernfelves*
This Argument therefore,
Things
Things equal to one and the fame Tiring^ are
equal to one another j
Therefore thofe two Triangles, each equal to the
Square of a Line of three Inches , are equal
between themfelves j
is complete in its Kind, and contains all that is
neceflary towards a juft and legitimate Conclu-
fion. For the firft or univerfal Propofition is
felf-evident, and therefore requires no farther
Proof. And as the Truth of the Particular is
infeparably connected with that of the Univer-
fal, it follows from it by an obvious and una-
voidable Confequence.
XII. Now in all Cafes of this Alindutittt
kind where Proportions are deduc- to fjlhgifm*
ofjomt one
ed one from another, on account of Form or ether.
a known and evident Connection, we are faid
to reafoa by immediate Confequence. Such a Co-
herence of Propofitions, manifeft at firft fight,
and forcing itfelf upon the Mind, frequently
occurs in Reafoning. Logicians have explained
at fome length, the feveral Suppofitions upon
which it takes place, and allow of all immediate
Conferences that follow in Conformity to them.
It is however obfervable, that thefe Arguments,
though feemingly complete, becaufe the Con-
clufion follows necelTarily from the fingle Pro-
pofition that goes before, may yet be confidered
as real Enthymemes, whofe Major, which is a
conditional Propofition, is wanting. The Syl-
M logifm
loglfm but juft mentioned, when reprefented ac-
cording to this View, will run as follows :
If Things equal to one and the fame Tiring are
equal to one another ; thefe two Triangles,
each equal to a Square whofe Side is three
Inches, are alfo equal between themfelves.
But Things equal to one and the fame Thing,
are equal to one another ;
Therefore alfo thefe Triangles, &c. are equal
between themfelves.
This Obfervation will be found to hold in all
immediate Confequences whatfoever, infomuch that
they are in fa& no more than Enthymemes of hy-
pothetical Syllogifms. But then it is particular
to them, that the Ground on which the Conclu-
fion refts, namely, its Coherence with the Minor,
is of itfelf apparent, and feen immediately to flow
from the Rules and Reafons of Logick. As
it is therefore intirely unneceflary to exprefs a
felf-evident Connection, the Major, whofe Office
that is, is conftantly omitted} nay, and feems
fo very little needful to enforce the Conclufion,
as to be accounted commonly no Part of the Ar-
gument at all. It muft indeed be owned, that
the foregoing immediate Consequence might have
been reduced to zfimple, as well as an hypothetical
Syllogifm. This will be evident to any one who
gives himfelf the Trouble to make the Experi-
ment. But it is not my Defign to enter farther
into
( 243 )
into thefe Niceties, what has been faid fufficing
to fhew, that all Arguments confiding of but
two Propofitions are real Entbymemes, and redu-
cible to complete Syllogtfms of fome one Form
or other. As therefore the Ground on which
the Conclufion refts, muft needs be always the
fame with that of the Syllogifms to which they be-
long, we have here an univerfal Criterion, whereby
at all times to afcertain the Juftnefs and Validity
of our Reafonings in this Way.
XIII. The next Species of Rea-
A Sontes of
foning we (hall take notice of here 5 plain fimpic
is what is commonly known by the 3 'S'J ms
Name of a Sorites. This is a Way of arguing,
in which a great Number of Propofitions are for
linked together, that the Predicate of one be-
comes continually the Subject of the next follow-
ing, until at laft a Conclufion is formed, by
bringing together the Subject of the firft Propo-
fition and the Predicate of the laft. Of this kind
is the following Argument :
God is omnipotent.
An omnipotent Being can do every thing pojjlble.
He that can do every thing pojfible, can da
whatever involves not a Contradiction :
Therefore Goo' can do whatever Involves not a
Contradiction.
This particular Combination of Propofitions
may be continued to any Length we pleafe,
M z with-
> ( 244 )'
without in the leaft weakening the Ground up-
on which the Conclufion refts. The Rcafon is,
becaufe the Sorites itfelf may be refolved into as
many fimple Syllogifms as there are middle
Terms in it j where this is found univerfally to
hold, that when fuch a Refolution is made, and
the Syllogifms are placed in train, the Conclu-
fion of the laft in the Series is alfo the Conclu-
fion of the Sorites. This kind of Argument there-
fore, as it ferves to unite feveral Syllogifms into
one, muft ftand upon the fame Foundation with
the Syllogifms of which it confilrs, and is in-
deed, properly fpeaking, no other than a com-
pendious Way of Reafoning fyllogiftically. Any
one may be fatisfied of this at Pleafure, if he but
takes the Trouble of refolving the foregoing
Sorites into two diftindt Syllogifms. For he
will there find, that he arrives at the fame Con-
clufion, and that too by the very fame Train of
thinking, but with abundantly more Words,
and the Addition of two fuperfluous Propofi-
tions.
. c . e XIV. WHAT is here faid of
A Sorttei of
hypothetical plain fimple Propofitions, may be
well applied to thofe that are con-
ditional ; that is, any Number of them may be
fo joined together in a Series, that the Con-
fcquent of one, fhall become continually the
Antecedent of the next following j in which
Cafe, by eftablifliing the Antecedent of the firit
8 Fro-
( 245 )
Propofition, we eftablifh the Confequent of the
laft, or by removing the laft Confequent, remove
alfo the firft Antecedent. This Way of Rea-
foning is exemplified in the following Argu-
ment :
If we love any Per fan, all Emotions of Hatred
towards him ceafe.
If all Emotions of Hatred towards a Perfott
ceafe j ^ve cannot rejoice in his Misfortunes*
If we rejoice not in his Misfortunes, we cer-
tainly wijb him no Injury,
llwefore if we love a^ P erf on, we wijh him
no Injury.
It is evident that this Sorites, as well as the laft,
may be refolved into a Series of diftincl Syllo-
gifms, with this only Difference, that here the
Syllogifms are all conditional. But as the Con-
clufion of the laft Syllogifm in the Series is the
fame with the Concluflon of the Sorites, it is
plain, that this alfo is a compendious Way of
Reafoning, whofe Evidence arifes from the Evi-
dence of the feveral fingle Syllogifms into which
it may be refolved.
XV. I COME now to that kind of ,, _ . _
The Ground of
Argument which Logicians call In- Reafoning by
. . . / L i_ TT Indufiioit*
duftion ; m order to the right Un-
derftanding of which, it will be neceflary to ob-
ferve, that our general Ideas are for the moft
part capable of various Subdivifions. Thus the
Idea of the loweft Species may be fubdivided
M into
into its feveral Individuals ; the Idea of any
Genus, into the different Species it compre-
hends; and fo of the reft. If then we fuppofc
this Diftribution to be duly made, and fo as to
take in the whole Extent of the Idea to which
it belongs; then it is plain, that all the Sub-
divifions or Parts of any Idea taken together
conftitute that whole Idea. Thus the feveral
Individuals of any Species taken together con-
ftitute the whole Species, and all the various
Species comprehended under any Genus, make
up the v/hole Genus. This being allowed, it is
apparent, that whatfoever may be affirmed of all
the feveral Subdivifions and ClafTes of any Idea,
ought to be affirmed of the whole general Idea to
which thefe Subdivifions belong. What may
be affirmed of all the Individuals of any Species,
may be affirmed of the whole Species ; and what
may be affirmed of all trie Species of any Genus,
may alfo be affirmed of the whole Genus ; be-
caufe all the Individuals taken together, are the
fame with the Species, and all the Species taken
together, the fame with the Genus.
XVI. THIS Way of arguing
The Form and . . r . r ..
Sirufiurt of where we infer umverially concern-
t* ?$"*' in? any Idea, what we had before
ty laaufiiin. z> J
affirmed or denied feparately, of all
its feveral Subdivifions and Parts, is called Rea-
foning by Induction. Thus if we fuppofe the
whole Tribe of Animals, fubdivided into Men,
Beafts,
( 247 )
Eeafts, Birds, Infe&s, and Fifties, and then- rea-
fon concerning them after this Manner : AH
Mtn Jiave a Power of beginning Motion ; all Beafts,
Birds, and Infefis, have a Power of beginning Mo-
tion j all Fijhes have a Power of 'beginning Motion ;
therefore all Animals have a Power of beginning
Motion : The Argument is an Induttion. When
the Subdivisions are juft, fo as to take in the
whole general Idea, and the Enumeration is
perfect, that is, extends to all and every of the
inferior Clafles or Parts ; there the Induction is
complete, and the manner of Reafoning by In-
duftion is apparently concluilve.
XVII. THE laft Species of Syl- Tit Ground
logifms I fhall take notice of in this t y?~
Chapter, is that commonly diftin- Dilemma.
guilhed by the Name of a Dilemma. A Dilemma
is an Argument by which we endeavour to
prove the Abfurdity or Falfehood of fome Afler-
tion. In order to this we aflame a conditional
Propofition; the Antecedent of which is the Af-
fertion to be difproved and the Confequent a
disjunctive Propofition, enumerating all the pof-
fible Suppofitions upon which that AfFertion can
take place. If then it appears, that all thefe fe-
veral Suppofitions ought to be rejected, it is
plain, that the Antecedent, or Aflertion, itfelf,
muft be fo too. When therefore fuch a Pro-
pofition as that before-mentioned, is made the
Major of any Syllogifm ; if the Minor rejedts all
M 4 the
the Suppofitions contained in the Conicquent, ft
follows neceflarily, that the Conclufion ought to
reje<5l the Antecedent, which, as we have faid, is
the very Aflertion to be difproved. This parti-
c,ular Way of arguing, is that which Logicians
call a Dilemma', and from the Account here given
of it, it appears, that we may in general define
it, to be an hypothetical SyllogifM, where the Con-
fequent of the Major is a disjunctive Propofition^
which is -wholly taken away or removed in the Mi-
nor. Of this kind is the following :
JfGod did not create the World perf eft in its
kind) it miift either proceed from want of
Inclination, or from want of Power.
But it could not proceed either from want of
Inclination^ or from want of Power.
Therefore he created the World per feel in its,
kind. Or, which is the fame thing : 'Tis
abfurd tefay that he did not create the World
perfe.ft in its kind.
Jn ua ; ve ,fai XVHK The Nature then of a.
Dilemma is univerfally this. The
*
cflt. . _
Major is a conditional rropoluion,.
whofe Confequent contains all the feveral Sup-
pofitions upon which the Antecedent can take
place. As therefore thefe Suppofitions are whol-
ly removed into the Minor y it is evident that
the Antecedent muft be fo too ; infomuch that
we here always argue from the Removal of the
Confequent to the Removal of the Antecedent..
That
( 249 J
That is, a Dilemma is an Argument, in the trio*
dus tollens of hypothetical Syllogifms, as Logici-
ans love to (peak. Hence it is plain, that if the
Antecedent of the Major is an affirmative Propo-
fitiori, the Conclufion of the Dilemma will be
negative ; but if it is a negative Propofition, the
Conclufion will be affirmative. I cannot dif-
mifs this Subject without obferving, that as
there is fomething very curious and entertaining
in the Structure of a Dilemma, fo is it a Manner
of Reafoning that occurs frequently in mathema-
tical Demonstrations. Nothing is more com-
mon with Euclid^ when about to mew the Equa-
lity of two given Figures, or which is the fame
thing, to prove the Abfurdity of aflerting them
unequal ; nothing, 1 fay, is more common
with him than to afiume, that if the one is not
equal to the other, it mujl be either greater or lefs :
and having deftroyed both thefe Suppofitions,
upon which alone the Aflertion can ftand, he
thence very naturally infers, that the Aflertion
itfelf is falfe. Now this is precifely the Reafon-
ing of a Dilemma, and in every Step coincides;
with the Frame and Compofition of that Argu-
ment, as we have defcribed it above*
M $ CHAP,
C 250 )
CHAP. V.
Of DEMONSTRATION.
of Reafowg I. T J AV I N G difpatched what
by a Cincate- """
T J
"""
JL JL
- / rr
ration of Sy i- JL JL fecmcd necefiacy to be laid
gifms, we now proceed to fuppiy their Ufe and
Application in Reafoning. We have feen, that
in all the different Appearances they put on, we
ftill arrive at a juft and legitimate Conclufion :
Now it often happens, that the Conclufion of
one Syllogifm becomes a previous Propofition
in another, by which means great Numbers of
them are fometimes linked together in a Series,
and Truths are made to follow one another in
Train. And as in fuch a Concatenation of Syl-
logifms, all the various Ways of Reafoning that
are truly conclufive, may be with Safety intro-
duced ; hence it is- plain, that in deducing any
Truth from its firft Principles, efpecially when
it lies at a confiderable Diftance from them, we
are at Liberty to combine all the feveral kinds of
Arguments above explained, according as they
are found beft to fuit the End and Purpofe of our
Inquiries. When a Propofition is thus, by means
of SyllogifmSj collected from others more evident
and
and known, it is faid to be proved j fo that we may
in the general define the Proof of a Propofition y
to be a Syllogifm,. or Series of Syllogifms, col-
Jecling that Propofition from known and evident
Truths. But more particularly, if the Syllo-
gifms of which the Proof confifts, admit of no
Premifes but Definitions, felf-evident Truths,
and Propofitions already eftablifhed, then is the
Argument fo conftituted called a Demon/oration j
whereby it appears, that Demonftrations are ul-
timately founded on Definitions and felf-evident
Propofitions.
II. BUT as a D'emonftration oft- Ms 3 tt, g if Kf
times confifts of a long Chain of wtarjuver
T r u 11 i. TTT reducible to
Proofs, where all the various Ways tbefrft Fi~
of arguing have place, and where the gure '
Ground of Evidence muft of courfe be different irr
different Parts, agreeably to the Form of the Ar-
gument made ufe of; it may not perhaps be un-
acceptable, if we here endeavour to reduce the
Evidence of Demonftration. to one fimple Prin-
ciple, whence, as a (lire and unalterable Foun-
dation, the Certainty of it may in all Cafes be
derived. In order to this we muft obferve, that
all Syllogifms whatfoever, whether compound,
multiform, or defective, are reducible to plain
fimple Syllogifins in fome one of the four Fi-
gures. But this is not all. Syllogifms of the firft
Figure in particular admit of all poffible Con-
clufions; that is, any Propofition whatfoever,
M 6 whether
c *5 y
whether an univerfal Affirmative, or univerfaV
Negative, a particular Affirmative or particu-
lar Negative, which fourfold Divifion, as we
have already demonftrated in the fecond Part,
embraces all their Varieties ; any one, I fay,
of thefe may be inferred, by virtue of fome Syl-
logifm in the firft Figure. By this means it
happens that the Syllogifms of all the other Fi-
gures are reducible alfo to Syllogifms of the firft
Figure, and may be confidered as ftanding en the
fame Foundation with them. We cannot here
demonftrate and explain the Manner of this Re-
duclion, becaufe it would too much fwell the
Bulk of this Treatife. It is enough to take no-
tice, that the Thing is univerfally known and
allowed among Logicians, to whofe Writings
we refer fuch as defire farther Satisfaction in this
Matter. This then being laid down, it is plain,
that any Demonftration whatfoever may be con-
fidered as compofed of a Series of Syllogifms, all
in the firft Figure. For fince all the Syllogifms,
that enter the Demonftration, are reduced to-
Syllogifms of fome one of the four Figures, and
fince the Syllogifms of all the other Figures are
farther reducible to Syllogifms of the firft Fi-
gure, it is evident, that the whole Demonftra-
tion may be refolved into a Series of thefe laft
Syllogifms. Let us now if pofllble difcover the
Ground upon which the Conclufion refts, in
Syllogifras of the firft Figure j becaufe by fo do-
( 253 ) %
ing, we fhall come at an univerfal Principle of
Certainty, whence the Evidence of all Demon-
ftrations in all their Parts may be ultimately de-
rived.
III. THE Rules then of the firft TbiGrcur.dof
Figure are briefly thefe. The mid- ffijffil*
die Term is the Subject of the Major gurt.
Propofition, and the Predicate of the Minor.
The Major is always an univerfal Propofition,
and the Minor always affirmative. Let us now
fee what Effect thefe Rules will have in Reafon-
ing. The Major is an univerfal Propofition,
of which the middle Term is the Subject, and
the Predicate of the Conclufion the Predicate.
Hence it appears, that in the Major^ the Pre-
dicate of the Conclufion is always affirmed or de-
nied univerfally of the middle Term. Again, the
Minor is an affirmative Propofition, whereof
the Subjeft of the Conclufion is the Subject, and
the middle Term the Predicate. Here then the
middle Term is affirmed of the Subjeft of the Con-
clufion: that is, the SubjeSl of the Conclufion is
affirmed to be comprehended under, or to make
a Part of the middle Term. . Thus then we fee
what is done in the Premifes of a Syllogifm of
the firft Figure. The Predicate of the Conclu-
fion is univerfally affirmed or denied of fome
Idea. The Subjett of the Conclufion is affirmed
to be, or to make a Part of that Idea. Hence
it naturally and unavoidably follows, that the
Predicate
( 254 )
Prtdicate of the Conclufion ought to be affirmed 07
denied of the Subject. To illuftrate this by an
Example, we (hall refume one of the Syllogifms
of the firft Chapter :
Every Creature poj/ejfed of Reafcn and Liberty
is accountable for his Actions.
Man is a Creature poffejfed of Reafon and
Liberty :
Therefore Man is accountable for his Actions.
Here in the firft Proportion, the Predicate of
the Conclufion Accountablenefs is affirmed of all
Creatures that have Reafon and Liberty* Again,
in the fecond Propofition, Man y the Subject of
the Conclufion, is affirmed to be, or to make
a Part of this Clafs of Creatures. Hence the
Conclufion neceflarily and unavoidably follows,
viz. that Man is accountable for his Actions. I
fay this follows neceiTarily and unavoidably.
Becaufe if Reafon and Liberty be that which
conftitutes a Creature accountable^ and Man has
Reafon and Liberty, it is plain he has that
which conftitutes him accountable. In like man-
ner, where the Major is a negative Propofition,
or denies the Predicate of the Conclufion univerfally
of the middle Term, as the Minor always afTerts
the SubjecJ of the Conclujion to be or make a Part
of that middle Term, it is no lefs evident, that
the Predicate of the Conclufon ought in this Cafe
to be denied of the Subject. So that the Ground
of Reafoning in all Syllogifms of the firft Fi-
gure
gurc is manifeftly this: JPTjatever may le af-
firmed univerfally of any Idea, may be affirmed of
(very or any Number of Particulars comprehended,
under that Idea. And again : Whatever may be
denied univerfally of any fdea, may be in like Man-
ner denied of every or any Number of its Indivi-
duals. Thefe two Propofitions are called by
Logicians the Diflum de omni, and Dictum de
nullo, and are indeed the great Principles of
fyllogiftick Reafoning j inafmuch as all Con-
clufions whatfoever, either reft immediately
upon them, or upon Propofitions deduced from
them. But what adds greatly to their Value is,
that they are really felf-evidertt Truths, and
fuch as we cannot gain fay, without running
into an exprefs Con trad idlion. To affirm, for
Inftance, that No man is perfefl, and yet argue
that Some Men are perfeft ; or to fay that All
Men are mortal, and yet that Some Men are not
mortal^ is to aflfert a Thing to be and not to be
at the fame Time.
IV. AND now I think we are fuf- Dtmonflranan
r. . , . . i ff. an infallible
hciently authorized to affirm, that Guide toTmb
in all Syllogifms of the firft Figure, *<*&' tainty.
if the Premifes are true, the Conclufton muft needs
be true. If it be true that the Predicate of the
Conclufion, whether affirmative or negative, a-
grees univerfally to fome Idea, and if it be alfo
true, that the Subjeft of the Conclufion is a Part
of or comprehended under that Idea, then it
neceiTarily
neceflarily follows, that the Predicate of the Cert-
clttfjon agrees alfo to the Subjeft. For to afTert
the contrary, would be to run counter to fome
one of the two Principles before eftablifhed ;
that is, it would be to maintain an evident Con-
tradiction. And thus we are come at laft to
the Point we have been all along endeavouring
to eftablifh, namely ; that every Proportion
which can be demonflrated is neceflarily true.
