has equal or unequal angles, is not mentioned in the
demonstration, and has no influence upon it. _Abstracta_ exist only in this
sense. In considering the individual Paul I can attend exclusively to those
characteristics which he has in common with all men or with all living
beings, but it is impossible for me to represent this complex of common
qualities apart from his individual peculiarities. Self-observation shows
that we have no general concepts; reason, that we can have none, for the
combination of opposite elements in one idea would be a contradiction in
terms. Motion in general, neither swift nor slow, extension in general,
at once great and small, abstract matter without sensuous
determinations--these can neither exist nor be perceived.

[Footnote 1: Against the Berkeleyan denial of abstract notions the popular
philosopher, Joh. Jak. Engel, directed an essay, _Ueber die Realitaet
allgemeiner Begriffe_ (Engel's _Schriften_, vol. x.), to which attention
has been called by O. Liebmann, _Analysis tier Wirklichkeit_, 2d ed., p.
473.]

The "materialistic" hypothesis--so Berkeley terms the assumption that a
material world exists apart from perceiving mind, and independently of
being perceived--is, first, unnecessary, for the facts which it is to
explain can be explained as well, or even better, without it; and, second,
false, since it is a contradiction to suppose that an object can exist
unperceived, and that a sensation or idea is the copy of anything itself
not a sensation or idea. Ideas are the only objects of the understanding.
Sensible qualities (white, sweet) are subjective states of the soul; sense
objects (sugar), sensation-complexes. If sensations need a substantial
support, this is the soul which perceives them, not an external thing which
can neither perceive nor be perceived. Single ideas, and those combined
into objects, can exist nowhere else than in the mind; the being of sense
objects consists in their being perceived (_esse est percipi_). I see light
and feel heat, and combine these sensations of sight and touch into the
substance fire, because I know from experience that they constantly
accompany and suggest each other.[1] The assumption of an "object" apart
from the idea is as useless as its existence would be. Why should God
create a world of real things without the mind, when these can neither
enter into the mind, nor (because unperceived) be copied by its ideas, nor
(because they themselves lac