Hence it is that no process of argument is so perfect, as that which is conducted by means of symbols. In Arithmetic 1 is 1, and just 1, and never anything else but 1; it never is 2, it has no tendency to change its meaning, and to become 2; it has no portion, quality, admixture of 2 in its meaning. And 6 under all circumstances is 3 times 2, and the sum of 2 and 4; nor can the whole world supply anything to throw doubt upon these elementary positions. It is not so with language. Take, by contrast, the word “inference,” which I have been using: it may stand for the act of inferring, as I have used it; or for the connecting principle, or _inferentia_, between premisses and conclusions; or for the conclusion itself. And sometimes it will be difficult, in a particular sentence, to say which it bears of these three senses. And so again in Algebra, _a_ is never _x_, or anything but _a_, wherever it is found; and _a_ and _b_ are always standard quantities, to which _x_ and _y_ are always to be referred, and by which they are always to be measured. In Geometry again, the subjects of argument, points, lines, and surfaces, are precise creations of the mind, suggested indeed by external objects, but meaning nothing but what they are defined to mean: they have no colour, no motion, no heat, no qualities which address themselves to the ear or to the palate; so that, in whatever combinations or relations the words denoting them occur, and to whomsoever they come, those words never vary in their meaning, but are just of the same measure and weight at one time and at another. What is true of Arithmetic, Algebra, and Geometry, is true also of Aristotelic argumentation in its typical modes and figures. It compares two given words separately with a third, and then determines how they stand towards each other, in a _bona fide_ identity of sense. In consequence, its formal process is best conducted by means of symbols, A, B, and C. While it keeps to these, it is safe; it has the cogency of mathematical reasoning, and draws its conclusions by a rule as unerring as it is blind.