For as every Demonftration may be refolved into
a Series of Syllogifms all in the firft Figure, and
as in any one of thefe Syllogifms, if the Pre-
mifes are true, the Conclufion muft needs be fo
too : it evidently follows, that if all the feveral
Premifes are true, all the feveral Conclufions
are fo, and confequently the Conclufion alfo of
the laft Syllogifm, which is always the Propo-
fition to be demonftrated. Now that all the
Premifes of a Demonftration are true, will ea-
fily appear, from 'the very Nature and Definition
of that Form of Reafoning. A Demonftration,
as we have faid, is a Series of Syllogifms, all
whofe Premifes are either Definitions, felf-evi-
dent Truths, or Propofitions already eftablifhed.
Definitions are identical Propofitions, wherein
we connect the Defcription of an Idea with
the Name by which we choofe to have that
Idea called ; and therefore as to their Truth
there can be no Difpute. Self-evident Propo-
fitions appear true of themfelves, and leave no
Doubt
Doubt or Uncertainty in the Mind. Propofitioris
before eftablifhed, are no other than Conclu-
fions, gained by one or more Steps from Defini-
tions and felf-evident Principles j that is, from
true Premifes, and therefore muft needs be true.
Whence all the previous Proportions of a De-
inonftration, being we fee manifeftly true, the
laft Conclufion, or Propofition to be demon-
ftrated, muft be fo too. So that Demonftration
not only leads to certain Truth, but we have
here a clear View of the Ground and Founda-
tion of that Certainty. For as in demonftrating
we may be faid to do nothing more than com-
bine a Series of Syllogifms together, all refting
on the fame Bottom j it is plain, that one uni-
form Ground of Certainty runs thro' the whole,
and that the Conclufions are every where built
upon fome one of the two Principles before
eftablifhed as the Foundation of all our Rea-
foning. Thefe two Principles are eafily re-
duced into one, and may be exprefied thus:
Whatever Predicate, whether affirmative or nega-
tive, agrees univ erf ally to any Idea, the fame muft
needs agree to every or any Number of Individuals,
comprehended under that Idea. And thus at
length we" have, according to our firft Defign,
reduced the Certainty of Demonftration to one
fimple and univerfal Principle, which carries
Us own Evidence along with it, and which is
indeed
( 258 )
indeed the ultimate Foundation of all fyllogiftick
Reasoning.
ibt Ru/et of V. DEMONSTRATION therefore,
ajufficiemC^. feeing as an infallible Guide to
terienfor the Truth, and ftanding on fo fure and
dljlln^uljhing -
bttioetnTruib unalterable a Bans, we may now
*dF a i]tbo,d. venture to a fT ert , w hat I doubt not
will appear a Paradox to many ; namely, that
the Rules of Logiclc furnifh a fufficient Criterion
for the diftinguifhing between Truth and Falfe-
hood. For fmce every Proportion that can be
demonftrated, is neceflarily true, he is able to
diftinguifh Truth from Falfehood, who can with
Certainty judge when a Propofition is duly
demonftrated. Now a Demonftration is, as we
have faid, nothing more than a Concatenation
of Syllogifms, all whofe Premifes are Defini-
tions, felf-evident Truths, or Propofitions pre-
vioufly eftablifhed. To judge therefore of the
Validity of a Demonftration, we muft be able
to diftinguifh whether the Definitions that en-
ter it are genuine, and truly defcriptive of the
Ideas they are meant to exhibit : whether the
Propofitions alTumed without Proof as intuitive
Truths, have really that Self-evidence to which
they lay claim : whether the Syllogifms are
drawn up in due Form, and agreeable to the
Laws of Argumentation : in fine, whether they
are combined together in a juft and orderly
( 259 )
Manner, fo that no demonftrable Propositions
ferve any where as Premifes unlefs they are
Conclufions of previous Syllogifms. Now it
is the Bufmefs of Logick, in explaining the
/everal Operations of the Mind, fully to inftruct
us in all thefe Points. It teaches the Nature
and End of Definitions, and lays down the
Rules by which they ought to be framed. It
unfolds the feveral Species of Propofitions, and
diftinguifhes the felf-evident from the demon-
ftrable. It delineates slfo the different Forms
of Syllogtfms, and explains the Laws of Argu-
mentation proper to each. In fine, it defcribes
the Manner of combining Syllogifms fo as that
they may form a Train of Reafoning, and lead
to the fucceflive Difcovery of Truth. The
Precepts of Logick therefore, as they enable us
to judge with Certainty, when a Propofition is
duly demonftrated, furnifh a fure Criterion for
the diftinguifhing between Truth and Falfe-
hood.
VI. BUT perhaps .it may be ob- . ,
/ And extending
iected, that Demonftration is a thing to all Cafes
i i where a cer-
very rare and uncommon, as being tain Know .
the Prerogative of but a few Sci- '<* '/Truth
* , f , . is attainable.
ences, and therefore the Criterion
here given can be of no great Ufe. I anfwer,
that wherever by the bare Contemplation of our
Ideas, Truth is difcoverable, there alfo De-
monftration may be obtained. Now that I think
is
( 260 }
is an abundantly fufficient Criterion, which en-
ables us to judge with Certainty, in all Cafes
where the Knowledge of Truth comes within
our Reach ; for with Difcoveries that lie be-
yond the Limits of the human Mind we have
properly no Bufmefs nor Concernment. When
a Proportion is demonftrated, we are certain of
its Truth. When, on the contrary, our Ideas
are fuch as have no vifible Connection nor
Repugnance, and therefore furnifh not the pro-
per Means of tracing their Agreement or Dif-
agreement, there we are fure that Knowledge,
Scientifical Knowledge I mean, is not attain-
able. But where there is fome Foundation of
Reafoning, which yet amounts not to the full
Evidence of Demonftration, there the Precepts
of Logick, by teaching us to determine aright
of the Degree of Proof, and of what is ftill
wanting to render it full and complete, enable
us to make a due Eftimate of the Meafures of
Probability, and to proportion our Aflent to
the Grounds on which the Proportion flands.
And this is all we can pofftbly arrive at, or
even fo much as hope for, in the Exercife of
Faculties fo imperfect and limited as ours. For
it were the Height of Folly to expect a Criterion
that fhould enable us to diftinguiih Truth from
Falfehood, in Cafes where a certain Knowledge
of Truth is not attainable.
VII. WE
VII. WE have now done with ne ^^; Bf .
what regards the Ground and Evi- tun of DC-
-IT. monjtratloit
dence of Demonftration ; but be- into- d\na
fore we conclude this Chapter, it aad '*>"*>
may not be improper to take Notice of the Dif-
tin&ion of it into direfl and Indirect. A direft
Demonjlratlon is, when beginning with Defini-
tions, felf-evident Propofitions, or known and
allowed Truths, we form a Train of Syllogifms,
and combine them in an orderly Manner, con-
tinuing the Series thro' a Variety of fuccefilve
Steps, until at laft we arrive at a Syllogifm,
whofe Conclufion is the Propofition to be de-
monftrated. Proofs of this kind leave no Doubt
or Uncertainty behind them, becaufe all the fe-
veral Premifes being true, the Conclufions muft
be fo too, and of courfe the very laft Conclufion,
or Propofition to be proved. I mail not there-
fore any farther enlarge upon this Method of
demonftrating ; having I hope fufKciently ex-
plained it in the foregoing Part of this Chapter,
and fhewn wherein the Force and Validity of it
lies. The other Species of Demonftration is
the indiref?) or, as it is fometimes called, the
dpological. The Manner of proceeding here
is, by afluming a Propofition which direclly
contradids that we mean to demonftrate, and
thence by a continued Train of Reafoning, in
the Way of a direct Demonftration, deducing
fome
( 262 )
fome Abfurdity or manifelt Untruth. For here-
upon we conclude that the Propofition a/Turned
was falfe, and thence again by an immediate
Confequence, that the Propofition to be demon-
ftrated is true. Thus Euclid in his third Book
being to demonftrate, that Circles which touch one
another inwardly have not the fame Center ; aflumcs
the direct contrary to this, viz. that they have
the fame Center; and hence by an evident Train
of Reafoning proves, that a Part is tqual to the
JPliole. The Suppofition therefore leading to
the Abfurdity he concludes to be falfe, viz. that
Circles touching one another inwardly have the fame
Center^ and thence again immediately infers,
that they have not the fame Center.
GriundofRea- VIII. Now becaufe this Manner
J?!i?" of Demonftration is accounted by
^rations. fome not altogether fo clear and fa-
tisfa&ory, nor to come up to that full Degree
of Evidence, which we meet with in the diredl
Way of Proof; I fhall therefore endeavour here
to give a particular Illuftration of it, and to (hew
that it equally with the other leads to Truth and
Certainty. In order to this we muft obferve,
that two Propofitions are faid to be contradictory
one of another, when that which is aflerted to
be in the one, is aflerted not to be in the other.
Thus the Propofitions : Circles that touch one an-
ether inwardly have the fame Center ; and Circles
that
that touch one another inwardly have not the fame
Center : are Contradiflories ; becaufe the fecond
aflerts the direct contrary of what is aflerted in
the firft. Now in all contradictory Propofiti-
ons this holds univerfally, that one of them is
neceflarily true, and the other neceflarily falfe.
For if it be true, that Circles which touch one
another inwardly have not the fame Center, it
is unavoidably falfe that they have the fame
Center, On the other hand, if it be falfe that
they have the fame Center, it is neceflarily true
that they have not the fame Center. Since there-
fore, it is impoflible for them to be both true or
both falfe at the fame time, it unavoidably fol-
lows, that one is neceflarily true, and the other
neceflarily falfe. This then being allowed, which
is indeed felf-evident, if any two contradictory
Propofitions are afTumed, and one of them can
by a clear Tram of Reafoning be demonftrated
to be falfe, it neceflarily follows that the other
is true. For as the one is necefTarily true, and
the other neceflarily falfe, when we come to dif-
cover which is the falfe Propofition, we thereby
alfo know the other to be true.
IX. Now this is precifely the Indinsi Di-
_ _ _ . .. _. _. n ntonftrationt a
Manner of an indirect Demonltra- j ure Guide to
tion, as is evident from the Account Certa '""y'
given of it above. For there we aflume a Pro-
pofition which directly contradicts that we. mean
to demonftrate, and having by a continued Se-
ries
ries of Proofs fhewn it to be falfe, thence infer
that its Contradictory, or the Propofition to
be demonftrated, is true. As therefore this laft
Conclufion is certain and unavoidable, let us
next inquire, after what Manner we come to
be fatisfied of the Falfehood of the afTumed
Propofition, that fo no pofiible Doubt may re-
main, as to the Force and Validity of Demon-
ftrations of this kind. The Manner then is
plainly this. Beginning with the afTumed Pro-
pofition, we by the Help of Definitions, felf-
evident Truths, or Propofitions already efta-
blifhed, continue a Series of Reafoning, in the
Way of a direct Demonftration, until at length
we arrive at fome Abfurdity or known Falfe-
hood. Thus Euclid, in the Example before
mentioned, from the Suppofition that Circles
touching one another inwardly have the fame
Center, deduces that a Part is equal to the
Whole. Since therefore by a due and orderly
Procefs of Reafoning, we come at laft to a falfe
Conclufion, it is manifeft that all the Pre-
mifes cannot be true. For were all the Pre-
mifes true, the laft Conclufion muft be fo too,
* by what has been before demonftrated. Now
as to all the other Premifes made ufe of in the
Courfe of Reafoning, they are manifeft and
known Truths -by Suppofition, as being either
Definitions, felf-evident Propofitions, or Truths
eftablifhed. The aflumcd Propofitign is that
on!/
only as to which any Doubt or Uncertainty
remains. That alone therefore can be falfe, and
indeed from what has been already {hewn, mud
unavoidably be fo. And thus we fee, that in
indirect Demonstrations, two contradictory Pro-
positions being laid down, one of which is de-
monflrated to be falfe, the other, which is al-
ways the Propofition to be proved, muft necefla-
rily be true j fo that here, as well as in the direct
Way of Proof, we arrive at a clear and fatif-
factory Knowledge of Truth.
X. THIS is univerfally the Me- Apartau'ar
thod of Reafoning in all Apological c l/</'^'-
i O N red D:msn-
or indirect Demonftrations j but flranen.
there is one particular Cafe, which has fome-
thing fo fingular and curious in it, that well de-
ferves to be mentioned byitfelf; more efpecially,
as the Ground on which the Conclufion refts
will require fome farther Illuftration. It is in
fliort this : that if any Propofition is alTumed,
from which in a direct Train of Reafonins: we
O
can deduce its Contradictory, the Propofition
fo afTumed is falfe, and the contradictory one
true. For if we fuppofe the afTumed Propofi-
tion to be true, then, fince all the other Prcmifes
that enter the Demonftration are alfo true, we
fhall have a Series of Reafoning, confining
wholly of true Premifes ; whence the la ft Con-
clwfion, or Contradictory of the aiTumed Pro-
N
( 266 )
pofition, muft be true likewife. So that by this
Means we fhould have two contradictory Pro-
pofitions both true at the fame Time, which is
manifeftly impoflible. The afTumed Propofition
therefore whence this Abfurdity flows, muft ne-
cefiarily be falfe, and confequently its Contra-
dictory, which is here the Proportion deduced
from it, muft be true. If then any Propofition
is propofed to be demonftrated, and we ajjume
the ContradiRory of that Propofition, and thence
directly infer the Propofition to be demonftrated,
by this very Means we know that the Propofition
fo inferred is true. For fince from an aiTumed
Propofition we have deduced its Contradictory,
we are thereby certain that the afiumed Propofi-
tion is faifej and if fo, then its Contradictory, or
that deduced from it, which in this Cafe is the
fame with the Propofition to be demonftrated,
muft be true.
XI. THAT this is not a mere
A due Kntto- , . i r n TT*
ledge of the empty Speculation, void of all Ufe
?*fii> of an( j Application in Practice, is evi-
Logick indtf-
fcfaiiy re- dent from the Conduct of the Ma-
I'rPI/'r*"" ' thematicians, who have adopted this
judges cfDe- Manner of Reafoning, and given it
tncr/lraiien. .
a Place among their Uemonitra-
tions. We have a curious Inftance of it in the
twelfth Propofition of the ninth Book of the
Elements. Euclid there propofes to demon-
ftrate,
ftrate, that in any Series of Numbers, rlfingfrofn
Unity in Geometrical PrsgreJJlon^ all the Prims
Numbers that meafnre the lajl Term In the Series*
will alfo meafure the next after Unity. In order
to this he afiumes the Contradictory of the
Propofition to be demonftrated, namely; that
fame prime Number measuring the lajl Term In the
Series^ 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 aflumed Propofition to be falfe,
and that which is deduced from it, or its Contra-
dictory, which is the very Propofition he pro-
pofed to demonftrate, to be true. Now that
this is a juft and conclufive Way of Reafoning^
is abundantly manifeft, from what we have fo
clearly eftablifhed above. I would only here
obferve, how neceiTary fome Knowledge of the
Rules of Logick is, to enable us to judge of the
Force, Juftnefs, and Validity of Demonftrations;
fince fuch may fometimes occur, where the
Truth of the Propofition demonstrated will nei-
ther be owned nor perceived, unlefs we know
before-hand, by means of Logick, that a Con-
clufion fo deduced, is neceflarily true and valid,
For though it be readily allowed, that by tho-
mere Strength of our natural Faculties, we can at
once difcern, that of two contradictory Propo-
fitions, the one is neceflarily true, and the other
N 2 neceflarily
( 268 )
irecefiarily falfe : yet when they are fo linked to-
gether in a Demonftration, as that the one ferves
as a previous Propofition, whence the other is
deduced; it does not fo immediately appear,
without fome Knowledge of the Principles of
Logick, why that alone which is collected by
Reafoning, ought to be embraced as true, and
the other whence it is collected to be rejected
as falfe.
XII. HAVING thus I hope fuf-
And of itfilf r , , -it y,
f*jftent to nciently evinced the Certainty of
guard a- Demonftration in all its Branches,
gatr.jt En or
**df*ift and ihewn the Rules by which we
ought to proceed, in order to arrive
at a juft Conclufion, according to the various
Ways of arguing made ufe of; I hold it need-
lefs to enter upon a particular Confideration
of thofe feveral Species of falfe Reafoning
which Logicians diftinguifh by the Name of
Syphifms. He that thoroughly underflands the
Form and Structure of a good Argument, will
of himfelf readily difcern every Deviation from
it. And although Sophifms have been divided
into many Clafles, which are all called by found-
ing Names, that therefore carry in them much
Appearance of Learning ; yet are the Errors
themfelves fo very palpable and obvious, that I
Ihould think it loft Labour to write for a Man
capable of being milled by them. Here there-
fore
fore we choofe to conclude this third Part of Lo-
gicic, and {hall in the next Book give fome Ac-
count of Method^ which though infeparable from
Reafoning is neverthelefs always confidered by
Logicians as a diftindl Operation of the Mind j
becaufe its Influence is not confined to the mere
Exercife of the Reafoning Faculty, but extends
in fome Degree to all the Tranfaclions of the
Underftanding,
N a THE
THE
ELEMENTS
O F
L O G I C K.
BOOK IV.
CHAP. I.
Of Method in general, and the Divificn of if
info Analytick and Synthetick.
Ti-t UuJtr- I. "T "V T E have now done with
Ji ending feme- VV , r /l f^.
nm,s tmfhytd T T the three iuft Opera-
"?."" '"&"- tionsof the Mind, v/hofe Office it
fitter h noio
Truths. is to fearch after Truth, and enlarge
the Bounds of human Knowledge. There is
yet a fourth, which regards the Difpofal and
Arrangement of our Thoughts, when we endea-
vour fo to put them together, that their mutual
Connection
Connection and Dependence maybe dearly feen^
This is what Logicians call Method, and place
always the laft in Order in explaining the
Powers of the Underftanding ; becaufe it necef-
farily fuppofes a previous Exercife of our other
Faculties, and fome Progrefs made in Know-
ledge, before we can exert it in any extenfive
Degree. It often happens in the Purfuit 'of
Truth, that unexpected Discoveries prcfent them-
felves to the Mind, and thofe too relating to Sub-
jects very remote from that about which we are
at prefent employed. Even the Subjects them-
felves of our Enquiry, are not always chofen
with a due Regard to Order, and their Depen-
dence one upon another. Chance, our particu-
lar Way of Life, or fome prefent and preffing
Views, often prompt us to a Variety of Re-
iearches, that have but little Connection in the
Nature of Things. When therefore a Man ac-
cuftomed to much Thinking comes, after any
eonfiderable Interval of Time, to take a Survey
of his intellectual Acquifitions, he feldom finds
Reafon to be fatisfied with that Order and Dif-
pofuion, according to which, they made their
Entrance into his Underftanding. They are
there difperfed and fcattered, without Subordi-
nation, or anyjuft and regular Coherence j info-
much that the Subferviency of one Truth to the
Difcovery of another does not fo readily appear
N 4 to*
o the Mind. Hence Jie is convinced of the Nc-
ceffity of diftiibuting them into various Clafles,
.uid combining into an uniform Syftem whatever
relates to one and the fame Subject. Now this is
the true and proper Bulinefs of Method ; to af-
certain the various Divifions of human Know-
ledge, and fo to adjuft and connect the Parts in
every. Branch, that they may feem to grow one
out of another, and form a regular Body of Sci-
ence, rifing from firft Principles, and proceeding* 1
by an orderly Concatenation of Truths.
Sometimes in JI. IN this View of Things It IS
tr?.^ard> and p\ a ' ir} that we muft be before-hand
UlJfWtry uf
flct at are well acquainted with the Truths we
are to combine together : othcrwife
how could we difcern their feveral Connec-
tions and Relations, "or fo difpofe of them as their
mutual Dependence may require ? But now it
often happens, the Underftanding is employed,
not in the Arrangement and Competition of
known Truths, but in the Search and Difcovery
of fuch as are unknown. And here the Manner
of proceeding is very different, inafmuch as we
ailemble at once our whole Stock of Knowledge
relating to any Subject, and after a general Sur-
vjy of Things, begin with examining them fe-
parately and by Parts. Hence it comes to pafs,
that whereas at our firit fetting out, we were ac-
quainted only with fome of the grand Strokes
and
and Outlines, if I may fo fay of Truth, by thus
purfuing her through her feveral Windings and
Recefles, gradually difcover thofe more inward
and finer Touches, whence (he derives all her
Strength, Symmetry, and Beauty. And here it
is that when by a narrow Scrutiny into Thing?,
we have unravelled any Part of Knowledge, and
traced it to its firft and original Principles, info-
much that the whole Frame and Contexture of it
lies open to the View of the Mind ; here I fay it
is, that taking it the contrary Way, and begin-
ning with thefe Principles, we can fo adjuft and
put together the Parts, as the Order and Me-
thod of Science requires.
