A Treatise Concerning the Principles of Human Knowledge | Page 7

annexed them to every
common name they make use of?
15. NOR FOR THE ENLARGEMENT OF KNOWLEDGE.--Nor do I
think them a whit more needful for the ENLARGEMENT OF
KNOWLEDGE than for COMMUNICATION. It is, I know, a point
much insisted on, that all knowledge and demonstration are about
universal notions, to which I fully agree: but then it doth not appear to
me that those notions are formed by ABSTRACTION in the manner
PREMISED--UNIVERSALITY, so far as I can comprehend, not
consisting in the absolute, POSITIVE nature or conception of anything,
but in the RELATION it bears to the particulars signified or
represented by it; by virtue whereof it is that things, names, or notions,
being in their own nature PARTICULAR, are rendered UNIVERSAL.
Thus, when I demonstrate any proposition concerning triangles, it is to
be supposed that I have in view the universal idea of a triangle; which
ought not to be understood as if I could frame an idea of a triangle
which was neither equilateral, nor scalenon, nor equicrural; but only
that the particular triangle I consider, whether of this or that sort it

matters not, doth equally stand for and represent all rectilinear triangles
whatsoever, and is in that sense UNIVERSAL. All which seems very
plain and not to include any difficulty in it.
16. OBJECTION.--ANSWER.--But here it will be demanded, HOW
WE CAN KNOW ANY PROPOSITION TO BE TRUE OF ALL
PARTICULAR TRIANGLES, EXCEPT we have first seen it
DEMONSTRATED OF THE ABSTRACT IDEA OF A TRIANGLE
which equally agrees to all? For, because a property may be
demonstrated to agree to some one particular triangle, it will not thence
follow that it equally belongs to any other triangle, which in all respects
is not the same with it. For example, having demonstrated that the three
angles of an isosceles rectangular triangle are equal to two right ones, I
cannot therefore conclude this affection agrees to all other triangles
which have neither a right angle nor two equal sides. It seems therefore
that, to be certain this proposition is universally true, we must either
make a particular demonstration for every particular triangle, which is
impossible, or once for all demonstrate it of the ABSTRACT IDEA OF
A TRIANGLE, in which all the particulars do indifferently partake and
by which they are all equally represented. To which I answer, that,
though the idea I have in view whilst I make the demonstration be, for
instance, that of an isosceles rectangular triangle whose sides are of a
determinate length, I may nevertheless be certain it extends to all other
rectilinear triangles, of what sort or bigness soever. And that because
neither the right angle, nor the equality, nor determinate length of the
sides are at all concerned in the demonstration. It is true the diagram I
have in view includes all these particulars, but then there is not the least
mention made of them in the proof of the proposition. It is not said the
three angles are equal to two right ones, because one of them is a right
angle, or because the sides comprehending it are of the same length.
Which sufficiently shows that the right angle might have been oblique,
and the sides unequal, and for all that the demonstration have held good.
And for this reason it is that I conclude that to be true of any
obliquangular or scalenon which I had demonstrated of a particular
right--angled equicrural triangle, and not because I demonstrated the
proposition of the abstract idea of a triangle And here it must be
acknowledged that a man may consider a figure merely as triangular,

without attending to the particular qualities of the angles, or relations of
the sides. So far he may abstract; but this will never prove that he can
frame an abstract, general, inconsistent idea of a triangle. In like
manner we may consider Peter so far forth as man, or so far forth as
animal without framing the fore-mentioned abstract idea, either of man
or of animal, inasmuch as all that is perceived is not considered.
17. ADVANTAGE OF INVESTIGATING THE DOCTRINE OF
ABSTRACT GENERAL IDEAS.-- It were an endless as well as an
useless thing to trace the SCHOOLMEN, those great masters of
abstraction, through all the manifold inextricable labyrinths of error and
dispute which their doctrine of abstract natures and notions seems to
have led them into. What bickerings and controversies, and what a
learned dust have been raised about those matters, and what mighty
advantage has been from thence derived to mankind, are things at this
day too clearly known to need being insisted on. And it had been well
if the ill effects of that doctrine were confined to those only who make
the most avowed profession of it. When men