The Grammar of English Grammars

by Goold Brown

OBS. 15.—Most of the foregoing expressions, though all are perhaps intelligible enough in common practice, are, in some respect, difficult of analysis, or grammatical resolution. I think it possible, however, to frame an argument of some plausibility in favour of every one of them. Yet it is hardly to be supposed, that any teacher will judge them all to be alike justifiable, or feel no interest in the questions which have been raised about them. That the language of arithmetic is often defective or questionable in respect to grammar, may be seen not only in many an ill choice between the foregoing variant and contrasted modes of expression, but in sundry other examples, of a somewhat similar character, for which it may be less easy to find advocates and published arguments. What critic will not judge the following phraseology to be faulty? "4 times two units is 8 units, and 4 times 5 tens is twenty tens."—Chase's Common School Arithmetic, 1848, p. 42. Or this? "1 time 1 is l. 2 times 1 are 2; 1 time 4 is 4, 2 times 4 are 8."—Ray's Arithmetic, 1853. Or this? "8 and 7 is 15, 9's out leaves 6; 3 and 8 is 11, 9's out leaves 2."—Babcock's Practical Arithmetic, 1829, p. 22. Or this again? "3 times 3 is 9, and 2 we had to carry is 11."—Ib., p. 20.

OBS. 16.—There are several different opinions as to what constitutes the grammatical subject of the verb in any ordinary English expression of multiplication. Besides this, we have some variety in the phraseology which precedes the verb; so that it is by no means certain, either that the multiplying terms are always of the same part of speech, or that the true nominative to the verb is not essentially different in different examples. Some absurdly teach, that an abstract number is necessarily expressed by "a singular noun," with only a singular meaning; that such a number, when multiplied, is always, of itself the subject of the assertion; and, consequently, that the verb must be singular, as agreeing only with this "singular noun." Others, not knowing how to parse separately the multiplying word or words and the number multiplied, take them both or all together as "the grammatical subject" with which the verb must agree. But, among these latter expounders, there are two opposite opinions on the very essential point, whether this "entire expression" requires a singular verb or a plural one:—as, whether we ought to say, "Twice one is two," or, "Twice one are two;"—"Twice two is four," or, "Twice two are four;"—"Three times one is three," or, "Three times one are three;"—"Three times three is nine," or, "Three times three are nine." Others, again, according to Dr. Bullions, and possibly according to their own notion, find the grammatical subject, sometimes, if not generally, in the multiplying term only; as, perhaps, is the case with those who write or speak as follows: "If we say, 'Three times one are three,' we make 'times' the subject of the verb."—Bullions, Analyt. and Pract. Gram., 1849, p. 39. "Thus, 2 times 1 are 2; 2 times 2 are four; 2 times 3 are 6."—Chase's C. S. Arith., p. 43. "Say, 2 times O are O; 2 times 1 are 2."—Robinson's American Arith., 1825, p. 24.

OBS. 17.—Dr. Bullions, with a strange blunder of some sort in almost every sentence, propounds and defends his opinion on this subject thus: "Numeral adjectives, being also names of numbers, are often used as nouns, and so have the inflection and construction of nouns: thus, by twos, by tens, by fifties. Two is an even number. Twice two is four. Four is equal to twice two. In some arithmetics the language employed in the operation of multiplying—such as 'Twice two are four, twice three are six'—is incorrect. It should be, 'Twice two is four,' &c.; for the word two is used as a singular noun—the name of a number. The adverb 'twice' is not in construction with it, and consequently does not make it plural. The meaning is, 'The number two taken twice is equal to four.' For the same reason we should say, 'Three times two is six,' because the meaning is, 'Two taken three times is six.' If we say, 'Three times one are three,' we make 'times' the subject of the verb, whereas the subject of the verb really is 'one,' and 'times' is in the objective of number (§828). 2:4:: 6:12, should be read, 'As 2 is to 4, so is 6 to 12;' not 'As two are to four, so are six to twelve.' But when numerals denoting more than one, are used as adjectives, with a substantive expressed or understood, they must have a plural construction."—Bullions, Analyt. and Pract. Gram., 1849, p. 39.

OBS. 18.—Since nouns and adjectives are different parts of speech, the suggestion, that, "Numeral adjectives are also names, or nouns," is, upon the very face of it, a flat absurdity; and the notion that "the name of a number" above unity, conveys only and always the idea of unity, like an ordinary "singular noun," is an other. A number in arithmetic is most commonly an adjective in grammar; and it is always, in form, an expression that tells how many, or—"denotes how many things are spoken of."—Chase, p. 11. But the name of a number is also a number, whenever it is not made plural in form. Thus four is a number, but fours is not; so ten is a number, but tens is not. Arithmetical numbers, which run on to infinity, severally consist of a definite idea of how many; each is a precise count by the unit; one being the beginning of the series, and the measure of every successive step. Grammatical numbers are only the verbal forms which distinguish one thing from more of the same sort. Thus the word fours or tens, unless some arithmetical number be prefixed to it, signifies nothing but a mere plurality which repeats indefinitely the collective idea of four or ten.