III. BUT as thefe Things are beft
n , , ... n 11 T- JUuflrated hy
underftood when illuftrated by Lx- the Similitude
amples y efpecially if they are obvi- c / " Watcb '
ous, and taken from common Life; let us fup-
pofe any Machine, for inftance a Watch, pre-
fented to us, whofe Structure and Compofition
we are as yet unacquainted with, but want if
poflible to difcover. The Manner of proceeding
in this Cafe is, by taking the Whole to Pieces,
and examining the Parts feparately one aftec
another. When by fuch a Scrutiny we have
thoroughly informed ourfelves of the Frame and
Contexture of each, we then compare them to-
gether, in order to judge of their mutual Action
and Influence, By this means we gradually
N 5 trace
( 274 )
trace out the inward Make and Connpofition of ,
the Whole, and come at length to difcern, how
Parts of fuch a Form, and fo put together as we
found, in unravelling and taking them afunder,
conftitute that particular Machine called a
Watch, and contribute to all the fcveral Motions
and Phenomena obfervable in it. This Difco-
very being made, we can take Things the con-
trary Way, and beginning with the Parts, fo dif-
pofe and connect them, as their feveral Ufes and
Structures require, until at length we arrive at
the Whole itfelf, from the unravelling of which
thefe Parts refulted.
Ground f tie IV. AND as it is in tracing and
S$M*"* examining the Works of Art, fo it
Makedi. is in a great Meafure in unfolding
any Part of human Knowledge. For the Rela-
tions and mutual Habitudes of Thing?, do not
always immediately appear, upon comparing
them one with another. Hence we have re-
courfe to intermediate Ideas, and by Means of
them are furnifhed with thofe previous Propofi-
tions that lead to the Conclufion we are in queft
of. And if it fo happen, that the previous Pro-
pofitions themfelves are not fufficiently evident,
we endeavour by new middle Terms to afcertain
their Truth, ftill tracing Things backward in a
continued Series, until at length we arrive at fome
Syllogifm, where the Premifes are firft and felf-
evident
( 275
evident Principles. This done, we become per--
fe&ly fatisfied as to the Truth of all the Con-
elufions we have pafled through, inafmuch as-
they are now feen to frand upon the firm and im-
moveable Foundation of our intuitive Percep--
tions. And as we arrived at this Certainty, by
tracing Things backward to the original Prin-
ciples whence they flow, fo may we at any Time
renew it by a direct contrary Procefs, if begin-
ning with thefe Principles, we carry the Train
of our Thoughts forward, until they lead us by
a connected Chain of Proofs to the very laft Con-
clufion of the Series.
V. HENCE it appears,, that in Dwjion cf
i- r r i *. ' ^.L Me bad into
difpofmg and putting together our j aafytick ar , d
Thoughts, either for our own Ufe, Sytbetick.
that the Difcoveries we have made may at all
Times lie open to the Review of the Mind ; or
where we mean to communicate and unfold thefe
Difcoveries to others, there are two Ways of
proceeding equally within our Choice. For we
may fo propole the Truths relating to any Part
of Knowledge, as they prefented themfelves to
the Mind in the Manner of Inveftigation,
carrying on the Series of Proofs in a reverfe
Order, until they at laft terminate in firft Prin-
ciples : or beginning with thefe Principles we
may take the contrary Way, and from them de-.
duce,. by a direct Train of Reafoning, all the
N 6 feveral
feveral Proportions we want to efhiblifh. This
Diverfity in the Manner of arranging our
Thoughts gives rife to the twofold Divifion of
Method eftablifhed among Logicians. For Me-
thod, according to their Ufe of the Word, is no-
thing elfe but the Order and Difpofltion of our
Thoughts relating to any Subject. When Truths
are fo propofed and put together, as they were
or might have been difcovered, this is called
the Analytic Method, or the Method of Refolutwn \.
imfmuch as it traces Things backward to their
Source, and refolves Knowledge into its firft and-
original Principle. When on the other Hand they,
are deduced from thefe Principles, and. connected
according to t-heir mutual. Dependence,, infomuch
that the Truths fidl in Order tend always to the
Demonftration of thofe that follow, this confti-
tutes what we call the Sy.nthetick Method^ or Me-
thod of Ccmpofition. For here we proceed by ga-
thering together the feveral fcattered Parts of
Knowledge, and combining them into one Whole
or Syftem, in fuch Manner, that the Underftand-"
ing is enabled diftinclly to follow Truth through
all her different Stages and Gradations*
Called otber- VI. THERE is this farther to be
10 iii i be Me- XT f i t r
iko.i efiwen- taken Notice or, in relation to theie
i-T^'r* two Species of Method: that the
Method of
Kntr.ce. firft has alib obtained the Name of
the Method of Invention^ becaufc it cbfcrves the
Ordet
( 277 )
Order in which our Thoughts fucceed one an-
other in the Invention or Difcovery of Truth.
The other again is often denominated the Me-
thod of Doctrine or Injlruftion, i-nafmuch as in
laying our Thoughts before others, we generally
choofe to proceed in the Synthetici Manner, de-
ducing them from their nrft Principles. For
we are to obferve, that although there is great
Pleafure in purfuing Truth in the Method of
Inveftigation, becaufe it places us in the Con-
dition of the Inventor, and {hews the particular
Train and Procefs of Thinking by which he
arrived at his Difcoveries j yet it is not fo well
accommodated to the Purpofes of Evidence and
Conviction. For at our firft fetting out, we are
commonly unable to divine where the Analyfis
will lead us j infomuch that our Refearches are
for fome Time little better than a mere groping
in the Dark. And even after Light begins to
break in upon us, we are ftill obliged to many
Reviews, and a frequent Comparifon of the fe-
veral Steps of the Inveftigation among them-
felves. Nay, when we have unravelled the
Whole, and reached the very Foundation on
which our Difcoveries ftand, all our Certainty
in regard to their Truth will be found in a
great Meafure to arife from that Connexion we
are now able to difcern between them and firft
Principles, taken in the Order of Competition.
But iu the Synthetick Manner of difpofing our
Thoughts,
Thoughts, the Cafe is quite different. For as we
here begin with intuitive Truths, and advance
by regular Deductions from them, every Step of
the Procedure brings Evidence and Conviction
along with it ; fo that in our Progrefs from one
Part of Knowledge to another, we have always
a clear Perception of the Ground on which our
AfTent refts. In communicating therefore our
Difcoveries to others, this Method is apparently
to be chofen, as it wonderfully improves and
enlightens the Underiranding, and leads to an.
immediate Perception of Truth, And hence it
is, that in the following Pages, we choofe to
diftinguifh it by the Name of the Method of Sc i-
ence ; not only as in the Ufe of it we arrive at
Science and Certainty, but becaufe it is in Fail
the Method, in which all thofe Parts of human
Knowledge that properly bear the Name of
Sciences are and ought to be delivered. But we
now proceed to explain thefc two Kinds of Me-
thod more particularly.
CHAP. II,
Of the Method of Invention.
Origin of the 1. T)Y the Method of Invention we
underftand fuch a Difpofition
and Jniernom
f human Lifr. and Arrangement of our Thoughts,
as follows the natural Procedure of the Under-
Handing,
( 279 )
ftanding, and prefents them in the Order in
which they fucceed one another in the Invefti-
gation and Difcovery of Truth. Now it is
plain, that to handle a Subject fuccefsfully ac-
cording to this Method, we have no more to
do than obferve the feveral Steps and Advances
of our Minds, and fairly copy them out to the
View of others. And indeed it will be found
to hold in general, with regard to all the active
Parts of human Life, efpecially when reduced
to that which is in the Schools termed an Art j
that the Rules by which we conduct ourfelves
are no other than a Series of Obfervations drawn
from the Attention of the Mind to what pafles,
while we exercife our Faculties in that particu-
lar Way. For when we fet about any Inven-
tion or Difcovery, we are always pufhed on by
fome inward Principle, Difpofition, or Aptitude
fhall I call it, which we experience in ourfelves,
and which makes us believe, that the Thing we
are in queft of is not altogether beyond our
Reach. We therefore begin with efTaying our
Strength, and are fometimes fuccefsful, though
perhaps more frequently not. But as the Mind,
when earneftly bent upon any Purfuit, is not
eafily difcouraged by a few Difappointments,
we are only fet upon renewing our Endeavours,
and by an obftinate Perfeverance, and repeated
Trials, often arrive at the Difcovery of what
we have in View. Now it is natural for a Man
of
of a curious and inquifitive Turn, after having
mattered any Part of Knowledge with great La-
bour and Difficulty, to fet himfelf to examine
how he happened to rnifcarry in his firft At-
tempts, and by what particular Method of Pro-
cedure he at length came to be fuccefsful. By
this Means we difcover on the one Hand, thofe
Rocks and Shelves which ftand moft in our Way,
and are apt to difturb and check our Progrefs j
and on the other, that more fure and certain
Courfe, which if we continue in fteadily, will
bring us to the Attainment of what we are in
Purfuit of. Hence fpring ail the Arts and In-
ventions of human Life, which, as we have
already faid, are founded upon a Series of Rules
and Obfcrvations, pointing out the true and
genuine Manner of arriving at any Attainment.
When the Mind refts fatisfied in a baie Con-
templation of the Rules,, and the Reafons on
which they are founded, this Kind of Know-
ledge is called Speculative. But if we proceed
farther, and endeavour to apply thefe Rules to
Practice, fo as to acquire a Habit of exerting
them on all proper Occafions, we are then faid to
be poflefled of the Art itfelf.
II. FROM what has been faid it
WlyintrcatiKg
f the Method appears, that in order diltinctly tQ
l L l e 'figw explain the Method of Invention,.
fine Account if we mutt take a View of the Under-
tbe Art iijtlf. n .
funding as employed in the Search
and
and Inveftigation of Truth. For by duly at-
tending to its Procedure and Advances, we fhall
not only difcover the Rules by which it con-
duels itfelf, but be enabled alfo to trace out
the feveral Helps and Contrivances it makes
ufe of, for the more fpeedy and effectual At-
tainment of its Ends. And when thefe Parti-
culars are once known, it, will not be difficult
for us, in laying open our Difcoveries to others,
to combine our Thoughts agreeably to the Me-
thod here required. Becaufe having fixed and
afcertained the Rules of it, and being perfectly
acquainted with the Conduct and Manner -of
the Mind, we need only take a Review of the
feveral Truths as they fucceed one another in
the Series of Inveftigation, fet them in order
before us, and fairly tranfcribe the Appearance
they make to the Underftanding. Hence it is
that Logicians, in treating of the Method of
Invention, have not merely confined themfelves
to the laying down of Directions for the Dif-
pofal and Arrangement of our Thoughts ; but
have rather explained the Art itfelf, and efta-
blifhed thofe Rules by which the Mind ought to
proceed in the Exercife of its inventive Powers.
For they rightly judged, that if thefe were once
thoroughly underftood, the ether could no
longer remain unknown. By this Means it
happens that the Method of Invention is' become
another
C
another Expreffion for the Art of 'Invention, and
very often denotes the Conduct and Procedure
of the Underftanding in the Search of Truth.
And as fome Knowledge of the Principles of
the Art, is in a Manner abfolutely necefTary
towards a true Conception of the Rules by
which we ought to govern and difpofe our
Thoughts in treating Subjects after this Me-
thod ; we fliall therefore follow the Example
of other Logicians, and endeavour to give fome
fhort Account of the Bufinefs of Invention, and
of thofe feveral Helps and Contrivances by
which the Mind is enabled to facilitate and en-
large its Difcoveries.
III. IT has been already obferved,,
A'.ttarion and n i
e. cemtrtbtnjj-ve that when the Mind employs itfelf
U^nJi.g ; the s h of unknown Truths,
toe tnparatary
i^uaijcatiint it begins with aflembling at once its
t Ini/tntitn. , . -, . _ , r , , , .
whole Stock or Knowledge relating
to the SubjecT:, and after a general Survey of
Things, fets about examining them feparately
and by Parts. Now as in this feparate Exami-
nation, the Number of Parts continually in-
ereafe upon us j and as it is farther necefliiry r
that we fuivey them on all Sides, compare them
one. with another, and accurately trace their
mutual Habitudes and Refpecls ; it is from
hence apparent, that in the Exercife of Inven-
tion, two Things arc of principal Confideration..
Firft,
Firft, an enlarged and comprehenfive Under-
ftanding, able to take in the great Multitude
of Particulars that frequently come under our
Notice. Secondly, a ftrong Habit of Atten-
tion, that lets nothing remarkable flip its View,
and diftinguifhes carefully all thofe Circum-
ftances which tend to the illuftrating and clear-
ing the Subject we are upon. Thefe are the
great and preparatory Qualifications, without
which it were in vain to hope that any confi-
derable Advance could be made in enlarging
the Bounds of human Knowledge. Nor ought
we to efteem it a fmall Advantage, that they
are in fome Meafure in our own Power, and
may, by a proper Cultivation, be improved and
ftrengthened to a Degree almoft beyond Belief.
We find by Experience, that the Study of Ma-
thematicks in particular is greatly ferviceable to
this End. Habits we all know grow ftronger
by Exercife, and as in this Science there is a
perpetual Call upon our Attention, it by De-
grees becomes natural to us, fo as that we can
preferve it fteady and uniform, through long and
intricate Calculations, and that with little or
no Fatigue to the Underftanding. But a yet
more wonderful Advantage arifing from the
Culture of the Mathematicks is this, that hereby
we in fome Meafure extend the Dimenfions of
the human Mind, enlarge its Compafs of Per-
ception, and accuftom it to wide and compre-
henfive
henfive Views of Things. For whereas at our
firft fetting out, we often find it extremely dif-
ficult to matter a fhort and eafy Demonftration,
and trace the Connection of its feveral Parts j
yet as we advance in the Science, the Under-
ftanding is feen gradually to dilate, and ftretch
itfelf to a greater Size ; infomuch that a long
and intricate Series of Reafoning is often taken
in with fcarce any Labour of Thought j and not
only fo, but we can in fome Cafes, with a fingle
Glance of our Minds, run through an entire
Syftem of Truths, and extend our View at once
to all the feveral Links that unite and hold them,
together.
IV. WHEN we are furnifhed
j judicious
Choice of inter' with thefe two preparatory Quali-
tfZt fications, the next Requifite to the
Rtquiftte in Difcovery of Truth is, a judicious
tbll Art. ,, . T
Choice or intermediate Ideas. We
have feen in the third Part of this Treatife, that
many of our Ideas are of fuch a Nature as not to
difcover their feveral Habitudes and Relations by
any immediate Comparifon one with another.
In this Cafe we mufl have Recourfe to inter-
mediate Ideas ; and the great Art lies in finding
out fuch as have an obvious and perceivable
Connection with the Ideas whofe Relations we
enquire after. For thus it is that we are fur-
nifhed with known and evident Truths, to
ferve as Premifes for the Difcovery of fuch as
are
are unknown. And indeed the whole Bufmefs
of Invention feems in a great Meafure to lie in
the due Afiemblage and Difpofition of thefe
preliminary Truths. For they not only lead
us Step by Step to the Difcovery we are in
queft of, but are fo abfolutely neceflary in the
Cafe, that without them it were in vain to at-
tempt it ; nothing being more certain than that
unknown Propofitions can no otherwife be
traced but by means of fome Connection they
have with fuch as are known. Nay, Reafon
itfelf, which is indeed the Art of Knowledge,
and the Faculty by which we pufh on our Dif-
coveries ; yet by the very Definition of it im-
plies no more, than an Ability of deducing un-
known Truths from Principles or Propofitions
that are already known. Now although this
happy Choice of intermediate Ideas, fo as to
furnifh a due Train of previous Propofitions,
that fhall lead us fuccefnvely from one Difco-
very to another, depends in fome Meafure upon
a natural Sagacity and Quicknefs of Mind ; it
is yet certain from Experience, that even here
much may be effe&ed by a ftubborn 'Applica-
tion and Induftry. In order to this it is in the
firft place neceflary that we have an extenfive
Knowledge of Things, and fome general Ac-
quaintance with the whole Circle of Arts and
Sciences. Wide and extended Views add great
Force and Penetration to the Mind, and enlarge
its
its Capacity of judging. And if to this we join
in the fecond place a more particular and inti-
mate. Study of whatever relates to the Subject
about which our Enquiries are employed, we
feem to bid fair for Succefs in our Attempts.
For thus we are provided with an ample Va-
riety out of which to choofe our intermediate
Ideas, and are therefore more likely to difcover
fome among them that will furnifli out the pre-
vious Propofitions neceflary in any Train of
Reafoning.
Sigaciyaada V. IT is not indeed to be denied,
3*'t>""Js "f that when we have even got all our
Undtr Handing
greatly pro- Materials about us, much ftill de-
' muted by tbt , TV
Study of pends upon a certain Dexterity and
Algebra. Addrefs, in fingling out the moft
proper, and applying them fkilfully for the Dif-
covery of Truth. This is that Talent which
is known by the Name of Sagacity, and com-
monly fuppofed to be altogether the Gift of Na-
ture. But yet I think it is beyond Difpute,
that Practice, Experience, and a watchful At-
tention to the Procedure of our own Minds
while employed in the Exercife of Reafoning, are
even here of very great Avail. It is a Truth
well known to thofe who have made any confi-
derable Progrefs in the Study of Algebra, that
an Addrefs and Skill in managing intricate
Queftions may be very often obtained, by a
careful Imitation of the beft Models. For
although
although when we firft fet out about the Solu-
tion of Equations, we are puzzled at every
Step, and think we can never enough admire
the Sagacity of thofe who prefent us with ele-
gant Models in that Way ; yet by Degrees we
ourfelves arrive at a great Maftery, not only in
devifing proper Equations, and coupling them
artfully together, fo as from the more compli-
cated to derive others that are fimple j but alfo
in contriving ufeful Subftitutions, to free our
Calculations from Fractions, and thofe Intrica-
cies that arife from Surds and irrational Quan-
tities. Nor is it a fmall Pleafure attending the
Profecution of this Study, that we thus difcern
the growing Strength of our own Minds, and
fee ourfelves approaching nearer and nearer to
that Sagacity and Quicknefs of Understanding
which we fee fo much admired in others, and
were at firft apt to conclude altogether beyond
our Reach.
VI. WE have now confidered
i r T r- T Where Art
thofe Requifites to Invention, that andManagt-
have their Foundation in the natu- ment a . re rt ~
quired in the
ral Talents of the Mind: an en- Bufmijtof
i i i i r TT i Invention.
larged and comprehennve Under-
ftanding, a ftrong Habit of Attention, a Saga-
city and Quieknefs in difcerning and applying
intermediate Ideas. Let us next take a View
of fuch other Helps as more immediately de-
pend upon Art and Management, and fliew
9 the
C
the Addrefs of the Mind, in contriving Means
to facilitate its Difcoveries, and free it from all
unneceflary Fatigue and Labour. For we are
to obferve, that tho' the Capacity of the Intel-
lect may be greatly enlarged by Ufe and Excr-
cife, yet ftill our Views are confined within cer-
tain Bounds, beyond which a finite Underftand-
ing cannot reach. And as it often happens in
the Inveftigation of Truth, efpecially where it
lies at a confiderable Diftance from firft Prm-
ciples, that the Number of Connections and
Relations are fo great, as not to be taken in at
once by the moft improved Underftanding ; it is
therefore one great Branch of the Art of In-
vention, to take Account of thefe Relations as
they come into View, and difpofe of them in
fuch Manner, that they always lie open to the
Infpec~tion of the Mind, when difpofed to turn
its Attention that Way. By this Means, with-
out perplexing ourfelves with too many Confi-
derations at once, we have yet thefe Relations
at Command, when neceflary to be taken notice
of in the Profecution of our Difcoveries : and
the Underftanding thus free and difengaged, can
bend its Powers more intenfely towards that par-
ticular Part of the Invefligatien it is at prefent
concerned with. Now in this, according to
my Apprehenfion, lies the great Art of human
Knowledge ; to manage with Skill the Capacity
of the Intellect, and contrive fuch Helps, as may
bring
bring the mo{l wide and extended Objects within
the Compafs of its natural Powers. When
therefore the Multitude of Relations increafe
very faft upon us, and grow too unwieldy to be
dealt with in the Lump, we muft combine them
in different Claries, and fo difpofe of the feveral
Parts, as that they may at all times lie open to
the leifurely Survey of the Mind. By this means
we avoid Perplexity and Confufion, and are en-
abled to conduit our Refearches, without being
puzzled with that infinite Crowd of Particulars,
that frequently fall under our Notice in long and
difficult Investigations. For by carrying our
Attention fucceffively from one Part to another,
we can upon occafion take in the whole ; and
knowing alfo the Order and Difpofition of the
Parts, may have recourfe to any of them at plea-
fure, when its Aid becomes neceflary in the
Courfe of our Enquiries.
