"Treatise" - читать интересную книгу автора (Berkeley George)

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