OBS. 19.—All actual names of numbers calculative, except one, (for naught, though it fills a place among numbers, is, in itself, a mere negation of number; and such terms as oneness, unity, duality, are not used in calculation,) are collective nouns—a circumstance which seems to make the discussion of the present topic appropriate to the location which is here given it under Rule 15th. Each of them denotes a particular aggregate of units. And if each, as signifying one whole, may convey the idea of unity, and take a singular verb; each, again, as denoting so many units, may quite as naturally take a plural verb, and be made to convey the idea of plurality. For the mere abstractness of numbers, or their separation from all "particular objects," by no means obliges us to limit them always to the construction with verbs singular. If it is right to say, "Two is an even number;" it is certainly no error to say, "Two are an even number." If it is allowable to say, "As 2 is to 4, so is 6 to 12;" it is as well, if not better, to say, "As two are to four, so are six to twelve." If it is correct to say, "Four is equal to twice two;" it is quite as grammatical to say, "Four are equal to twice two." Bullions bids say, "Twice two is four," and, "Three times two is six;" but I very much prefer to say, "Twice two are four," and, "Three times two are six." The Doctor's reasoning, whereby he condemns the latter phraseology, is founded only upon false assumptions. This I expect to show; and more—that the word which he prefers, is wrong.

OBS. 20.—As to what constitutes the subject of the verb in multiplication, I have already noticed three different opinions. There are yet three or four more, which must not be overlooked in a general examination of this grammatical dispute. Dr. Bullions's notion on this point, is stated with so little consistency, that one can hardly say what it is. At first, he seems to find his nominative in the multiplicand, "used as a singular noun;" but, when he ponders a little on the text, "Twice two is four," he finds the leading term not to be the word "two," but the word "number," understood. He resolves, indeed, that no one of the four words used, "is in construction with" any of the rest; for he thinks, "The meaning is, 'The number two taken twice is equal to four.'" Here, then, is a fourth opinion in relation to the subject of the verb: it must be "number" understood. Again, it is conceded by the same hand, that, "When numerals denoting more than one, are used as adjectives, with a substantive expressed or understood, they must have a plural construction." Now who can show that this is not the case in general with the numerals of multiplication? To explain the syntax of "Twice two are four," what can be more rational than to say, "The sense is, 'Twice two units, or things, are four?'" Is it not plain, that twice two things, of any sort, are four things of that same sort, and only so? Twice two duads are how many? Answer: Four duads, or eight units. Here, then, is a fifth opinion,—and a very fair one too,—according to which we have for the subject of the verb, not "two" nor "twice" nor "twice two," nor "number," understood before "two," but the plural noun "units" or "things" implied in or after the multiplicand.

OBS. 21.—It is a doctrine taught by sundry grammarians, and to some extent true, that a neuter verb between two nominatives "may agree with either of them." (See Note 5th to Rule 14th, and the footnote.) When, therefore, a person who knows this, meets with such examples as, "Twice one are two;"—"Twice one unit are two units;"—"Thrice one are three;"—he will of course be apt to refer the verb to the nominative which follows it, rather than to that which precedes it; taking the meaning to be, "Two are twice one;"—"Two units are twice one unit;"—"Three are thrice one." Now, if such is the sense, the construction in each of these instances is right, because it accords with such sense; the interpretation is right also, because it is the only one adapted to such a construction; and we have, concerning the subject of the verb, a sixth opinion,—a very proper one too,—that it is found, not where it is most natural to look for it, in the expression of the factors, but in a noun which is either uttered or implied in the product. But, no doubt, it is better to avoid this construction, by using such a verb as may be said to agree with the number multiplied. Again, and lastly, there may be, touching all such cases as, "Twice one are two," a seventh opinion, that the subject of the verb is the product taken substantively, and not as a numeral adjective. This idea, or the more comprehensive one, that all abstract numbers are nouns substantive, settles nothing concerning the main question, What form of the verb is required by an abstract number above unity? If the number be supposed an adjective, referring to the implied term units, or things, the verb must of course be plural; but if it be called a collective noun, the verb only follows and fixes "the idea of plurality," or "the idea of unity," as the writer or speaker chooses to adopt the one or the other.