VII. FIRST then I fay, that an An Br/ t er t y
orderly Combination of things, and Difpoftuncf
J great L'fe in
clafTing them together with Art and acting ob~
Addrefs, brings great and otherwife ^t&^tf
unmanageable Objects, upon a Level the Under-
with the Powers of the Mind. We ^ Ir ' g "
have feen in the firft Part of this Treatife how by
taking Numbers in a Progreflive Series, and ac-
cording to an uniform Law of Compofition, the
moft bulky and formidable Collections are com-
O prehended
C 290 }
prehended with Eafc, and leave diftinct Impref-
iions in the Underftanding. For the feveral
Stages of the Progreflion ferve as fo many Steps
to the Mind, by which it afcends gradually to
the higheft Combinations ; and as it can carry
its Views from one to another with great Eafe
and Expedition, it is thence enabled to run over
all the Parts feparately, and thereby rife to a juft
Conception of the Whole. The fame thing hap-
pens in all our ether complex Notions, efpecially
when they grow very large and complicated ;
for then it is that we become fenfible of the Ne-
ceifity of eftablifhing a certain Order and Gra-
dation in the Manner of combining the Parts.
This has been already explained at fome Length,
in the Chapter of the Compofition and Refolu-
tion of our Ideas ; where we have traced the gra-
dual Progrefs of the Mind through all the dif-
ferent Orders of Perception, and fhewn, that
the moft expeditious Way of arriving at a juft
Knowledge of the more compounded Notices of
the Underftanding, is by advancing regularly
through all the intermediate Steps. Hence it is
eafy to perceive what Advantages muft arife
from a like Conduct, in regard to thofe feveral
Relations and Connections, upon which the In-
veftigation of Truth depends. For as by this
means we are enabled to bring them all within
the Reach of the Mind, they can each in their
Turns be made ufe of upon Occafion, and fur-
nifh
nifti their Afliftance towards the Difcovery of
what we are in queft of. Now this is' of princi-
pal Confideration in the Bufinefs of Invention,
to have our Thoughts fo much under Command^
that in comparing Things together, in order to
difcover the Refult of their mutual Connecti-
ons and Dependence, all the feveral Lights that
tend to the clearing the Subject we are upon,
may lie diftindtly open to the Underftanding>
fo as- nothing material fhall efcape its View:
becaufe an Overfight of this kind in fumming
up the Account, muft not only greatly retard
its Advances, but in many Cafes check its Pro-
grefs altogether.
VIII. BUT fecondly, another Ad- Antinen-
vantase arifing from this orderly ttbl g ui '"
' proceed gra-
Difpofition is, that hereby we free dually and
the Mind from all unnecefTary Fa- e lvveftig*i-
tigue, and leave it to fix its A.tten- thn efTrutb.
tion upon any Part feparately, without perplex-
ing itfelf -with the Confideration o the Whole.
Unknown Truths, as we have already obferved,
are only to be traced by means of the Relation
between them and others that are known. When
therefore thefe Relations become very numerous,
it muft needs greatly diftracl the Mind, were it
to have its Attention continually upon the
Stretch after fuch a Multitude of Particulars at
once. But now, by the Method of clafling and
O 2 ordering
ordering our Perceptions above explained, this
Inconvenience is wholly prevented. For a juft
Diftribution of things, as it afcertains diftincl-
]y the Place of each, enables us to call any of
them into View at Pleafure, when the prefent
Confideration of it becomes neceflary. Hence
the Mind, proceeding gradually through the fe-
veral Relations of its Ideas, and marking the
Refults of them at every Step, can always pro-
portion its Enquiries to its Strength ; and con-
fining itfelf to fuch a Number of Objects as it
can take in and manage with Eafe, fees more
diftin&ly all the Confequences that arife from
comparing them one with another. When
therefore it comes afterwards to take a Review of
thefe its feveral Advances, as by this means the
Amount of every Step of the Invefligation is fair-
Jy laid open to its Infpetion, by adjufting and
putting thefe together in due Order and Method,
it is enabled at laft to difcern the Refult of the
Whole. And thus as before in the Compofition
of our Ideas, fo likewife here in the Search and
Difcovery of Truth, we are fain to proceed gra-
dually, and by a Series of fucceflive Stages. For
thefe are fo many refting Places to the Mind,
whence to look about it, furvey the Conclufions
it has already gained, and fee what Helps they
afford, towards the obtaining of others which it
muft flill pafs through before it reaches the End
of the Inveftigation, Hence it often happens,
that
( 2 93 )
that very remote and diftant Truths, which lie
far beyond the Reach of any fmgle Effort of the
Mind, are yet by this progreflive Method fuc-
cefsfully brought to light, and that too with lefs
Fatigue to the Underftanding than could at firft
have well been imagined. For although the
whole Procefs, taken together, is frequently much
too large to come within the View of the Mind
at once ; and therefore confidered in that Light
may be faid truly to exceed its Grafp ; yet the
fcveral Steps of the Inveftigation by ihemfelves
are often e&fy and manageable enough ; fo tha:
by proceeding gradually from one to another,
and thoroughly mattering the Parts as we advance^
we carry on our Refearches with wondrous Dif-
patch, and are at length conducted to that very
Truth, with a View to the Difcovery of which
the Inquifition itfelf was fet on foot.
IX. BUT -now perhaps it may not jy ge i, ra ar j
be improper, if we endeavour to slritbmetick
illuftrate thefe Obfervations by an .w%botk> A t\
Example, and fet ourfelves to trace /'"'
the Conduct and Manner of the A'lind, when-
employed in the Exercife of Invention. There
are two great Branches of the Mathematicks pe-
culiarly fitted to furnifli us with Models in this
Way. Arltbmetlck I mean, and Algebra. Algebra
is univerfally known to be the very Art and Prin-
ciple of Invention ; and in Arithmetick too, we
O 3 are
( 294 )
are frequently put upon the finding out of un-
known Numbers, by Means of their Relations
and Connections with others that are known : as
where it is required to find a Number equal to
this Sum of two others, or the Product of two
others. I choofe to borrow my Examples chiefly
irom this laft Science, both becaufe they will be
more within the Reach of thofe for whom this
Treatife is principally defigned ; as likewife, be-
caufe Arithmetick furnifhes the beft Models of
a happy Sagacity and Management, in clafling
and regulating our Perceptions. So that here
more than in any other Branch of human Know-
ledge, we fhall have an Opportunity of obferv-
ing, how much an orderly Difpofition of Things
tecc!s to the Eafe and Succefs of our Enquiries,
by leaving us to canvafs the Parts feparately, and
thereby rife to a gradual Conception of the Whole
without entangling ourfelves with too many Con-
fiderations at once, in any (ingle Step of the In-
veftigation. For it will indeed be found, that
a Dexterity and Addrefs in the Ufe of this laft
Advantage ferves to facilitate and promote our
Difcoveries, almoft beyond Imagination or Be-
lief.
M'tbod X. W E have already explained
7 the Manner of reducing Numbers
. i nto Clafles and of diftinguifliing
thefe Clafles by their fcveral Names. And now
we are farther to obferve, that the prefent Me-
thod
( 295 )
thod of Notation is fo contrived, as exaftly to
fall in with this Form of numbering- For as in
the Names of Numbers, we rife from Units to
Tens, from Tens to Hundreds, from Hundreds to
Thoufands, &c> fo likewife in their Notation,
the fame Figures, in different Places, fignify
thefe feveral Combinations. Thus 2 in the firft
Place on the right Hand denotes two Units, in
the fecond Place it expreffes fo many Tens, in
the third Hundreds, in the fourth Thoufands.
By this means it happens, that when a Number
is written down in Figures, as every Figure in
it exprefles fome diftincl Combination, and all
thefe Combinations together make up the total-
Sum j fo may the feveral Figures be confidtred
as the conftituent Parts of the number. Thus
the Number 2436, is evidently by the very No-
tation diftinguifhed into four Parts, marked by
the four Figures that ferve to exprefs it. For
the firft denotes two Thoufand, the fecond four
Hundred, the third Thirty or three Tens, and the
fourth Six. Thefe feveral Parts, tho' they here
appear in a conjoined Form r may yet be alfo
exprefled feparately thus, 2000, 400, 30, and 6,
and the Amount is exadtly the fame.
XI. THJS then being the Cafe, if *r be Helps
it is required to find a Number equal thence derived
* _ to-wardt an
to the Sum of two others given; our tafy Addition
Buiinefc is,, to examine feparately ****"*
O 4 thefe
( 296 )
ftefe given Numbers, and if they appear too large
and bulky to be dealt with by a fingle Effort of
Thought, then, fmce the very Notation diftin-
guifhes them into different Parts, we 'muft con-
tent ourfelves with confidering the Parts afunder,
and finding their Sums one after another. For
fmce the whole is equal to all its Parts, if we find
the Sums of the feveral Parts of which any two
Numbers confift, we certainly find the total Sum
of the two Numbers. And therefore, thefe dif-
ferent Sums, united and put together, according
to the eftablifhed Rules of Notation, will be the
very Number we are in queft of. Let it be pro-
pofed, for inftance, to find a Number equal to
the Sum of thefe two: 2436, and 4352. As the
finding of this by a fingle Effort of Thought
would be too violent an Exercife for the Mind,
I confider the Figures reprefenting thefe Num-
bers as the Parts of which they confift, and there-
fore fet myfelf to difcover their Sums one after
another. Thus 2, the firft Figure on the right
Hand of the one, added to 6, the firft Figure on
the right hand of the other, makes 8, which is
therefore the Sum of thefe two Parts. Again,
the Sum of 5 and 3, the two Figures or Parts in
the fecond Place, is like wife 8. But now as Fi-
gures in the fecond Place, denote not fimple Units,
but Tens ; hence it is plain, that 5 and 3 here,
fignify five Tens and three Tens, or 50 and 30,
whofe Sum therefore muft be eight Tcns t or 80.
And
( 297 )
And here again I call to mind, that having al-
ready obtained one Figure of the Sum, if I place
that now found immediately after it, it will
thereby {land alfo in the fecond Place, and fo
really exprefs, as it ought to do, eight Tens, or
80. And thus it is happily contrived, that tho'
in the Addition of the Tens, I confider the Fi-
gures compofing them as denoting only fimple
Units, which makes the Operation eafier and
lefs perplexed ; yet by the Place their Sum ob-
tains in the Number found, it exprefles the real
Amount of the Parts added, taken in their full
and complete Values. The fame Thing happens
in fumming the Hundreds and Thoufands ; that is,
though the Figures exprefling thefe Combina-
tions, are added together as fimple Units ; yet
their Sums, {landing in the third and fourth Places
of the Number found, thereby really denote the
Hundreds and Thoufands, and fo reprefent the
true Value of the Parts added.
XII. HERE then we have a mani- Btcaufe in tkt-
feft Proof of the great Advantages /"*"'*?'.
O by lukicb it it
derived from an artful Method of carried en, the
, ff. T> . -i-^ , Mind is put
claliing our Perceptions. Jb or as the ,., /,-/, *
Numbers themfelves are by this Fati ae -
Means diftinguifhed into different Parts, which
brings them more readily within the Compafs of
the. Underftanding; fo by taking thefe Parts fe-
"O 5 parately,
parately, the Operations about Numbers are ren-
dered very eafy and fimple. And indeed it is par-
ticularly worthy our Notice, and tho' in adding
two very large Numbers together, the whole Pro-
cefs is of fufficient Length; yet the feveral Steps
"by which it is conducted, are managed with in-
credible Difpatch, and fcarce any Fatigue to the
Mind. This is apparent in the Example given
above, where we fee, that in every Advance from
one Part to another, nothing more is required
than to add together the two Figures in the like
Places of the Numbers to be fummed. But what
is yet more wonderful, tho r in the Progrefs of a
long Operation, the Figures rife in their V r alue as
we advance, and grow to fignify Thoitfands, Mil-
lions. Billions, &c. yet fo happily, a re they contriv-
ed for exprefling the different Parts of Numbers,
that in every Step of the. Procedure we confider
them as denoting only fimple Units, all other
Deficiencies being made up, by the Places their
Sums obtain in the total Amount. And thus it is-
fo ordered in this admirable Form of Notation,
that however large the Numbers are that come
under Examination, they are neverthelefs ma-
naged with the fame Eafe as the moft fimple and
obvious Collections j becaufe in the feveral Ope-
rations about them, the Mind is neither tied down?
to the View of too many Parts at once, nor en-
tangled
(' 299 )
tangled with any Confiderations regarding the
Bulk and Compofition of thofe Parts.
XIII. AND if thefe Advantages rbis farter
are fo very manifeft in the firft and w/-^ p
on Example
jfimpleft Rules of Arithmeticlc, much in Multiple
more do they difcover themfelves in- ca " on '
thofe that are intricate and complex. Let a Man
endeavour' in his Thoughts to find the Product
of two Numbers, each confiding of twenty or
thirty Places, and that without confidering the
Parts feparately ; I believe he will foon be fenfi-
ble, that it is a Difcovery far beyond the Limits
of the human Mind. But now in the progreffive
Method above explained, nothing is more fimple
and eafy. For if we take the firtt Figure on the
right Hand of the one Number, and by it multiply
every Figure of the other feparately ; thefe feve-
ral Produces, connected according to the eftablifli-
ed Laws of Notation, muft truly reprefent the to-
tal Product of this other, by that Part of the mul-
tiplying Number. Let us fuppofe, for Inftance,,
the Figure in the Unit's Place of the Multiplier to .
be 2, and the three laft Places of the Multiplicand
to be 432. Then, 2 multiplying 2 produces 4,
which therefore is the firft Part of the Product.
Again, 2 multiplying 3 produces 6. But now 3
ftanding in the fecond Place of the Multiplicand,
denotes in its real Value three Tens, or 30, which
therefore taken twice, amounts to fix Tens or 60.
O 6 And
( 30 )
And accordingly the Figure 6, coming after 4 al-
ready found, is thereby thrown into the fecond
Place of the Product, and fo truly exprefies 60,
its full and adequate Value. The fame thing hap-
pens in multiplying 4, which {landing in the Place
of Hundreds, its Product by 2 is 800. But this
very Sum the Figure 8, produced from 2 and 4,
really denotes in the total Product. Becaufe
coming after 64, the two Parts already found, it
is thereby determined to the third Place, where
it of Courfe exprefles fo many Hundreds. This
Procefs, as is evident, may be continued to any
length we pleafe ; and it is remarkable that in
like Manner as in Addition, tho' the Value of
the Figures in the Multiplicand continually rifes
upon us, yet we all along proceed with them as
firnple Units; becaufe the Places of the feveral
Produces in the total Amount, reprefent the juft
Refult of multiplying the Figures together, ac-
cording to their true and adequate Value.
XIV. HAVING thus obtained the
Of the Diji>o-
ftionoftte Product by the firft Figure of the
(iveral Pro- . - , . .. ' - . .
duSi in order Multiplier, we next take that in the
to Addition, fecond Place, and proceed with it in
the fame Manner. This fecond Operation gives
us the Effect of that Figure, confidered as a fim-
ple Digit. But as it flood in the fecond Place,
and therefore really denoted fo many Tent 9 hence
it is plain that the Product now gained muft be
yet
( 3 01 )
yet multiplied by Ten, in order to exprefs the
true Product fought. This is accordingly done
in the Operation, by placing the firft Figure of
this fecond Product under the fecond Figure
of the firft Product. For this, when they come
to be added together, has the fame Effect as
annexing a Cypher, or multiplying by Ten, as
every one knows who is in the leaft acquainted
with the Rules of Arithmetick. In like Man-
ner, when we multiply by the Figure in the
third Place, as this new Product is placed ftill
one Figure backwards, we do in effect annex
two Cyphers to it, or multiply it by a Hundred.
And this we ought certainly to do ; becaufe
having confidered the multiplying Figure as
denoting only fimple Units, when it really ex-
preffed fo many Hundreds, the firft Operation
gives no more than the hundredth Part of the
true Product. The Cafe is the fame in multiply-
ing by the fourth or fifth Figures, becaufe the
Products ftill running backwards, we thereby in
effect annex as many Cyphers to them as brings
them up feverally to their refpective adequate
Value. By this means it happens, that though
the Figures of the Multiplier in every Advance,
denote ftill higher and higher Combinations,
yet we all along proceed with them as fimple
Digits ; the Difpofition of the feveral Products
in order to Addition making up for all the
Deficiencies that arife from this Way of confi-
dering
( 302 )
dering them. When in this Method of Pro--
cedure, we have obtained the Product of the
Multiplicand into all the different Parts of the
Multiplier, by adding thefe Produces together
we obtain alfo the total Product of the two
Numbers. For fince the whole is equal to all
its Parts, nothing is more evident, than that
the Product of any one Number into another,
muft be equal to its Product into all the Parts
of that other : and therefore the fevera! partial
Produces united into one Sum, cannot but truly*
reprefent the real Product fought.
Arithmetical XV. THUS we fee, that in Quef-
operation*, l>y t j ons o f Multiplication, thoueh the
being carried
tin in a pro- whole Proccfs is fometimes fuffici-
S$ .rf ently long and tedious, yet the fe-
eafy and in- yeral Steps by which it is carried
telliglblc. . . _^
on are all very level to the rowers
of the Underftanding. For from the Account
given above it appears, that nothing more is re-
quired in any of them than barely to multiply
one Digit by another. But now this eafy Rule
ef Operation is wholly derived from the before-
mentioned Addrefs in clafling our Perceptions.
For to this it is owing, that the Numbers under
Consideration are diftinguifhed into Parts, and
that the feveral Parts are alfo clearly repre-
fented to the Mind in the very Form of Nota-
.tion. Now as thefe Parts have an invariable
Relation one to another, and advance in their
Value
Value by an uniform Law of Progrefiion ; the
Underftanding by means of fuch a Link can
eafily hold them together, and carry its Views
from Stage to Stage without Perplexity or Con-
fufion. Hence it happens, that however large
and mighty the Numbers are, fo as far to ex-
ceed the immediate Grafp of the Mindj yet by
running gradually through the feveral Combi-
nations of which they are made up, we at
length comprehend them in their full Extent,
And becaufe it would be impoflible for the Un-
derftanding to multiply very large Numbers one
into another, by a fimple Effort of Thought;
therefore here alfo it confiders the Parts fepa-
rately, and, taking them in an orderly Series,
advances by a Variety of fucceffive Steps. It
is true indeed in the Progrefs of the Operation,
the feveral Figures rife in their Value r but this
Confideration enters not the Work itfelf. For
there, as we have already feen, though the
Characters are taken as denoting only fimple
Units, yet the Order and Difpofition of the
partial Produces, exhibits each according to its
real Amount. Hence in every Step, we have
only to multiply one Digit by another, which as
it is attended with fcarce any Difficulty, the
whole Procefs is carried on with wondrous Dif-
patch. And thus by a Series of eafy Opera-
tions, we at length rife to Difcoveries, which
in any other Method of Procedure, would have
been
been found altogether beyond the Reach of tlie
Mind.
