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 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.