OBS. 22.—It is marvellous, that four or five monosyllables, uttered together in a common simple sentence, could give rise to all this diversity of opinion concerning the subject of the verb; but, after all, the chief difficulty presented by the phraseology of multiplication, is that of ascertaining, not "the grammatical subject of the verb," but the grammatical relation between the multiplier and the multiplicand—the true way of parsing the terms once, twice, three times, &c., but especially the word times. That there must be some such relation, is obvious; but what is it? and how is it to be known? To most persons, undoubtedly, "Twice two," and, "Three times two," seem to be regular phrases, in which the words cannot lack syntactical connexion; yet Dr. Bullions, who is great authority with some thinkers, denies all immediate or direct relation between the word "two," and the term before it, preferring to parse both "twice" and "three times" as adjuncts to the participle "taken," understood. He says, "The adverb 'twice' is not in construction with 'two,' and consequently does not make it plural." His first assertion here is, in my opinion, untrue; and the second implies the very erroneous doctrine, that the word twice, if it relate to a singular term, will "make it plural." From a misconception like this, it probably is, that some who ought to be very accurate in speech, are afraid to say, "Twice one is two," or, "Thrice one is three," judging the singular verb to be wrong; and some there are who think, that "usage will not permit" a careful scholar so to speak. Now, analysis favours the singular form here; and it is contrary to a plain principle of General Grammar, to suppose that a plural verb can be demanded by any phrase which is made collectively the subject of the assertion. (See Note 3d, and Obs. 13th, 14th, 15th, and 16th, under Rule 14th.) Are is, therefore, not required here; and, if allowable, it is so only on the supposition that the leading nominative is put after it.

OBS. 23.—In Blanchard's small Arithmetic, published in 1854, the following inculcations occur: "When we say, 3 times 4 trees are 12 trees, we have reference to the objects counted; but in saying 3 times 4 is twelve, we mean, that 3 times the number 4, is the number 12. Here we use 4 and 12, not as numeral adjectives, but as nouns, the names of particular numbers, and as such, each conveys the idea of unity, and the entire expression is the subject of is, and conveys the idea of unity."—P. iv. Here we have, with an additional error concerning "the entire expression," a repetition of Dr. Bullions's erroneous assumption, that the name of a particular number, as being "a singular noun," must "convey the idea of unity," though the number itself be a distinct plurality. These men talk as if there were an absurdity in affirming that "the number 4" is plural! But, if four be taken as only one thing, how can three multiply this one thing into twelve? It is by no means proper to affirm, that, "Every four, taken three times, is, or are, twelve;" for three instances, or "times," of the figure 4, or of the word four, are only three 4's, or three verbal fours. And is it not because "the number 4" is plural—is in itself four units—and because the word four, or the figure 4, conveys explicitly the idea of this plurality, that the multiplication table is true, where it says, "3 times 4 are 12?" It is not right to say, "Three times one quaternion is twelve;" nor is it quite unobjectionable to say, with Blanchard "3 times the number 4, is the number 12." Besides, this pretended interpretation explains nothing. The syntax of the shorter text, "3 times 4 is 12," is in no way justified or illustrated by it. Who does not perceive that the four here spoken of must be four units, or four things of some sort; and that no such "four," multiplied by 3, or till "3 times," can "convey the idea of unity," or match a singular verb? Dr. Webster did not so conceive of this "abstract number," or of "the entire expression" in which it is multiplied; for he says, "Four times four amount to sixteen."—American Dict., w. Time.

OBS. 24.—In fact no phrase of multiplication is of such a nature that it can, with any plausibility be reckoned a composite subject of the verb. Once, twice, and thrice, are adverbs; and each of them may, in general, be parsed as relating directly to the multiplicand. Their construction, as well as that of the plural verb, is agreeable to the Latin norm; as, when Cicero says of somebody, "Si, bis bina quot essent, didicisset,"—"If he had learned how many twice two are."—See Ainsworth's Dict., w. Binus. The phrases, "one time," for once, and "two times" for twice, seem puerile expressions: they are not often used by competent teachers. Thrice is a good word, but more elegant than popular. Above twice, we use the phrases, three times, four times, and the like, which are severally composed of a numeral adjective and the noun times. If these words were united, as some think they ought to be, the compounds would be adverbs of time repeated; as, threetimes, fourtimes, &c., analogous to sometimes. Each word would answer, as each phrase now does, to the question, How often? These expressions are taken by some as having a direct adverbial relation to the terms which they qualify; but they are perhaps most commonly explained as being dependent on some preposition understood. See Obs. 1st on Rule 5th, and Obs. 6th on Rule 7th.