I'te Art of XVI. SINCE therefore by a due
ehffiif our and orc j cr ] y Difpofition of our Ideas,
Perception
the great we can bring the moft wide and ex-
hft'umMtof tended Objeds upon a Level with
In-vtntion. the Powers of the Underftanding :
and fince by this alfo we abridge the Fatigue
and Labour of the Mind, and enable it to carry
on its Refearches in a progrelTive Method, with-
out which Contrivance, almoft all the more re-
mote and diftant Truths of the Sciences muft
have lain for ever hid from our knowledge ; I
think we may venture to affirm, that the Art
of regulating and clailing our Perceptions is
the great Mean and Inftrument of Invention.
It is for this Reafon that I have endeavoured
in fo particular a Manner to illuftrate it from
Examples in Numbers; becaufe we have here
not only a perfect Model of the Art itfelf, but
fee alfo in the cleared manner, what Helps it
furnifhes towards a ready Comprehenfion of
Objects, and a mafterly Inveftigation of Truth.
Nor let any one find fault, as if we had infifted
rather too long upon Matters that are obvious
and known to all. For I am apt to think,
that though very few are Strangers to the re-
ceived Method of Notation, and the common
Rules of Operation in Arithmetick ; yet it is
not every one that fets himfelf to confider the
Addrefs
( 305 )
Addrefs and Sagacity that may be feen in the
Contrivance of them, or to unravel thofe Prin-
ciples of Investigation, which we have here fo
clearly deduced from them. And this I take to
be the Reafon, that we fometimes meet with
Inftances of Men, who tho' thoroughly verfed
in the Art of Invention, with regard to fome
particular Branches of Knowledge; yet if taken
out of their ufual Track, find themfelves im-
mediately at a Stand, as if wholly bereft of
Genius and Penetration. With fuch men In-
vention is a mere Habit, carried on in a Man-
ner purely mechanical, without any Know-
ledge of the Grounds and Reafons upon which
the feveral Rules of Invefligation are founded.
Hence they are unfurnifhed with thofe general
Obfervations, which may be alike ufefully ap-
plied in all Sciences, with only fome little necef-
fary Variations, fuited to the Nature of the Sub-
ject we are upon. And indeed I know of no
furer Way to arrive at a fruitful and ready In-
vention, than by attending carefully to the Pro-
cedure of our own Minds, in the Exercife of
this dirtinguifhed Faculty ; becaufe from the
particular Rules relating to any one Branch, we
are often enabled to derive fuch general Remarks,
as tend to lay open the very Foundation and
Principles of the Art itfeif.
XVII. IF
Tie Manner of XVII. IF HOW VVC tUOl OUr
*?"*?? " Thoughts from Aritbmetick to Alge-
tee Rejolution
J Algebraic bra? here alfo we fhall find, that the
great Art of Invention lies, in fo re-
gulating and difpofmg our Notices of Things,
that we may be enabled to proceed gradually
in the Search of Truth. For it is the principal
Aim of this Science, by exhibiting the feveral
Relations of Things in a kind of fym,bolical
Language, fo to reprefent them to the Ima-
gination, as that we may carry our Attention
from one to another, in any Order we pleafe.
Hence, however numerous thofe Relations are,
yet by taking only fuch a Number of them into
Confederation at once, as is fuited to the Reach
and Capacity of the Underftanding, we avoid
Perplexity and Confufion in our Refearches,
and never put our Faculties too much upon
the Stretch, fo as to lofe ourfelves amidft the
Multiplicity of our own Thoughts. As there-
fore in Arithmetlcki we rife to a juft Conception
of the greateft Numbers, by confidering them as
made up of various progrefllve Combinations ;.
fo likcwife in Algebra, thofe manifold Relations
that often intervene, between known and un-
known Quantities, are clearly reprefented to
the Mind, by throwing them into a Series of
diflincl Equations. And as the moft difficult
Queftions relating to Numbers are managed
with
( 307 )
with Eafe, becaufe we can take the Parts or
Figures feparately, and proceed with them one
after another ; fo alfo the moft intricate Prob-
lems of Algebra are in like Manner readily un-
folded, by examining the feveral Equations
apart, and unravelling them according to cer-
tain eftablifhed Rules of Operation. And here
it is well worth our Notice, that in very com-
plicated Problems, producing a great Number
of different Equations, it for the moft part fo
happens, that every one of them includes a Va-
riety of unknown Quantities. When therefo/6
we come to folve them feparately, as it would
too much diftracT: and entangle the Mind, to en-
gage in the Purfuit of fo many different Ob-
jects at once; our firft Bufmefs is, by artfully
coupling the feveral Equations together, or by
the various Ways of Multiplication, Subtrac-
tion, Addition, and Subflitution, to derive
others from them more fimple, until at length
by fuch a gradual Procefs we arrive at fome
new Equation, with only one unknown Quan-
tity. This done, we fet ourfelves to confider
the Equation laft found, and having now to do
with an Object fuited to the Strength and Ca-
pacity of the Mind, eafily by the eftabliflied
Rules of the Art, difcover the Quantity fought.
In this Manner we proceed with all the feveral
unknown Quantities one after another, and
having by a Series of difrincT: Operations traced
them
them fcparately, the Queftion is thereby com-
pletely refolved.
Ofibofeotbtr XVIII. HENCE it appears, that
jrtijicmvtocb the Bufmefs of Invention, as prac-
may be conji- '
dired a, f u hfi. tifed in Algebra, depends entirely
iZ"t' upn the Art of abridging our
Thoughts, reducing the Number
of Particulars taken under Conllderation at once
to the feweft pofllble, and eftablifliing that pro-
greflive Method of Inveftigation, which we have
already fo fully explained from Examples in
Arithmetick. I might eafily fhew that the
fame Obfervation holds equally in other Sci-
ences ; but having already exceeded the Bounds
I at firft prefcribed to myfelf in this Chapter,
fhall only add, that befides the grand Inftru-
ments of Knowledge already mentioned, there
are innumerable other Artifices, arifing out of
the particular Nature of the Subjefl we are
upon, and which may be confidered as fuhfi-
diary Helps to Invention. Thus in Geometry,
many Demonstrations of Problems and Theo-
rems are wholly derived from the Conftruction
of the Figure made u.fe of, and the drawing of
Lines from one Point to another. In like man-
ner in Algebra, the devifing of proper Equa-
tions from the Conditions of the Queftion pro-
pofed, and contriving neat ExprefTions for the
unknown Quantities, contribute not a little t<a
the eafy Solution of Problems, And when we
have
fiave even carried on the Inveftigation to fome
fingle Equation with only one unknown Quan--
tity ; as that unknown Quantity may be vari-
oufly perplexed and entangled with others that
are known, fo as to require a Multiplicity of
different Operations, before it can be difen-
gaged, which often involves us in long and
intricate Calculations, and brings Surds and
irrational Quantities in our Way; Algebraifts,
to prevent in fome Meafure thefe Inconveni-
ences, and fhorten as much as poflible the
Procefs, have fallen upon feveral Methods of
Subftitution, which are of great Service in
very complicated Queftions. But thefe and
fuch like Artifices of Invention, cannot be ex-
plained at length in this fhort EfTay. It is
enough to have given the Reader a Hint of them,
and put him in the Way of unravelling them,
himfelf, when he comes to apply his Thoughts
to thofe particular Branches of Knowledge where
they are feverally made ufe of.
XIX. THERE is one Thing how- Of tie great
, . , , jidvantavef
ever, that in a particular manner de- arifingf^m a
ferves to be taken Notice of, before b ?W ^ ot<t '
' tion or Ex-
we difmifs this Subject j and that is, prcffion of our
the great Advantages that may re-
dound to Science, by a happy Notation or Ex-
preflion of our Thoughts. It is owing entirely
to this, and the Method of denoting the feveral
Combinations of Numbers by Figures ftanding
in
in different Places, that the moft complicated
Operations in Arithmetick are managed with fo
much Eafe and Difpatch. Nor is it lefs appa-
rent, that the Difcovcries made by Algebra, are
wholly to be imputed to that fymbolical Lan-
guage made ufe of in it. For by this means we
are enabled to reprefent the Relations of Things
in the Form of Equations, and by varioufly
proceeding with thefe Equations, to trace out
Step by Step the feveral Particulars we are in
queft of. Add to all this, that by fuch a No-
tation, the Eyes and Imagination are alfo made
fubfervient to the Difcovery of Truth. For
the Thoughts of the Mind rife up and difap-
pear, .according as we fet ourfelves to call them
into View; and therefore, without any particu-
lar Method of fixing and afcertaining them as
they occur, the retrieving them again when out
of Sight, would often be no lefs painful than the
very firft Exercife of deducing them one from
another. When therefore in the Purfuit of
Truth we carry our Attention forward from
one Part of the Inveftigation to another, as ne-
verthelefs we have frequent Occafion to look
back upon the Difcoveries already pafled through,
could thefe be no otherwife brought into View,
than by the fame Courfe of thinking in which
they were firft traced, fo many different Atten-
tions at once muft needs greatly diftraft the
Mind, and be attended with infinite Trouble
and
and Fatigue. But now, the Method of fixing
and afcertaining our Thoughts by a happy and
well-chofen Notation, entirely removes all thefe
Obftacles. For thus, when we have Occafion
to run to any former Difcoveries, as Care is
taken all along to delineate them in proper
Characters, we need only caft our Eye upon
that Part of the Procefs where they ftand ex-
prefled, which will lay them at once open to
the Mind in their true and genuine Form. By
this means we can at any Time take a quick
and ready Survey of our Progrefs, and running
over the feveral Conclufions already gained,
fee more diftin&ly what Helps they furnifh to-
wards the obtaining of thofe others we are ftill
in Purfuit of. Nay further, as the Amount of
every Step of the Inveftigation h'es fairly before
us, by comparing them varioufly among them-
felves, and adjufting them one to another, we
come at length to difcern the Refult of the whole,
and are enabled to form our feveral Difcoveries
into an uniform and well-connected Syftem of
Truths, which is the great End and Aim of all
our Enquiries.
XX. UPON the whole then it ap-
, ... Recapitulation,
pears, that in order to proceed fuc-
cefsfully in the Exercife of Invention, we muft
endeavour as much as poffible to enlarge the
Capacity of the Mind, by accuftoming it to
wide and comprehenfive Views of Things :
9 that
that we mud habituate ourfelves to a ftrong
and unfhaken Attention, which carefully dif-
tinguifhes all the Circumftances that come in
our Way, and lets nothing material flip its
Notice : In fine, that we muft furnifh ourfelves
with an ample Variety of intermediate Ideas,
and be much in the Exercife of fingling them
out and applying them for the Difcovery of
Truth. Thefe preparatory Qualifications ob-
tained, what depends upon Art lies chiefly in
the Manner of combining our Perceptions,
and clafling them together with Addrefs, fo as
to eftablifli a prcgreflive Method of Inveftiga-
tion. And here it is of great Importance, to
contrive a proper Notation or Expreflion of
our Thoughts, fuch as may exhibit them ac-
cording to their real Appearance in the Mind,
and diftinHy reprefent their feveral Divifions,
Clafles, and Relations. This is clearly feen in
the Manner of computing by Figures in Arith-
metick, but more particularly in that fymbo-
lical Language, which hath been hitherto fo fuc-
cefsfully applied in unravelling of Algebraical
Problems. Thus furnifhed, we may at any time
fet about the Inveftigation of Truth ; and if
we take Care to note down the feveral Steps of
the Procefs, as the Mind advances from one
Difcovery to another, fuch an Arrangement or
Difpofition of our Thoughts conftitutes what
is called the Method of Invention. For thus it is
plain,
( 3'3 )
plain that we follow the natural Procedure of
the Underftanding, and make the Truths we
have unravelled to fucceed one another, accord-
ing to the Order in which they prefent them-
felves to the Mind, while employed in tracing
and finding them out. And here again it well
deferves our Notice, that as by this means the
whole Inveftigation lies diftindlly before us ; fo
by comparing the feveral Steps of it among them-
felves, and obferving the Relation they bear one
to another, we are enabled to form our Difco-
veries into a regular Sylrem of Knowledge, where
the Truths advanced are duly linked together,
and deduced in an orderly Series from firft Prin-
ciples. This other Manner of combining our
Thoughts, is diftinguifhed by the Name of the
Method of Science, which therefore now offers
itfelf to be explained, and is accordingly the
Subject of the enfuing Chapter.
CHAP. lit-
Of fbe Method cf Science.
I. TN order to give the jufter Idea
JL of the Rules peculiar to this
n i i-n. -
Species of Method, and eitabhin pi,tu* of our
them upon their proper Foundation, 3
it will be neceflary to begin with fet- v*tbang
tling the Meaning of the Word Sci~ ffatl>re '
P
tncf, and {hewing to what Parts of human Know-
ledge that Term may be mod fitly applied. We
have already obferved in the firft Chapter of the
fecond Book, that there are three feveral Ways
of coming at the Knowledge of Truth. Firft,
by contemplating the Ideas in our own Minds.
Secondly, by the Information of the Senfes.
Thirdly, by the Teftimony of others. When
we fet ourfelves to confider the Ideas in our own
Minds, we varioufly compare them together, in
order to judge of their Agreement or Difagree-
nient. Now as all the Truths deduced in this
Way, flow from certain Connections and Rela-
tions, difcerned between the Ideas themfelves;
and as when the fame Ideas are brought into
Compari-fon, the fame Relations muft ever and
invariably fubfift between them; hence it is
plain, that the Knowledge acquired by the Con-
templation of our Ideas, is of a neceflary and
unchangeable Nature. But farther, as thefe
Relations between our Ideas, are not only fup-
pofed to be real in themfelves, but alfo to be
feen and difcerned by the Mindj and as when
we clearly perceive a Connection or Repugnance
between any two Ideas, we cannot avoid judg-
ing them to agree or difagree accordingly ; it evi-
dently follows, that our Knowledge of this Kind is
attended with abfolute Certainty and Conviction,
jnfpmuch that it is impoffible for us to withhold
.our
our Affent, or entertain any Doubt as to the Rea-
lity of Truths fo ofFered to the Underftanding.
The Relation of Equality between the whole
and all its Parts is apparent to every one who
has formed to himfelf a diftindl Notion of what
the Words IPhole and Fart ftand for. No Man,
therefore, who has thefe two Ideas in his Mind,
can poffibly doubt of the Truth of this Propofi-
tion, that the Whole is equal to all its Parts. For
this would be only endeavouring to perfuade him-
felf, that that was not, which he plainly and un-
avoidably perceives to be. So that in all Cafes
where we difcern a Relation between any of our
Ideas, whether immediately by comparing them,
one with another, or by means of intermediate
Ideas, that lay it open diftin&Jy to the Under-
ftanding; the Knowledge thence arifmg is cer-
tain and infallible. I fay infallible ; becaufe we
not only perceive and own the Truth of Propofi-
tions fo ofFered to the Mind, but having at the
fame time a clear View of the Ground on which
our Aflent refts, are intirely fatisfied within our-
felves, that we cannot polfibiy be deceived in
this Perception.
II. THIS fecond Way of coming A fanning
at Knowledge is by the means of the f ; om tbt In ~
} formation of
Senfes. From them we receive Infor- '<&< Stnjet, te-
c L T -/L c r^i r g" s undoubttd
mation or the t-xiftence of Objects jjuranc*, but
without us, of the Union and Con- '* < ^ / V < "? //
.._ PoJJibility of
junction cf different Qualities in the tdrgdtteivtj.
P 2 fame
fame Subject, and of the Operations of Bodies one
upon another. Thus our Eyes tell us, that there
is in the Univerfe fuch a Body as we call the Sun,
our Sight and. Touch, that Light and Heat, or at
leaft the Power of exciting thofe Perceptions in
us, co-exift in that Body ; and laftly, by the fame
Sight we alfo learn, that Fire has the Power of
difiblving Metals, or of reducing Wood to Char-
coal and Alhes. ButTiow with regard to this
Kind of Knowledge we are to obferve, that tho*
when the Organs of the Body are rightly difpofed
and operate in a natural Way, we never doubt
the Teftimony of our Senfes, but form moft of
the Schemes of Life upon their Information ; yet
are not the Truths of this Clafs attended with
that abfolute and infallible AfTurance, which
belongs to thofe derived from the Contemplation
of our own Ideas. We find that the Senfes
frequently reprefent Objects as really exifting,
which yet have no Being but in our own Ima-
ginations ; as in Dreams, Phrenfies, and the
Deliriums of a Fever. A Diforder too in the
Organs, makes us often afcribe Qualities to Bo-
dies, intirely different from thofe they appear
to poilefs at other Times. Thus a Man in the
Jaundice fhall fancy every Object prefented to
him yellow; and in bodily Diftempers, where
the Tafte is greatly vitiated, what naturally
produces the Idea of Sweetnefs, is fometimes
attended with a quite contrary Senfation. It
is
i-s true, thefe Irregularities neither ought,- nor
indeed do they with confiderate men in any
ways tend, to discredit the Teftimony of Ex-
perience. He that, awake, in his Senfes, and
fatisfied that his Organs operated duly, fhould
take it into his Head to doubt whether Fire
would burn, or Arfenick poifon him, and there-
fore rafhly venture upon thefe Objects, would
foon be convinced of his Error, in a Way not
much to his liking. As neverthelefs the fenfes
do fometimes impofe upon us,, there is no abfo-
lute and infallible Security that they may not
at others j therefore the AfTurance they produce,
though reafonable, fatisfying, and diffidently
well founded to determine us in the feveral Ac-
tions and Occurrences of Life, is yet of fuch a
Nature, as not necefiarily to exclude all Poifi-
bility of being deceived. Hence fome Men o
fo far as to maintain, that we ought to diftruft
our Senfes altogether : nay, whole Seels among
the Ancients, becaufe of this bare Poflibility,
which really extends no farther than to Matters
of Experience and Tejlimony^ yet eftabliihed it as
a Principle, that we ought to doubt of every
thing. Nor are there wanting Philofophers
among the Moderns, who upon the fame Grounds
deny the Exifteace of Bodies, and afcribe the
Perceptions excited in us, not to the Action of
external Matter, but to certain eftablifhed Laws
in Nature, which operate upon us in fuch Man-
P 3 er
rcr as to produce all thofe fevcral Effects that
Teem to flow from the real Prefence of Obje&s
varioufly affecting our Perception. It is not my
Dehgn here to enter into a particular Difcuflion
of thefe Matters: all I aim at is to (hew, that
the Teftimony of the Senfes, though fufficient
to convince fober and reafonable Men, yet does
not fo unavoidably extort our Aflent, as to leave
no room for Sufpicion or Diftruft.
Aif . un(led III. THE third and lad Way of
UIM Teflon*- coming at Truth is, by the Report
ry, tfajliil , _, -.. r i T 1 !.-
rrt rfu : certain and Teftimony of others. This re-
x a t u rt >t bouk gan ] s c hiefly paft Facts and Tranf-
in mar.y Ctjei J *
embraced actions, which having no longer any
without Wa- -i- . rt i i. i
iitnnv or >./- ^xiltence, cannot be brought witnm
tru ft* the prcfent Sphere of our Obferva^
tion. For as thefe could never have fallen under
our CogniAunce, but by the Relations of fuch as
had fufficient Opportunities of being informed ;
it is hence apparent, that all our Knowledge of
this Kind. is wholly founded upon the Convey-
ance of Tertimony. But now, although this
in many Cafes is a fufficient Ground of Aflenr,
fo as to produce a ready Belief in the Mind,
yet is it liable to ftill greater Objections than
even the Reports of Experience. Our Senfes, it
is true, on fome Occafions , deceive us, and
therefore they may pofiibly on others. But this
bare Poflibility creates little or no Diftruft j be-
caufe there are fixed Rules of judging, when
they
they operate according to Nature, and when they
are prevented or given up to Caprice. It is other-
wife in Matters of mere human Testimony. For
there, befides the Suppolition that the Perfons
themfelves may have been deceived, there is a
farther Poflibility, that they may have confpired*
to impofe upon others by a falfe Relation. This
Confideration has the greater Weight, as we
frequently meet with fuch Inftances of Difm-
genuity among Men, and know it to be their
Intereft in fome particular Cafes, to diflemble
and mifreprefent the Truth. It would never-
thelefs be the Height of Folly, to reject all hu-
man Teftimony without Diftinclion, becaufe'
of this bare Poflibility. Who can doubt whe-
ther there ever were in the World fuch Conque-
rors as Alexander and Julius Cafar ? There is
no abfolute Contradiction indeed in fuppoftng,
that Hiftorians may have confpired to deceive
us. But fuch an univerfal Concurrence to a
Falfehood, without one contradicting Voice, ts-
fo extremely improbable, and fo very unlike
what ufually happens in the World, that a wifer
Man could as foon perfuade himfelf to believe
the grofleft Abfurdity, as to admit of a Suppo-
fition fo remote from every Appearance of Truth.
