eas. As all beings are particular things, so all ideas are particular
ideas.

[Footnote 1: Cf. also Fraser's _Berkeley_ (Blackwood's Philosophical
Classics) 1881; Eraser's _Selections from Berkeley_, 4th ed., 1891; and
Krauth's edition of the _Principles_, 1874, with notes from several
sources, especially those translated from Ueberweg.--TR.]

Berkeley looks on the refutation of these two fundamental mistakes--the
assumption of general ideas in the mind, and the belief in the existence
of a material world outside it--as his life work, holding them the chief
sources of atheism, doubt, and philosophical discord. The first of these
errors arises from the use of language. Because we employ words which
denote more than one object, we have believed ourselves warranted in
concluding that we have ideas which correspond to the extension of the
words in question, and which contain only those characteristics which are
uniformly found in all objects so named. This, however, is not the case.[1]
We speak of many things which we cannot represent: names do not always
stand for ideas. The definition of the word triangle as a three-sided
figure bounded by straight lines, makes demands upon us which our faculties
of imagination are never fully able to meet; for the triangle that we
represent to ourselves is always either right-angled or oblique-angled, and
not--as we must demand from the abstract conception of the figure--both and
neither at once. The name "man" includes men and women, children and the
aged, but we are never able to represent a man except as an individual of a
definite age and sex. Nevertheless we are in a position to make a safe
use of these non-presentative but useful abbreviations, and by means of a
particular idea to develop truths of wider application. This takes place
when, in the demonstration, those qualities are not considered which
distinguish the idea from others with a like name. In this case the
given idea stands for all others which are known by the same name; the
representative idea is not universal, but serves as such. Thus when I have
demonstrated the proposition, the sum of all the angles of a triangle is
equal to two right angles, for a given triangle, I do not need to prove
it for every triangle thereafter. For not only the color and size of the
triangle are indifferent, but its other peculiarities as well; the question
whether it is right-angled or obtuse-angled, whether it has equal
sides, whether it