best also to use visible ideas only for visible objects and qualities, of which they are the natural representatives, and to denote all other qualities by words considered as arbitrary signs. And yet the representation of other quantities by geometrical ones, and of other ideas by visible ones, is apt to make a more vivid impression upon the fancy, and a more lasting one upon the memory. In similes, fables, parables, allegories, visible ideas are used for this reason to denote general and intellectual ones.
Since words may be compared to the letters used in algebra, language itself may be termed one species of algebra; and, conversely, algebra is nothing more than the language which is peculiarly fitted to explain quantity of all kinds. As the letters, which in algebra stand immediately for quantities, answer to the words which are immediate representatives of ideas, and the algebraic signs for addition, &c. to the particles, so the single letters, which are sometimes used by algebraists to denote sums or differences, powers or roots universal of other letters, for brevity and convenience, answer to such words as have long definitions, to terms of art, &c. which are introduced into the sciences for the sake of compendiousness. Now, if every thing relating to language had something analogous to it in algebra, one might hope to explain the difficulties and perplexities attending the theory of language by the corresponding particulars in algebra, where every thing is clear, and acknowledged by all that have made it their study. However, we have here no independent point whereon to stand, since, if a person be disposed to call the rules of algebra in question, we have no way of demonstrating them to him, but by using words, the things to be explained by algebra for that purpose. If we suppose indeed the sceptical person to allow only that simple language, which is necessary for demonstrating the rules of algebra, the thing would be done; and, as I observed just now, it seems impossible to become acquainted with this, and at the same time to disallow it.
Cor. III. It will easily appear, from the observations here made upon words, and the associations which adhere to them, that the languages of different ages and nations must bear a great general resemblance to each other, and yet have considerable particular differences; whence any one may be translated into any other, so as to convey the same ideas in general, and yet not with perfect precision and exactness. They must resemble one another, because the phænomena of nature, which they are all intended to express, and the uses and exigences of human life, to which they minister, have a general resemblance. But then, as the bodily make and genius of each people, the air, soil, and climate, commerce, arts, sciences, religion, &c. make considerable differences in different ages and nations, it is natural to expect, that the languages should have proportionable differences in respect of each other.