Hence the Fars of Hiftory, when well attefred,
:\TQ readily embraced by the Mind j and though
the Evidence attending them be not fuch
as produces a neceflary and infallible AfTurance,
P4 it
( 320 )
it h yet abundantly fufficicnt to juftify our Be-
lief, and leave thofe without Excufe, who upon
the bare Ground of Pofiibility, are for reje&ing
JntireJy the Conveyance of Teftimony.
<, . IV. UPON the whole then it ap-
A*'!tnctt>ciongi
intfrtiyro that pears,that abfolute Certainty, fuch as
}S attended with unavoidable Afient,
which it de- anc l excludes all Pdflibility of being
rivtdjrtm tbe . ... . r , , . ,
Conumpiaticn deceived, is to be found only in the
Contemplation of our own Ideas. In
Matters of Experience and Teftimony, Men we
lee may frame Pretences for Sufpicion and Dif-
iruft : but in that Part of Knowledge which re-
gards the Relations of our Ideas, none fuch can
have place. For as all thefe feveral Relations are
either immediately difcerned by the Mind, or
traced by means of immediate Ideas, where Self-
Evidence is fuppofed to accompany -every Step
of the Procedure, it is abfolutely impofiible for
a Man to perfuade himfelf that that is not,
which he plainly and neceflarily perceives to be.
Now it is to Knowledge attended with this laft
Kind of Evidence alone, that in Stri&nefs and
Propriety of Speech we attribute the Name of
Science. For Science implies Perception and Dif-
cernment, what we ourfelves fee and cannot
avoid feeing ; and therefore has place only in
Matters of abfolute Certainty, where the Truths
advanced are either intuitive Propofitions, or
deduced
( 321 ) .
deduced from them in a Way of ftricl Demon-
ftration. And as this kind of Certainty is no
where to be found, but in inveftigating the Re-
lations of our Ideas ; hence it is plain, that Science,
properly fpeaking, regards wholly the firft Branch
of human Knowledge; that which we have faid
is derived from a Contemplation of the Ideas in
our own Minds.
V. BUT here I expect it will be -,
Our Kvoio-
afked, if Science and Demonjlration l<dgecftbe
belong only to the Confideration of Ifobj^it'not
our own Ideas, what Kind of Know- ia ' u "' ve '
ledge it is that we have relating to Bodies, their
Powers, Properties, and Operations one upon
another ? To this I anfwer, that we have already
diitinguifhed it by the Name of Natural or Ex-
perimental, But that we may fee more diftintly
wherein the Difference between Scientifical and
Natural Knowledge lies, it may not be improper
to add the following Obfervations. When we
caft our Eyes towards the Sun, we immediately
conclude, that there exifts an Object: without us,
correfponding to the Idea in our Minds. We
are however to take Notice, that this Conclufion
does not arife from any necefTary and unavoid-
able Connexion difcerned, between the Appear-
ance of the Idea in the Mind, and the real Ex-
iftence of the Object without us. We all know
by Experience, that Ideas may be excited, and
P 5
( 3" )
that too by a feeming Operation of Obje&s upon
our Senfes, when there are in Fact no fuch Ob-
jects exifting j as in Dreams, and the Deliriums
of a Fever. Upon what then is the before-
mentioned Conclufion properly grounded ? Why
evidently upon this : that as we are fatisfied our
Organs operate duly, and know that every Ef-
fect muft have a Caufe, nothing is more natural
than to fuppofe, that where an Idea is excited in
the Mind, fome Object exifts correfponding to
the Idea, which is the Caufe of that Appear-
ance. But as this Conclufion, by what we have
feen, is not necefiary and unavoidable, hence
there is no Intuition in the Cafe, but merely a
probable Conjecture, or reafonable Preemption,
grounded upon an intuitive Truth.
VI. AGAIN, when a Piece of
Absolute Ccr- ...
tamy in na- Gold is difiolved in jfquci Regia, we
and own the Effed pro-
toivbat falls (juced, but cannot be faid in Stridl-
tinder tur im~ .
mediate A'o- ^ e fs and Propriety ofbpeech, to have
*'" any Perception or Difcernment of it.
The Reafon is, becaufe being unacquainted with
the intimate Nature both of dqua Regia and
Gold, we cannot, from the Ideas of them in our
Minds, deduce why the one operates upon the
other in that particular Manner. Hence it is,
that our Knowledge of the Fats and Operations
of Nature extends not with Certainty beyond
the
C 3*3 )
tire prefcnt Inftance, or what falls under our imv
mediate Notice j fo that in all our Refearches re-
lating to them, we muft proceed in the Way of
Trial and Experiment, there being here no gene*
ral or univerfal Truths, whereon to found fcien*
tifical Deductions. Becaufe the Solution of Gold
in Aqua Regla holds in one Experiment, we
cannot thence infallibly conclude that it will
hold in another. For not knowing upon what
it is, in either of thefe Bodies, that the Effect here
mentioned depends, we have no abfolute Cer-
tainty in any new Experiment we propofe to
make, that the Objects to be applied one to ano-
ther have that precife Texture and Conftitu-
tion from which this Solution refults. Chemifts
know by Experience, that Bodies which go by
the fame Name, and have the fame outward Ap-
pearance, are not always however exactly alike
in their Powers and Operations. In vain do they
often fearch for thofe Properties in one Piece of
Antimony, which on former Occafions they may
have found in another; and by this means, to
their no fmall Mortification, find themfelves fre-
quently difappointed, in very coftly and promif-
ing Experiments, Nor have we any exprefs
and pofitive AfTurance, that the very Bodies with
which we have formerly made Experiments,
continue fo exactly the fame, as to afford the
like Appearances in any fucceeding Trial. A
P 6 thoufand
( 324 )
thoufand Changes happen every Moment in the
natural World, without our having the leaft
Knowledge or Perception of them. An Altera-
tion in our Atmofphere, the Approach or Recefs
of the Sun, his Declination toward the North
or South, not only vary the outward Face of
Things, but occafion many Changes in the hu-
man Conftitution itfelf, which we yet perceive
jiot when they happen ; nor fhould ever be fen-
lible of, but by the Effects and Confequences re-
lulting from them. And whether Alterations
analogous to thefe may not fometimes be pro-
duced in the Frame and Texture of many Bodies
that furround us, is what we cannot with Cer-
tainty determine. Hence, from an Experiment's
lucceeding in one Inftance, we cannot infallibly
argue that it will fucceed in another, even with
the fame Body. The Thing may indeed be pro-
bable, and that in the higheft Degree ; but as
there is ftill a Poffibility that fome Change may
have happened to the Body, unknown to us,
there can be no abfolute Certainty in the Cafe.
VJI. HAD we fuch an intimate
WbatKindtf A . . , , c ...
Kno-wUdgc of Acquaintance with the Structure
Body -wnld both of dqua Regia and Gold, as to
dejtr-vttbe t i 7 -,-r
Ka*e of Set- be able thence to diicern why the
one fo operates upon the other as
to occafion its Diflblution j infomuch that from
the Ideas of them in our own Minds we could
clearly
( 3*5 )
clearly deduce, that Bodies of fuch a Make ap-
plied one to another, rhuft neceflarily produce
the EffecT: here mentioned ; our Knowledge
would then be fcientifical, and ftand upon the
Foundation either of Intuition or Dcmonjlration^
according as the Perception was immediate, or
attained by means of intervening Ideas. In this
Cafe therefore, having two ftandard Ideas in
our Minds, whofe Relations we perfectly well
know ; wherever we found Objects conform-
able to thefe Ideas, we could then pronounce
with Certainty, that the Application of them
one to another would be attended with the
above Effect : becaufe whatever is true in Idea,
is unavoidably fo alfo in Reality of Things,
where Things exift anfwerable to thefe Ideas.
If it be true in Idea, that a Parallelogram is
the double of a Triangle, ftanding upon the
fame Bafe, and between the fame Parallels j the
fame will be true of every real Triangle and
Parallelogram, that exift with the Conditions
here mentioned. We are likewife to obferve,
that the Changes to which Bodies are daily
liable, could produce no Confufion or Perplexity
in natural Knowledge, did it ftand upon the
Foundation here mentioned. For in fuch a
Cafe, the Powers and Properties of Obje&s be-
ing deduced from the Ideas of them in our own
Minds, would no otherwife be applied to Things
really exifting, than as thefe Things are found
perfectly
perfectly conformable to our Ideas. When'
therefore an Alteration happened in any Body,
as it would by this means differ from that ftand-
ard Idea whence its former Properties were
feen to flow, we muft of courfe be fenfible,
that fome fuitable Change would follow in the
Properties themfelves, and that its Powers and
Operations in regard of other Bodies would
not be in all refpects the fame.
VIIL B UT what is MI more re-
or.iyFtur.da- markable ; we fhould upon this
tlon of return! .
buppohtion be able to determine
the mutual Action and Influence of Bodies,.
without having Recourfe to Trial or Experi-
ment. Had we, for inftance, a perfect Know-
ledge of the intimate Nature and Compofition
of an animal Body, and of that particular Poifon
that is infufed into it by the Bite of a Viper,
fo as clearly and diftindtly to difcern how they
are adapted one to another ; we might thence
fcientifically deduce, without the Help of Ex-
periments, that the Bite of a Viper would fo
unhinge the human Fabrick, and produce fuch
Ferments and Combuftions in it, as muft ne-
ceflarily be followed by a total Extinction of all
the vital Functions, and leave that admirable
Machine a mere lifelefs Lump. But as fuch
perfect and adequate Ideas of Objects, and their
mutual Habitudes one to another, are plainly
beyond the Reach of our prefent Faculties j it
were
( 327 )
were vain for us to think of improving natural
Knowledge by abftract Reafoning or fcienti-
fical Dedu&ions. Experience is here the true
and proper Foundation of our Judgments, nor
can we by any other means arrive at a Difco-
very of the feveral Powers and Properties of Bo-
dies. How long might a Man contemplate the
Nature of Hemlock, examine the Stru&ure of
its Parts in a Microfcope, and torture and ana-
lyfe it by all the Procefles of Chemiftry, be-
fore he could pronounce with Certainty the
Effect: it will have upon a human Body ? One
fingle Experiment lays that open in an Inftant,
which all the Wit and Invention of Men would
never of themfelves have been able to trace.
The fame holds in all the other Parts of natural
Philofophy. Our Difcoverks relating to Elec-
tricity, the Powers and Properties of the Load-
ftone, the Force of Gunpowder, &Y. were not
gained by Reafoning, or the Confideration of
our abftracl: Ideas, but by means of Experi-
ments made with the Bodies themfelves. Hence
it happened, that while the Philofophy of Ari-
ftotle prevailed in the Schools, which dealt much
in Metaphyfical Notions, occult Qualities, Sym-
pathies, Antipathies, and fuch like Words with-
out Meaning; the Knowledge of Nature was
at a Stand : becaufe Men pretended to argue
abftra&edly about Things of which they had
no perfect and adequate Ideas, whereon to
ground
( 3*8 )
ground fuch a Method of Reafoning. But
now in the prefent Age, that we have returned
to the Way of Trial and Experiment, which
is indeed the only true Foundation of natural
Philofophy ; great Advances have already been
made, and the Profpedt of ftill greater lies be-
fore us.
D,ff<r<n fe k. IX * AND thus at len S th we ma 7
t-wetn fciend- fufficiently underftand wherein the
ral Know-"' P r P er DifFereiice lies, between fci-
leJge. entifical and natural Knowledge.
In Matters of Science we argue from the Ideas
in our own Minds, and the Connections and
Relations they liave one to another. And as
when thefe Relations are fet clearly and plainly
before us, we cannot avoid perceiving and
owning them, hence all the Truths of this
Clafs produce abfolute Certainty in the Mind,
and are attended with a neceflary and unavoid-
able Aflent. It is oiherwife in the Cafe of
natural Knowledge. Intuition and inward Per-
ception have here no Place. We difcern not
the Powers and Properties of thofe Objects that
furround us, by any View and Comparifon of
the Ideas of them one with another, but merely
by Experience, and the Impreflions they make
on the Senfes. But now the Reports of Senfe
happening in fome Inftances to deceive us, we
have no infallible Aflurance that they may not
in others j which weakens not a little the Evi-
dence
( 3*9 )
dence attending this Kind of Knowledge, and
leaves room for fufpicion and Diftruft. Nay,
what is yet more confiderable, as we have no
perfect and adequate Ideas of Bodies, repre-
fenting their inward Conftitution, or laying
open the Foundation upon which their Quali-
ties depend, we can form no univerfal Propo-
fitions about them, applicable with Certainty
in all particular Inftances. Fire, we fay, dif-
folves Metals. This, though exprefled inde-
finitely, is however only a particular Truth,
nor can be extended with abfolute Aflurance,
beyond the feveral Trials made. The Reafon
is, that being ignorant of the inward Frame and
Compofition both of Fire and Metals ; when
Objects are offered to us under that Name, we
have therefore no pofitive Certainty that they
are of the very Make and Texture requifite to
the Succefs of the Experiment. The Thing
may indeed be probable in the higheft Degree,
but for want of ftandard and fettled Ideas, we
can never arrive at a clear and abfolute Per-
ception in the Cafe.
X. As neverthelefs it is certain n e Manntr
that many general conclufions in f RiJ J ol " n S
in natural
natural Philofophy are embraced Knoictedgt.
without Doubt or Hefitation ; nay, that we
form moft of the Schemes and Purfuits of Life
upon that Foundation ; it will naturally be afked
here, how come we by this Affurance ? I anfwer,
not
not fcientificalty, and in the way ef (trier. De-
monrtration, but by Analogy, and an Induction,
f Experiments. We diftinguifh Fire, for in-
france, by fuch of its Qualities as lie more im-
mediately open to the Notice of the Senfes ;
among which Light and Heat are the moft con-
fiderable. Examining Bill farther into its Na-
ture, we find it likewife pofTefied of the Power
of diffblving Metals. But this new Property
not having any neceflary Connection that we
can trace, with thofe other Qualities by which
Fire is diflinguifhed, we cannot therefore argue
with Certainty, that wherever Light and Heat,
fcff. are, the Power of difiblving Metals co-exifts
with them. 'Tis not till after we have tried the
Thing in a Variety of Experiments, and found
it always to hold, that we begin to prefume
there may be really fome fuch Connection, tho*
our Views are too fhort and imperfect to difco-
vcr it. Hence we are led to frame a general
Conclufion, arguing from what has already
happened, to what will happen again in the
like Cafes; infomuch that where we meet with
all the other Properties of Fire in any Body, we
have not the leaft Doubt but that upon Trial,-
the Power above-mentioned will be found to
belong to it alfo. This is called Reafoning by
Analogy^ and it is, as we fee, founded intirely
upon Induction, and Experiments made with
particular Objects j the more precife and accu-
rate
rate our Ideas of thefe Objects are, and tb*
greater the Variety of Experiments upon which
\ve build our Reafoning, the more certain and
undoubted will the Conclufions be. 'Tis in
this Manner we arrive at all the general Truths
of natural Knowledge : as that the Bite of cer-
tain Animals is mortal j that a Needle touched
by a Loadftone points to the North ; that Gra-
vity belongs univerfally to all Bodies j and in-
numerable others, which though not capable
of ftricl: Demonftration, are neverthelefs as
readily embraced upon the Foundation of Ana-
logy, as the moft obvious and intuitive Judg-
ments j nay, and become fixed and fteady Prin-
ciples of Action in all the Aims and Purfuits of
Life.
XI. AND here again it is parti- jj ow evtn
cularly remarkable, that having af- >''""//
Riafoiiiig may
certained the general Properties of be imroduetd
Things by Analogy, if we proceed
next to eltablifh thefe as Poftulata in Philofophy,
we can upon this Foundation build ftrit and
mathematical Demonftrations, and thereby in-
troduce fcicntifeal Reafoning into natural Know-
ledge. In this Manner Sir Ifaac Newton^ having
determined the Laws of Gravity by a Variety
of Experiments, and laying it down as a Prin-
ciple, that it operates according to thofe Laws
thro' the whole Syftem of Nature j has thence,
in
( 33* )
in a Way of ftrit Dcmonftration, deduced the
whole Theory of the heavenly Motions. For
granting once this Pojlulatum^ that Gravity be-
longs univerfaliy to all Bodies, and that it acts
according to their folid Content, decreafing
with the Difrance in a given Ratio ; what Sir
Jfaac has determined in regard to the Planetary
Motions, follows from the bare Confideration
of our own Ideas j that is, neceffarily and fci~
entifically. Thus likewife in Optics, if we lay
it down as a Principle, that Light is propagated
on all Sides in right Lines, and that the Rays
of it are reflected and refracted according to
certain fixed invariable Laws, all which is
known to be true by Experience j we can upon
this Foundation eftablifh mathematically the
Theory of Vifion. The fame happens in Me-
chanicksy Hydrojlaiicks^ Pneumatuks^ &c. where
from Pojlulata afcertained by Experience, the
whole Theory relating to thefe Branches of
Knowledge follows in a Way of ftrift Demon-
ftration. And this I take to be the Reafon
why many Parts of natural Philofophy are ho-
noured with the name of Sciences. Not that
they are ultimately founded upon Intuition j.
but that the feveral Principles peculiar to them
being aflumed upon the Foundation of Experi-
ence, the Theory deduced from thefe Principles
is eftabhfhed \>y fcientifical Reafoning.
XII. COULD
( 333 )
XII. COULD we indeed difcerti
any neceflary Connection between P"
' _. the ultimate
Gravity and the known eiiential Ground of t,ur
Qualities of Matter, infomuch that A -^ nt '
it was infeparabie from the very Idea of it ; the
whole Theory of the Planetary Motions would
then be ftri&ly and properly fcientificoL For
feeing, from the Notion of Gravity, we can
demonftratively determine the Laws that Bo-
dies will obferve in their Revolutions, in any
known Circumftances ; if the Circumftances
relating to any Syftem of Bodies can be traced,
and Gravity is fuppofed eflential to them, we
can then, from the bare Confideration of our
own Ideas, deduce all their Motions and Phse~
nomena. Now this is precifely what Sir Jfaac
has done in regard to our Planetary Syftem. He
has determined the Circumftances of the Bodies
that compofe it, in refpeft of Situation, Dif-
tance, Magnitude, &c. all which being fup-
pofed, if they are efientially actuated by Gra-
vity, their feveral Revolutions and Appearances
muft be equally eflential. But as the Principle
of Gravitation cannot be accounted for by the
known Qualities of Matter, neither can this
Theory be immediately deduced from the Idea
of : Body ; and therefore, tho' our Reafoning
in this Part of Philofophy be truly fcientifical,
yet as the Principle upon which that Reafoning
is grounded, is derived from Experience, the
Theory
( 334 )
Theory itfelf muft needs ultimately reft upon the
fame Foundation. And thus even the Doctrine
of the Planetary Motions, though feemingly
eftablifhed by mathematical Reafoning, falls yer,
in Stridtnefs and Propriety of Speech, under the
r' Head of natural Knowledge. For in this pre-
cifely confifts the Difference between Science,
and what we call the Philofophy of Nature; that
the one is grounded ultimately on Intuition, the
other on Experience. As the Obfervation here
made holds alike in all the other Branches of na-
tural Philofophy, into which fcientifical Reafon-
ing has been introduced ; it is hence apparent,
that they are not Sciences^ in the ftrict and proper
Senfe of the Word, but only by a certain Latitude
of ExprelTion common enough in all Languages.
What we have therefore faid above relating to
the Impoflibility of improving natural Know-
ledge by fcientifical Deductions, is not con-
tradicted by any thing advanced in this Section.
