That the Predications of Geometry are of the same nature with those of Arithmetic, is a truth of the greatest importance, and capable of being established by very obvious reasoning. It is well known, that all reasoning about quantity can be expressed in the form of algebraic equations. But the two sides of an algebraic equation are of necessity two marks or two names for the same thing; of which the one on the right-hand side is more distinct, at least to the present purpose of the inquirer, than the one on the left-hand side; and the whole purpose of an algebraic investigation, which is a mere series of changes of names, is to obtain, at last, a distinct name, a name the marking power of which is perfectly known to us, on the right-hand side of the equation. The language of geometry 191 itself, in the more simple cases, makes manifest the same observation. The amount of the three angles of a triangle, is twice a right angle. I arrive at this conclusion, as it is called, by a process of reasoning: that is to say, I find out a name “twice a right angle,” which much more distinctly points out to me a certain quantity, than my first name, “amount of the three angles of a triangle;” and the process by which I arrive at this name is a successive change of names, and nothing more; as any one may prove to himself by merely observing the steps of the demonstration.[57]
[57] I cannot see any propriety in the expression that when we infer the sum of the three angles of a triangle to be twice a right angle, the operation consists in finding a second name which more distinctly points out the quantity than the first name. When we assent to the proof of this theorem, we do much more than obtain a new and more expressive name for a known fact; we learn a fact previously unknown. It is true that one result of our knowledge of this theorem is to give us a name for the sum of the three angles, “the marking power of which is perfectly known to us:” but it was not for want of knowing the marking power of the phrase “sum of the three angles of a triangle” that we did not know what that sum amounted to. We knew perfectly what the expression “sum of the three angles” was appointed to mark. What we have obtained, that we did not previously possess, is not a better mark for the same thing, but an additional fact to mark the fact which is marked by predicating of that sum, the phrase “twice a right angle.”—Ed.
There is one important class of words, the NAMES of NAMES; of which we shall have occasion to take account more particularly [hereafter], and of which it is necessary here to speak only as they form a variety of Predication. A few examples will make the case 192 intelligible. WORD is a generical name for all Names. It is not the name of a Thing, as chair is the name of a thing, or watch, or picture. But word is a name for these several names; chair is a word, watch is a word, picture is a word, and so of all other names. Thus grammatical and logical terms are names of names. The word noun, is the name of one class of words, verb of another, preposition of another, and so on. The word sentence, is the name of a series of words put together for a certain purpose; the word paragraph the same; and so oration, discourse, essay, treatise, &c. The words genus and species, are not names of things, but of names. Genus is not the name of any thing called animal or any thing called body; it is a name of the names animal, body, and so on; the name animal is a genus, the name body is a genus; and in like manner is the name man a species, the name horse, the name crow, and so on. The name proposition, the name syllogism, are names of a series of words put together for a particular purpose; and so is the term definition; and the term argument. It will be easily seen that these words enter into Predication precisely on the same principles as other words. Either the more distinct is predicated of the less distinct, its equivalent; or the more comprehensive of the less comprehensive. Thus we say, that nouns and verbs are declinables; preposition and adverb indeclinables; where the more comprehensive terms are predicated of the less. Thus we say, that adjectives and verbs are attributes; where the more distinct is predicated of the less.[58]
[58] This exposition of the class of words which are properly names of names, belongs originally to Hobbes, and is highly 193 important. They are a kind of names, the signification of which is very often misunderstood, and has given occasion to much hazy speculation. It should however be remarked that the words genus and species are not solely names of names; they are ambiguous. A genus never indeed means (as many of the schoolmen supposed) an abstract entity, distinct from all the individuals composing the class; but it often means the sum of those individuals taken collectively; the class as a whole, distinguished on the one hand from the single objects comprising it, and on the other hand from the class name.—Ed.
SECTION V.
PRONOUNS.
The principal part of the artifice of Naming is now explained. We have considered the nature of the more necessary marks, and the manner in which they are combined so as to represent the order of a train. Beside those marks, which are the fundamental part of language, there are several classes of auxiliary words or marks, the use of which is, to abbreviate expression, and to render it, what is of great importance, a more rapid vehicle of thought. These are usually comprehended under the titles of pronoun, adverb, preposition, and conjunction; a classification which, for our present purpose, has the best recommendation, that of being familiarly known.
It is to be distinctly understood, that in the account which is here to be given of the subsidiary parts of speech, it is but one part of the explanation of them which will be attempted. The ideas, which many of them stand for, are of the most complicated kind, and have not yet been expounded. We are, therefore, not yet prepared to point out the items which they mark. Our present business is only to indicate the mode in which they are used in Predication, as part of the great contrivance for marking the order of a train of ideas, and for economizing the number of words.
It is also necessary to observe, that I have limited myself, in this part, to brief indications, without 195 going into minute development, the length of which, it appeared to me, would not be compensated by the advantage.