ABSTRACT
Ability to perceive equality implies a correlative ability to perceive inequality: neither can exist without the other. But though inseparable in origin, the cognitions of equality and inequality, whether between things or relations, altogether differ in this; that whilst the one is essentially definite, the other is essentially indefinite. Incidentally, simple quantitative reasoning has been to a considerable extent treated of in the course of the foregoing analyses. The species of intuition serving to establish the equality of the successive forms of an equation— a species of intuition by which are recognized the general truths that the sums of equals are equal; that the differences of equals are equal; that if equals be multiplied by equals the products are equal, and if divided by equals the quotients are equal— is also accompanied by a converse species of intuition, in which the fact recognized is the inequality of two relations.
