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 since the mind can neither voluntarily originate them (_e.g._, cannot produce sensations of color in the dark) nor avoid having them at will, but only receive them from without, they are not creatures of the fancy, but the natural and regular productions of external things affecting us. In regard to the latter, the ideas of substances, we may be certain at least when the simple ideas which compose them have been found so connected in experience. Perception has an external cause, whose influence the mind is not able to withstand. The mutual corroboration furnished by the reports of the different senses, the painfulness of certain sensations, the clear distinction between ideas from actual perception and those from memory, the possibility of producing and predicting new sensations of an entirely definite nature in ourselves and