l qualities, sufficiently fulfill their divinely
ordained end, to serve us as instruments of knowledge, _i.e._, in the
discrimination of things.--An unreal and inadequate idea becomes false only
when it is referred to an object, whether this be the existence of a thing,
or its true essence, or an idea of other things. Truth and error belong
always to affirmations or negations, that is, to (it may be, tacit)
propositions. Ideas uncombined, unrelated, apart from judgments, ideas,
that is, as mere phenomena in the mind, are neither true nor false.

Knowledge is defined as the "perception of the connexion and agreement, or
disagreement and repugnancy" of two ideas; truth, as "the right joining or
separating of signs, _i.e._, ideas or words." The object of knowledge
is neither single ideas nor the relations of ideas to things, but the
_relations of ideas among themselves_. This view was at once paradoxical
and pregnant. If all cognition, as Locke suggests in objection to his own
theory, consists in perceiving the agreement or disagreement of our ideas,
are not the visions of the enthusiast and the reasonings of sober thinkers
alike certain? are not the propositions, A fairy is not a centaur, and a
centaur is a living being, just as true as that a circle is not a triangle,
and that the sum of the angles of a triangle is equal to two right angles?
The mind directly perceives nothing but its own ideas, but it seeks a
knowledge of things! If this is possible it can only be indirect
knowledge--the mind knows things through its ideas, and possesses criteria
which show that its ideas agree with things.

Two cases must be clearly distinguished, for a considerable number of our
ideas, viz., all complex ideas except those of substances, make no claim
to represent things, and consequently cannot represent them falsely. For
mathematical and moral ideas and principles, and the truth thereof, it is
entirely immaterial whether things and conditions correspondent to them
exist in nature or not. They are valid, even if nowhere actualized; they
are "eternal truths," not in the sense that they are known from childhood,
but in the sense that, as soon as known, they are immediately assented
to.[1] The case is different, however, with simple ideas and the ideas of
substances, which have their originals without the mind and which are to
correspond with these. In regard to the former we may always be certain
that they agree with real things, for sin