We there meant Deductions grounded ultimately
on Intuition, and derived from a Confideration of
the abftract Ideas of Objects in our own Minds ;
not fuch as flow from Pojlulata aflumed upon
the Foundation of Experience. For thefe laft,
as we have already obferved, are not truly and
properly fcientifical, but have obtained that Name
merely on account of the Way of Reafoning in
which they are collected from the faid Pojlu-
lata*
XIII. IF
( 335 )
XIII. IF then abfolute and in- ri>e Mantitr
-fallible Certainty is not to be ob- tf* e . a f.
in Hijiortcal
tained in Natural Knowledge, much Knowledge.
lefs can we expert it in Hiftorical. For here
Teftimony is the only Ground of Afienr, and
therefore the Polfibility of our being deceived,
is ftill greater than in the Cafe of Experience.
Not only he who reports the FacT: may himfelf - !
have formed a wrong Judgment j but-could we
even get over this Scruple, there is ftill Room
to fufpeft, that he may aim at impofing upon
us by a falfe Narration. In this Cafe therefore
it is plain, there can be no Intuition or inward
Perception of Truth, no ftricl: and abfolute De-
monftration, and confequently no Science. There
is however a Way of Reafoning even here, that
begets an intire Acquiefcence, and leads us to
embrace without wavering, the Fads and Re-
ports of Hiftory. If, for Inftance, it appears, -
that the Hiftorian was a Man of Veracity ; if
he was a competent Judge of what he relates ;
if he had fufficient Opportunities of being in-
formed j if the Book that bears his Name was
really writ by him ; if it had been handed down
to us uncorrupted ; in fine, if what he relates
is probable in itfelf, falls in naturally with the
other Events of that Age, and is attefted by
contemporary Writers : By thefe and fuch like
Arguments, founded partly on Criticifm, part-
ly on probable Conjcdure, we judge of paft
Tranf-
( 336 )
Tranfa&ions ; and though they are not capable
of fc ientijical Proof, yet in many Cafes we ar-
rive at an undoubted Aflurance of them. For
as it is abfurd to demand mathematical Demon-
ftration in Matters of P'a&, becaufe they admit
not of that Kind of Evidence ; it is no lefs fo to
doubt of their Reality, when they are proved by
the beft Arguments their Nature and Quality
will bear.
Scrpticifa* XIV. AND thus we fee, in the
neet/arify feveral Divifions of human Know-
txeiaaea frcm
Matttrt of ledge, both what is the Ground of
Scuna. Judging, and the Manner of Rea-
foning, peculiar to each. In Scientifical Know-
ledge, which regards wholly the abftradl Ideas
of the Mind, and thofe Relations and Con-
nections they have one with another ; our
Judgments are grounded on Intuition^ and the
Manner of Reafoning is by Demonftratlon. In
Natural Knowledge, refpecting Objects that
exift without us, their Powers, Properties,
and mutual Operations j we judge on the Foun-
dation of Experience^ and reafon by Induftion
and Analogy. Laftly, in, Hijlorical Knowledge^
which is chiefly converfant about paft Fads
and Tranfa&ions ; Teflimony is the Ground of
Judgment, and the Way of Reafoning is by
Criticifm and probable Conjefture. And now I
think we are able effectually to overthrow that
abfurd Kind of Scepticifm maintained by fome
9 of
( 337 )
of the Ancients, which brings all Propofitiona
upon a. Level, and reprefents them as equally
uncertain. What gave the firft Rife to this
Doctrine was, the Caprice of certain Philo-
fophers, who obferving that the Reports of
Senfe and Teftimony were in fome Inftances
deceitful, took thence Occafion to fuppofe that
they might be fo likewife in others, and there-
upon eftablifhed it as a Principle, that we
ought to doubt of eyery Thing. But even with
refptd to this Doubting we are to obferve, that
it can in Fact extend no farther than to Matters
of Experience and Tejlimony^ being totally and ne-
ceiTarily excluded from Scientifical Knowledge.
When Ideas make their Appearance in the Un-
der'tanding, it is impoffible for us to doubt of
their being there. And when the Relations of
any of our Ideas are clearly and diftinclly dif-
cerned by the Mind, either immediately, which
is Intuition, or by Means of intervening Ideas,
which is Demon/lration ; it would be in vain
for us to endeavour to perfuade ourfelves that
that is not, which we plainly and unavoidably
perceive to be. In this Cafe therefore we can-
not withhold our AiTent ; Truth forces its Way-
over all Oppofition, and breaks in w?th fo much
Light upon the Mind, as t9 beget abfolute and
infallible Certainty.
Q, XV. IK*
( 338 )
And tt be ad- ' I N D E D n Natural and
mitted -with Hiftorical Knowledge Scepticifm
Caution in i_ T>I L /
Matten of m *Y " ave "J a ce ; bccaufe, as we
Experience have faid, there is a Poflibility of
anJTiflimony. . . . .
our being deceived, .but then it is
to be obferved, that a bare Poflibility is a very
weak Ground whereon to bottom any Philo-
fophical Tenet. It is poflible that Great Britain
may be fwallowed up by the Sea before To-mor-
row ; but I believe no Man is on 'this Account
inclined to think that it will be fo. It is pof-
fible the whole human Race may be extinguifhed
the next Inftant ; yet this Poflibility creates no
Apprehenfion that the Thing itfelf will really
happen. In a Word, we ought to judge of
Things by the Proofs brought to fupport them,
not by bare abftrad: Poflibilities ; and when we
have all the Evidence they are capable of, that
alone is fufficient to convince, tho' perhaps the
contrary cannot be fhewn to imply a Contra-
diction. Will any wife and confidcrate Man
doubt whether there be fuch a Place as America^
becaufe we cannot prove by any neceflary Argu-
ment, that it is abfolutely impoffible all the Re-
lations concerning it fhould be falfe ? Strict and
rigorous Demonftrations belong not to Hiftory,
or the Philofophy of Nature. The Way of Rea-
foning in thefe Branches of Knowledge is by
Arguments drawn from Experience and Tefti-
mony. And when the Truth of any Propofition
is
( 339 )
is in this Manner fufficiently afcertained, info-
much that it appears with all the Evidence it is
capable of, and we have as great Reafon to be-
lieve that it is, as we could pofllbly have, fup*
pofing it were, is not this upon the Matter as
fatisfa&ory as a Demonftration ? It muft be
owned indeed, there is no inward Perception in
the Cafe, and therefore our Aflent cannot be faid
to be neceflary and unavoidable. Men may in.
thefe Matters be Scepticks if they pleafe j and if
they are refolved upon it, it is in vain to contend
with Qbftinacy and Perverfenefs. I cannot how-
ever but obferve, that if they will really aft up to
their own Principles, and treat all Things in
good earneft as uncertain, that admit not of ftri&
fcientifical Proof, their Conduit muft be the
very Madnefs of Folly. No Man can demon-
ftrate mathematically, that Poifon has not been
conveyed into his Meat or Drink. And if he
will be fo very cautious as not to tafte of either,
till he has reached this Degree of Certainty, I
know no other Remedy for him, but that in
great Gravity and Wifdom he muft die for Fear
of Death. The Truth of it is, the moft zealous
Patrons of Scepticifm^ after all their pretended
Doubts and Scruples, find it yet convenient to
behave in the feveral Occurrences of Life, as if
they gave entire Credit to the Reports of Senfe
and Teftimony. They will no more venture up-
on a Dofe of Arfenic, or rufh into the Midft of a
Q.2 glowing
( 340 )
glowing Furnace, than if they verily believed
Death would be the Confequence. And though
in this it muft be owned they act difcreetly, yet
have we hence at the fame Time a very convincing
Argument of the Abfurdity of thofe Notions they
affect to entertain. In Reality, can any Thing be
more ridiculous, than to give into a Scheme of
Thinking, which we find ourfelves neceflitated
to contradict in almoft every Occurrence of Life?
Opinions are not to be taken up out of Caprice
and Fancy, but to ferve as Principles of Action,
and ftanding Rules of Behaviour. When they
anfwer not this main Purpofe, they are unavail-
ing and fruitlefs, and an obftinate Adherence to
them, in Spite of the repeated Admonitions of
Experience, juftly deferves to be branded for
Folly. We f&all not therefore attempt to multi-
ply Arguments in a Matter fo obvious, it fuffi-
ciently anfwering our prefent Purpofe to have
fhown, that Doubting and Uncertainty have
no Place in fcientifical Knowledge, and that
even in Matters of Hiftory, and the Facts of
Nature, an undiftinguifhing Scepticifm would
be in the higheft Degree abfurd.
Sctcnct apfii- XVI. BUT here perhaps it will
cable to the b ftgj Wh ]j th j mighty N ojfe
CoKcerns of ' J 91
human Life, about Science, when even according
to the prefent Account, it feems to be fo very
capricious and arbitrary a Thing ? For feeing
it is wholly confined to the Confideration of our
Ideas,
( 34i )
Ideas, and we are at Liberty to frame and combine
thofe Ideas at Pleafure, this indeed opens a Way
to Caftles in the Air of our own building, to
many chimerical and fanciful Syftems, which
Men of warm and lively Imaginations love to
entertain themfelves with, but promifes little
of that Knowledge which is worth a wife Man's
Regard, and refpe&s the great Ends and Pur-
pofes of Life. Where is the Advantage of barely
contemplating our Ideas, and tracing their fe-
veral Habitudes and Relations, when it is in
Truth the Reality of Things that we are chiefly
concerned to know, and thofe Refpeds they
bear to us and one another ? To this I anfwer :
that if indeed our Ideas no way regarded Things
themfelves, the Knowledge acquired by their
Means would be of very little Confequence t.
human Life. But fince, as we have already ob-
ferved, whatever is true in Idea, is unavoidably
fo alfo in the Reality of Things, where Things
exift anfwerable to thefe Ideas ; it is apparent,
that by copying our Ideas with Care from the
real Objects of Nature, and framing them in
a Conformity to thofe Conjunctures and Cir-
cumftances in which we are moil likely to be
concerned, a Way is laid open to Difcoveries of
the greateft Importance to Mankind. For in
this Cafe, our feveral Reafonings and Conclw-
fions, holding no lefs of the Objects themfelves,
Q.3 than
( 342 )
than of the Ideas by which they are reprefented,
may be therefore applied with Certainty to thefe
Objects, as often as they fall under our Notice.
Thus Mathematicians, having formed to them-
felves Ideas of Cones, Cylinders, Sphere^,
Prifms, ffr. varioufiy compare them together,
examine their feveral Properties, and lay down
Rules by which to calculate their relative Bulk
and Dimenfions. But now as Bodies anfwering
ia Figure to thefe Ideas come frequently under
pur Obfervation, we have by this Means an Op-
portunity of applying Mathematical Knowledge
to the common Concerns of Life ; and by deter-
mining precifely the Quantity of Extenfion in
each Body, can the better judge how far they
will anfwer the Purpofes we have in View.
The fame Thing happens in Politicks and Mora-
lity. If we form to ourfelves Ideas of fuch Com-
munities, Connexions, Actions, and Conjunc-
tures, as do or may fubfift among Mankind ; all
our Reafonings and Conclusions will then refpecl
real Life, and ferve as fteady Maxims of Behavi-
our in the feveral Circumftances to which it is
liable. It is not therefore enough that we fet
about the Confideration of any Ideas at Random ;
we muft further take Care that thofe Ideas truly
regard Things themfelves : for altho' Knowledge
is always certain, when derived from the Con-
templation of our own Ideas, yet is it then only
ufeful and worthy aur Rega.rd a when it refpe&s
Ideas
( 343 )
Ideas taken from the real Objects of Nature, and
ftridly related to the Concerns of human Life.
XVII. HAVING thus fhown that <n,,; M/^W
there is fuch a Thing as Science, fixed J Science be-
ad afcertained the Bounds of it, and pertaining our
explained its great Ufe and Impor- &'<*'
tance in the Affairs of Mankind j it now remains
that we lay down the Rules of Method peculiar
to this Branch of Knowledge, and give fome Ac-
count of the Manner in which that Certainty
and Conviction which are infeparable from it,
may be moft naturally and effectually produced.
Science, as we have faid, regards wholly the ab-
ftradt Ideas of the Mind, and the Relations they
have one to another. The great Secret there-
fore of attaining it lies, in fo managing and con-
ducting our Thoughts, as that thefe feveral Re-
lations may be laid open to the View of the Un-
derftanding;, and become the necefTary and un-
avoidable Objects of our Perception. In order
to this we muft make it our firft Care, diftin&ly
to frame and fettle the Ideas about which our
Enquiries are to be employed. For as the Re-
lations fubfifting between them can no otherwife
be difcerned, than by comparing them one with
another ; and as this Comparifon neceflarily fup-
pofes that the Ideas themfelves are actually in
the Mind, and at that very Time under our im-
mediate InfpeCtion ; it plainly follows, that all
Science muft begin with fixing and afcertain-
0.4 ing
( 344 )
ing thofe Ideas. Now our Ideas, as has been
already obferved in the firft Book, come all very
naturally within the Divifion of Simple and Com-
plex. Simple Ideas are excited by a&ual Im-
preflions made upon the Undci (landing j and as
they exift under one uniform Appearance, with-
out Variety or Compofition, are in no Danger of
being miftaken, or confounded one with another.
It is otherwife in our Complex Conceptions. For
thefe confifting of many fimple Ideas joined to-
gether, great Care muft be taken, that we ac-
quaint ourfelves with the true Number combin-
ed, and the Order and Manner of their Connec-
tion. By this Means alone are thefe our moft
intricate Notices kept diftin& and invariable, in-
fomuch that in all our feveral Views of them,
they ever have the fame Appearance, and exhi-
bit the fame Habitudes and Refpe&s. Here there-
fore, properly fpeaking, the Art of Knowledge
begins. Fpr altho' we find it eafy enough to
bound and fettle our Ideas, where they confift
of but few limple Perceptions ; yet when they
grow to be very complicated, it often requires
great Addrefs and Management to throw them
imo fuch Views as may prevent that Confufion
which is apt to arife from the joint Confidera-
tion of a Multiplicity of different Objects.
Hence that Gradation in the Compofition of our
Ideas, which we have explained at large in the
laft Chapter of the firft Book. For as they are
by
( 345 )
by this Means formed into different Orders, and
thefe Orders arife continually one out of ano-
ther j the Underftanding, by taking them in a
juft Succeflion, gradually mounts to the higheft
Conceptions, and can at any Time, with incredi-
ble Eafe and Expedition bring all their Parts dif-
tinclily into View. To know therefore the full
Value of this Contrivance, we muft attentively
confider the ftridl Connection that obtains be-
tween the feveral ClafTes of our Perceptions
* -
when difpofed in fuch a Series. Every Succeeding
Order is formed out of thofe Combinations that
conftitute the Rank next below it. And as irk
advancing from one Degree to another, we are
always to proportion the Number of Notices
united, to the Strength and Capacity of the
Mind ; it is apparent that by fuch a Procedure
the Ideas will be thoroughly afcertained in every
Step, and however large and bulky, lie yet fairly
within our Grafp. This obvioufly accounts for
that wonderful Clearnefs of Apprehenlion, which
we often experience within ourfelves, even in
regard to the moft complicated Conceptions.
For though the Multitude of Parts in many
Cafes be great, I may fay beyond Belief, yet
as they have been all previously formed into fe-
parate Clafles, and the Clafles themfelves dif-
tindly fettled in the Undemanding } we find
it eafy, by fuch a Series of Steps, to rife to any
Idea how complex foever, and with a fingle
Q. 5 Glance
Glance of Thought embrace it in its full Ex-
tent.
Andcimmu- XVIlI. BtJT it is not enough
I^Melns of 1 l ^ at we barely f rm Ideas in our own
Dtfia'niont. Minds: We muft alfo contrive a
Way to render them ftable and permanent, that
when they difappear upon calling off our Atten-
tion, we may know how to retrieve them again
with Certainty. This is beft done by Words and
Descriptions, which ferve not only to fubje&
them to our own Review, but alfo to lay them
open to the Perception of others. And indeed
as one of the main Ends of reducing Knowledge
into the Form of a Science is, the eafy and ad*
vantageous Communication of Truth 5 it ought
always to be our firft Care, when we fet about
unfolding our Difcoveries, to exhibit the feveral
Conceptions to which they relate, in a juft and
accurate Series of Definitions. For till we have
diftinctly transferred our Ideas into the Under*
Handings of thofe to whom we addrefs ourfelves,
and taught their Connection with the appro*
priated Sounds, all our Reafonings will evidently
be without Efieft. If Men comprehend not the
true Import of our Words, and are therefore
led by them to bring wrong Ideas into Compa-
rifon, they can never fure fee Connections and
Habitudes that really fubfift not. But if on
the contrary the Terms we ufe exci-te thofe very
Perceptions in others, which they denote in
2 our
( 347 )
our own Minds ; then, as the feveral Relations
pointed out will lie fairly open to View, they
muft needs be difcerned with great Readinefs
and Eafe, and ftamp the Character of Certainty
upon all our Deductions.
XIX. THUS we fee, that the Me- rt,e Names ef
thod of Science begins with unfolding fiP' e Idta *
J torjliture the
our Ideas, and communicating them original and
by Means of Definitions. And here f e ^ s '^ y Lan .
it is of great Importance to obferve, <*
that there muft be in all Languages, certain Ori-
ginal and Elementary Names, whence our De-
fcriptions take their firft Rife, and beyond which
we cannot trace the Meaning and Signification
of Sounds. For fince our very Definitions are
made up of Words, if we fuppofe not fuch pri-
mitive and fundamental Terms, into which they
all refolve themfelves, and where they at laft ne-
ceffarily terminate, it is evident there would be
no End of explaining. Now it is peculiar to our
fimple Ideas, that they cannot be originally ex-
cited by Words, but muft always make their
firft Entrance into the Underftanding by the ac-
tual Operation of Objedls upon it. When there-
fore, in a Series of Definitions, we arrive at the
Names of thefe Ideas, 'tis plain we can pufli
our Defcriptions no farther, but are neceffitated
to fuppofe, that the Perceptions themfelves have
already found Admifiion into the Mind. If they
Q.6 have
have ftot, Definitions avail nothing ; nor can
they any other Way be imprefTed upon us, than
by betaking ourfelves to the feveral Objes in
which the Power of producing them refides.
Hence it appears, that the primary Articles of
Speech, into which the Whole of Language may
be ultimately refolved, are no other than the
Names of fimple Ideas. Thefe we fee admit not
Definitions. It is by Experience and Obferva-
tion that we grow acquainted with their Mean-
ing, and furnifh ourfelves with the Perceptions
they ferve to denote. For finding that thofe in
whofe Society we live, make ufe of certain ar-
ticulate Sounds, to mark the various Impreffions
of Objects, we too annex thefe Sounds to the
fame Impreffions, and thus come to underftand
the Import of their Words. This Way of Know-
ledge takes Place, in regard to all our fimplq
Ideas j but in many of thofe that are complex,
as they are the mere Creatures of the Underftand-
ing, and exift no-where out of the Mind, there
are of Courfe no real Objects without us, whence
they may be originally obtained. If therefore
they could not be communicated by Defcrip-
tions, we fhould be left wholly without the
Means of transferring them into the Minds of
others. But happily it fo falls out, that all
complex Conceptions whatfoever may be dif-
tindily exhibited in Definitions. For as they
are no more than different Combinations of fim-
pie
( 349 )
pie Ideas, if thefe fimple Ideas have already got
Admiffion into the Understanding, and the
Names ferving to exprefs them are known ; it
will be eafy, by defcribing the Order, Number,
and peculiar Connection of the Notices com-
bined, to raife in the Mind of another the com-
plex Notion refulting from them.
XX. SINCE then it is by fimple A K
Ideas and their Names, that we un-
fold all the other Conceptions of the pojed in band-
Mind ; it manifestly follows, that in
handling any Subje&feienti/ically, we
muft always fuppofe thofe to whom we addrefs
ourfelves previoufly furnifhed by Experience
with thefe firft Principles and Elements of
Knowledge. Nor is this by any Means an un-
reafonable Pojlulatum : Becaufe the fimple Ideas
that relate to the Sciences, being few in Num-
ber* and coming very often in our Way, it is
hardly poffible we fhould be unacquainted with
them, or not have frequently heard their Names
in Converfe with others. What principally de-
mands our Care is, to apply thofe Names aright,
and according to the ftri& Ufe and Propriety of
the Language in which we write. 'Tis feldom
allowable to change the Signification of Words,
efpecially thofe by which we denote fimple Ideas.
