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.