business of their childhood. And surely the great and multiplied
labour of framing abstract notions will be found a hard task for
that tender age. Is it not a hard thing to imagine that a couple of
children cannot prate together of their sugar-plums and rattles and
the rest of their little trinkets, till they have first tacked
together numberless inconsistencies, and so framed in their minds
abstract general ideas, and annexed them to every common name they
make use of?

  15. 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. 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. 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 consider the great pains,
industry, and parts that have for so many ages been laid out on the
cultivation and advancement of the sciences, and that
notwithstanding all this the far greater part of them remains full
of darkness and uncertainty, and disputes that are like never to
have an end, and even those that are thought to be supported by the
most clear and cogent demonstrations contain in them paradoxes which
are perfectly irreconcilable to the understandings of men, and that,
taking all together, a very small portion of them does supply any real
benefit to mankind, otherwise than by being an innocent diversion
and amusement- I say the consideration of all this is apt to throw
them into a despondency and perfect contempt of all study. But this
may perhaps cease upon a view of the false principles that have
obtained in the world, amongst all which there is none, methinks, hath
a more wide and extended sway over the thoughts of speculative men
than this of abstract general ideas.

  18. I come now to consider the source of this prevailing notion, and
that seems to me to be language. And surely nothing of less extent
than reason itself could have been the source of an opinion so
universally received. The truth of this appears as from other
reasons so also from the plain confession of the ablest patrons of