If however fuch a Liberty fhould at any Time be
found neceflary, we may ftill make ourfelves
underftood,
( 350 )
underftood, by mentioning the Idea under its
common Name, and fignifying its Connexion
with the newly-appropriated Sound. Indeed it
fcmetimes happens, that new and unufual Ideas
of this Kind are to be taken under Confideration,
which we muft therefore exprefs by Terms of
our own Invention. In this Cafe, as the Ideas
themfelves cannot be laid open by Definitions,
we refer to the feveral Obje&s whence they may
be obtained ; which though it excites not the
Perceptions immediately, yet fufficiently an-
fwers our Purpofe, by putting Men in a Way
of being furnifhed with them at Pleafure.
XXI. THIS Foundation being
The Order and , . . . f ^ . . r
CoMeflhnof J ai " the Communication of our
eurDefni'iom. com pl e x Conceptions by Definitions
becomes both eafy and certain. For fince the
Ideas themfelves are formed into different Or-
ders, and thefe Orders arife continually one out
of another ; nothing more is required on our
Part, than to obferve a like Method and Grada-
tion in our Defcriptions. As therefore the firft
Order of our compound -Notions is formed
immediately from fimple Ideas ; fo the Terms
appropriated to this Order muft be defined by
the Names of thefe Ideas. And as the fecond
and all the fucceeding Orders arife continually
cut of thofe Combinations that conftitute the
Clafles next below them, fo the Definitions
correfponding
/ ( 351 }
correfponding to thefe different Orders gra-
dually take in the Terms by which the feveral
inferior Divifions are regularly and fucceflively
exprefled. In fuch a Series of Oefcriptions, it
is evident at firft Sight, that nothing can be ob-
fcure and unintelligible. For as it begins with
the Names of fimple Ideas, whofe Meaning is
fuppofed to be known; and as in every Order
of Definitions, fuch Terms only occur, as have
been previously explained in the preceding Dif-
tributions j by advancing regularly from one
to another, we gradually furnifh ourfelves with
whatever is neceflary towards a diftincl: Con-
ception of all that is laid before us. Nor is it
a fmall Advantage attending this Difpofltion,
that the feveral Ideas defcribed are hereby ex-
ciied in the Underftanding, in the very Order
and Manner in which they are framed by a
Mind advancing uniformly from fimple to the
mod complicated Notions. Hence we fee dif-
tin&ly the various Dependence of Things, ami
being put into that very Train of Thinking
which leads dire&ly to Science and Certainty,
are drawn infenfibly to intereft ourfelves in the
Purfuit ; infomuch' that while in Fail we do
no more than follow a Guide and Conductor,
we can yet hardly forbear fancying ourfelves
engaged in the actual Exercife of deducing
one Part of Knowledge from another.
XXII. WHEN
( 352 )
Of tke tmrne- XXII. WHEN W6 have tllUS fixed
JUH andin- and afcertained our Ideas, and dif-
tvitive Refa- /-> i > M i i r\ f
tiot bttnttn tinctly exhibited them in Denm-
tur ides,. tions, we then enter upon the im-
portant Tafk of tracing their feveral Habitudes
and Relations. In order to this we fet about
comparing them among themfelves, and viewing
them in all the Variety of Lights, by which we
can hope to arrive at a Difcovery of their mu-
tual Agreement or Difagreement. And here it
happens, that fome Relations forwardly offer
themfelves to the Notice of the Underiranding,.
and become the neceflary Objects of Perception,
upon the very firft Application of our Ideas one
to another, Thofe are therefore immediately
owned, and conflitute our primary and intuitive
Judgments, being attended with the higheft De-
gree of Evidence, and producing abfolute Cer-
tainty in the Mind. But in many Cafes, the
Connection or Repugnance between our Ideas,
even when true and real, comes not yet within
our immediate View, but requires Search and
Examination to difcover it. On this Occafion,
we have Recourfe to intermediate Notices, and
if by Means of them we can mufter up a Train
of evident and known Truths, which, difpofed
in a regular Series of Argumentation, lead at
laft to a Conclufion expreffing the Relations we
are in Queft of, the Proof thence arifing is called
Demonflration. Now as the Conviction attend-
ing
( 353 )
ing Demonftration is no lefs neceflary and un-
avoidable than that which proceeds from, In-
tuition ; it evidently follows, that whether the
Relations between our Ideas are injtnediately
difcerned by the Mind, or whether they are
traced by Means of intervening Perceptions, in
either Cafe we arrive at Science and Certainty.
This however is particularly to be obferved,
that the more remote and diftant Refpels, be-
ing deduced from fuch as are obvious and felf-
evident, the Propofitions expreffing thefe laft
demand our firft Notice, and ought to be previ-
oufly eftablifhed, before we enter upon higher
Inveftigations. When therefore, in the Method
ff Science, we have finifhed the Bufinefs of De-
finitions; it muft be our next Care, diftin&ly
to unfold in Propofitions, thofe immediate and
intuitive Relations, which are neceflarily feen
and owned by the Mind, upon the very firft
comparing of our Ideas one with another. Thefe
Propofitions have obtained the Name of firft
Principles^ becaufe occurring firjl in the Order
of Knowledge, and being manifeft of themfelves,
they fuppofe not any prior Truths in the Mind,
whence they may be evidenced and explained.
It is not needful to enlarge here upon the Ne-
ceflity of Circumfpeclion and Care, in fettling
thefe primitive and fundamental Perceptions.
For fmce the whole Superftruclure of our Know-
ledge refts ultimately upon them, it is evident at
firft
( 354 )
firft Sight, that a Miftake in this Cafe muft at
once overturn and annihilate all our future
Reafonings. But having already explained the
Nature of thefe Propofitions in the fecond Book,
unfolded the Notion of Self-Evidence, and
taught the 'Manner of diftinguifhng between
the Truths of this Clafs, and thofe that are
demonftrable j \ve fhall for the prefent wave
any farther Confideration of this Subject, re-
ferring the Reader to what is there advanced,
if he defires fuller Information.
XXIII. THE firft and more im-
mediate Relations of our Ideas be-
jng thus pointed out, our next Bu-
in dimonfirat- _ . . . _ . - ,
finefs is, to mveltigate fuch as are
r '* 0!e **4 remote and diftant. And here it is
aijtant,
that we have Occafion for inter-
mediate Notices, and a fkilful Application of
intuitive Truths. But tho' felf-evident Pro-
pofitions be the ultimate Foundation of our
Reafoning, we are not on that Account to ima-
gine, that the Art of improving Knowledge
Jies in aflembling at Random a large and com-
prehenfive Stock of thefe. Even General Prin-
ciples^ confidered by themfelves, avail but little
towards the Inveftigation of Truth. They are
indeed ufeful as Media of Certainty, by pre-
ferving the Evidence of our Reafonings diftincr,
which never fail to convince, if, being purfued
to their Source, they are found to refolve them-
felves
( 355 )
felves into, and ultimately terminate in thefe
Principles. But when we fet about the In-
creafe and Enlargement of Science, far other
Helps are required. For here the whole Secret
confifts, in devtfing and fingling out fuch in-
termediate Ideas, as being compared with thofe
others whofe Relations we enquire after, may
furnifh out a -Train of obvious and known
Truths, ferving diftinctly to inveftigate the faid
Relations. Euclid, in the firft Book of the Ele-
ments, has demonftrated, that the three inward
Angles of a Triangle taken together, are equal t&
two Right Angles. The Reafoning by which he
eftablifhes that Proportion, refolves itfelf into
this general Principle : Things equal to one and
the fame Thing, are equal to vne another. Will
any one however pretend to fay, that a bare
Confideration of the Principle itfelf led him to
that Difcovery ? The mereft Novice in Ma-
thematicks would upon this Suppofition be
equally qualified for the Bufmefs of Invention,
with one that had made the greateft Progrefs;
inafmuch as thefe general Principles of the
Science are commonly alike known to both.
But the Truth of it is, Euclid having found
out Angles, to which the three Angles of a
Triangle, and two Right Angles, being com-
pared, were found feverally equal ; thereby af-
certained the Propofition in Queftion, by (hewing
it to terminate in the above Axiom, tho' perhaps
the
( 356 )
the Axiom itfelf was never once thought of dur-
ing the whole Courfe of the Inveftigation.
*/*,'* XXIV - AND here jt ma x not bc
rejoivabie into improper to obferve, that tho' it be
generalTrutbi) r 1 T> r
nftt \mmtdi- ufttsu in Kealoning, when we arrive
oteiyupcn at any p art icular felf-evident Pro-
f articular r
j<if-e-v,j>r<t pontion, to refer to the general
rofofitHns. Axiom under which it is compre-
hended : yet is not this done out of abfolute
Neceffity, or for the Sake of any additional
Confirmation. All intuitive Truths, whether
general or particular, {landing upon the fame
Foundation of immediate Perception, are ne-
ceflarily embraced for their own Sake, and re-
quire no mutual Illuftration one from another.
When therefore we have found, that the three
Angles of a Triangle, and two Right Angles,
are feverally equal to the Angles formed by one
Right Line {landing upon another, we thence
immediately difcern their Equality between
themfelves, independent of the general Axiom
into which this Truth maybe refolved. Nor do
we in Reality refer to that Axiom, by Way of
Evidence and Proof; but merely to {how the
Coincidence cf the Example under Notice, with
a previoufly eftabliflied general Principle. The
fame Thing happens in all other Demonftrations
whatfoever, which terminating thus in particu-
lar felf-evident Truths, are therefore of them-
felves fufficient to Certainty, and acquire not
any
( 357 )
new Force by being ultimately referred to
general Maxims. This I mention here, to ob-
viate a common Prejudice, whence many are led
to imagine, that particular intuitive Propofitions
derive their Evidence from thofe that are general,
as being neceflarily included in them. But fince
they both ftand upon the fame Foundation of
Certainty, and are admitted in confequence of
immediate Perception, they have therefore an
equal Claim to Self-Evidence, and cannot be
made plainer by any mutual Appeal.
XXV. As however it is ufual in Particular
the Method of Science to lay down J< l f- ""<*">*
rropofitiont
certain general Principles by Way fo called here,
of Foundation for our future Rea- $gJr"
fonings ; fome will perhaps object, Principle*.
that this feems to be a needlefs Precaution, fince
Demonftrations may fubfift without them, and
commonly terminate in particular felf-evident
Truths, peculiarly connected with the Subject
under Confideration. In order therefore to give
a diftindl Idea of the true Defign of this previous
Step, we fliall begin with obferving, that by
the particular Propofitions in which Demonftra-
tions terminate, muft not be underftood fuch as
are fo according to the ftridl Definition of the
Word, or in Oppofition to Univerfals ; but only
confined and limited Truths, when compared
with others that are more general. Thus the
Propofition, Circles equal to one and the fame
Circle,
( 358 )
Circle, are equal between thernfefoes, is in Strict ~
nefs and Propriety of Speech univerfal, becaufe
the Subject is taken in its full Extent, and the
Predicate agrees to all the Individuals compre-
hended under it. We here notwithftanding
confider it as only a particular Truth, becaufe
it is of a very limited Nature, when compared
with the general Axiom mentioned above j
Things equal to one and the fame Thing , are equal
to one another. For this not only extends to all
the various Species of Figures, but takes in
every Object without Exception, that comes
under the Denomination of Quantity.
GwralPrin. XXVI. THIS Point fettled, it
dples few will eafily appear, that the Method
fir ft to contra ft c .~ i T. i
tte Bottom of r premihng general Principles in
ur Reaftaiag. t h e Sciences anfwers thefe two
great and valuable Purpofes. Fir ft ^ to contract
the Bottom of our Reafoning, and bring it within
fuch Bounds as are fufficiently accommodated
to the Capacity of the Mind. For Demon-
flrations being carried on by Means of inter-
mediate Ideas, which muft always have fome
peculiar Connection with the Matter in Hand,
the particular felf-evident Propofitions in which
they terminate are almoft as various as the Sub-
jects to which they relate. Thus in invefti-
gating the Equality of different Objects, whe-
ther Angles, Triangles, Circles, Squares, &c,
the intuitive Truths on which the Proofs reft
always
( 359 )
always regard the particular Species, and may
be therefore multiplied in infinitum^ as well as
the Species themfelves. But now it is remark-
able that all thefe feveral Truths, numerous as
they may appear, are yet reducible to this one
general Principle already mentioned ; Things
equal to one and the fame Thing, are equal to one
another. The fame Obfervation will be found
to hold in other Parts of human Knowledge ;
infomuch that tho' the particular Truths on
which we bottom our Reafonings are really
innumerable j yet may they be all without Ex-
ception refolved into a very few general Max-
ims, and thereby brought readily within the
Compafs ^of the Underftanding. When there-
fore we begin with premifing thefe general
Truths, and as we advance in Science, take
Care univerfally to refolve our Demonftrations
into them ; this muft needs add a wonderful
Clearnefs and Perfpicuity to our Reafonings,
and by eftablifhing them upon a Foundation
previoufly admitted, and of whofe Strength and
Firmnefs we are abundantly fatisfied, give them
that irrefiitible Force and Influence, which
ferves to produce abfolute Certainty. Nor can
we poflibly imagine any Thing more elegant
and beautiful, than thus to behold Knowledge-
rifing from a firm and fathomable Root, bear-
ing its Head aloft, and fpreading forth into in-
numerable Branches of Science, j which though
variously
varioufly implicated and entangled, and ftretch-
ing to a vaft Extent, yet by their Union in
one common Stock, derive thence fo fure and
ftable a Support, that all the Aflaults of Cavil
and Scepticifm are not able to deftroy or loofen
their Connection.
XXVII. BUT Secondly, another
Secoad/y, to . .
afcenoin the Purpolc lerved by general Principles
Jijhcfs of it j that t| b] I h ] f jp
with mare
Fofe, and left tigue and Labour, and lefs Hazard
Hazard of r \/r-r r r ' r- i
Mi/carriage. ' Milcarriage, to latisfy ourlelves
as to the Juftnefs of thofe Reafon-
ings by which Science is eftablifhed. For fince
Demonftrations, when purfued to their Source,
terminate always in particular intuitive Truths,
which are therefore the ultimate Foundation of
Certainty ; it greatly imports us to beware,
that we receive not any Propofitions under
this Name, until we have diftin&ly fettled them
in our own Minds, and attained a full and clear
Perception of that Self-Evidence, on account
of which they are admitted without Proof.
But now thefe Propofitions being many in
Number, and differing according to the Nature
of the Subject about which our Refearches are
employed ; it muft greatly perplex and re-tard
our Reafonings, were we to check ourfelves
every Time they occur, in order to examine
them by the Rules of firft Principles. Nor is
it a Matter of flight Confideration, that in the
Heat
Heat and Hurry of demonftrating, while the
Mind is advancing eagerly from one Difcovery
to another, we fhould be often tempted to pafs
them over haftily, and without that Attention
their Importance requires ; which muft expofe
us to many Errors and Miftakes. Thtfe In-
conveniences are effe&ually prevented by the
Method of premifing general Truths : becaufe
upon referring particular Propofitions to them ;
as the Connection is obvious at firft Sight, and
cannot poflibly efcape our Notice, the Evidence
is difcerned to be the very fame with that of the
Principles to which they belong. And thus by
a bare Reference, without the Trouble of parti-
cular Examinations, the Grounds of Reafoning
are afcertained, and our Demon%ations found
ultimately to reft on Maxims pjevioufly cfta-
blifhed.
XXVIII. HAVING explained the oftbtMaa*
Ufe of general Principles, fhewn r>f j linking
them to be the great Medea of Cer- topthr^i*
tainty, and found, that in order to " dtrt <>' bt
1 L T> I i- forming of It-
enlarge the isounds of science, we gititate De-
rnuft have recourfe to intermediate >7 ""'/ r3 "' < ""-
Ideas, as by Means of them we are furnifhed with
the feveral previous Truths, of which Reafoning
confifts ; it now remains that we enquire in
what Manner thefe Truths are to be difpofed
and liaked together, towards the forming of juft
and legitimate DemonJIrationt. We have feen
R already
already in the preceding Book, that Syllogifms
drawn up according to the Rules there eftablifh-
ed, lead to a certain and infallible Conclufion.
If therefore evident and allowed Truths are dif-
pofed in a Syllogijtic Order, fo as to offer a regu-
lar Conclufion, that Conclufion is neceflarily
true and valid. And fince in every genuine Syl-
logifm, if the Premifes are true, the Conclufion
muft needs be true ; it manifeftly follows, that
the Conclufion already gained, being now a
known and eftabliflied Truth, may be admitted
as one of the Premifes of any fucceeding Syllo-
gifm, and thereby contribute towards the ob-
taining a new Conclufion. In this Manner may
Fyllogifms follow one another in Train, and lead
to a fucceffive Difcovery of Truth ; Care being
always taken, that the Premifes in every Step
are either felf-evident Propofitions, or Conclu-
fions previoufly eftablifhed. And indeed the whole
Art of demonfirating lies in this due and orderly
Combination of our Syllogifms. For as by this
means all the feveral Premifes made ufe of are
manifefUy true, all the feveral Conclufions muft
be fo too, and confcquently the very Jaft Con-
clufion of the Scries, which is therefore faid to
be dcmonjlrated. The fame Order is to be ob-
ferved in the Difpofition of the Dcmonftrations
themfelves. That is, thofe Propofitions are al-
W.ys firft to be demonftrated, which furnifli
Principles of Reafoning in others ; it being
upon
( 3*3 )
upon the Certainty of the Principles made Ufe
of, that the Certainty of the Truths deduced
from them depends. And fince even the dif-
ferent Branches and Divifions of Science have
a near Connection among themfelves, info-
much that the Knowledge of one is often pre-
fuppofed in another ; great Care muft be taken
to adjuft the feveral Parts with an Eye to this
Dependence, that thofe may always come firft
in Order, whence the Poftulata of Demonftra-
tion in others are borrowed.
XXIX. IN this Way /of putting why tit Me.-
together our Thoughts, it is evident tb . od . bt . re '*~
b plained is ;all-
at firft Sight, that however far we e d the M<tt>ad
carry our Refearches, Science and of Sci " !Cl '
Certainty will ftill attend us. But what is par-
ticularly elegant and happy in the Method now
explained, we hereby fee Knowledge rifing
out of its firft Elements, and difcern difti nelly
how thofe Elements are combined and inter-
woven, in order to the erecting a goodly Struc-
ture of Truth. Experience furnifhes us with
fimple Ideas and their Names, which are the
primary Materials of Thinking and Communi-
cation. Definitions teach how to unite and
bind thefe Ideas together, fo as to form them
into complex Notions of various Orders and
Degrees. The general Principles premifed in
Science exhibit to the Underftanding fuch in-
tuitive and fundamental Truths as exprefs the
immediate
immediate Relations between our Ideas, and con-
ftitute the ultimate Ground of Certainty. De~
tnonjlratlons link known and eftablifhed Truths
together in fuch Manner, that they neceflarily
lead to others which are unknown and remote.
In fine, the duly adjufting the feveral Branches
of Science, and the Demonftrations in every
Branch, lays Knowledge fo open to the Mind,
that we fee the Parts of it growing one out of
another, and embrace them with full Convic-
tion and Affurance. Thus are we gradually led
from fimple Ideas, through all the Windings and
Labyrinths of Truth, until we at length reach
the higheft and moft exalted Difcoveries of hu-
man Reafon. It is true the Method here laid
down hath hitherto been obferved ftri&ly only
among Mathematicians ; and is therefore by
many thought to be peculiar to Number and
Magnitude. But it appears evidently from what
we have faid above, that it may be equally ap-
plied in all fuch other Parts of Knowledge as re-
gard the abftract Ideas cf the Mind, and the
Relations fubfiiVmg between them. And fmce,
wherever it is applied, it neceflarily begets Science
and Certainty, we have hence chofen to denomi-
nate it the Method of kcience> the better to inti-
mate its true Nature and Extent.
FINIS.
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