"Four plus two equals six" (or "is equal to six" or "is six")

Question

You write

4 + 2 = 6

and say "four plus two equals (or is equal to or is) six."

In the question “Is equal to” or “equals”, I read the following comment:

Equals is equal being a verb, in the present tense. Is equal to is equal being a predicate adjective, with its auxiliary verb in the present tense. English is full of pairs like this, useful if one needs an extra syllable. [...] – John Lawler Jun 16 at 16:18

I am thoroughly confused about the bit "Is equal to is equal being a predicate adjective, with its auxiliary verb in the present tense". Is the verb in the present tense the word is? and is to the predicate with the adjective being equal?

Also, does the word is represent a verb in the present tense in the phrase, "four plus two is six"?

Finally, could you please provide another example that is useful if one needs an extra syllable.

Yes, I understand that they all mean the same thing. What I'm looking for is a grammatical syntax analysis with more examples, since, as John Lawler says, "English is full of pairs like this, useful if one needs an extra syllable."

(As an aside, I once read that this symbol "=" is called an "equals sign" in British English and is called an "equal sign" in American English. A related post can be found here.)

Answer 1

If one wants a complete grammatical analysis, one should be prepared for the view that be equal to is a transitive multi-word verb, a single lexeme.

("A lexeme is a unit of lexical meaning, which exists regardless of any inflectional endings it may have or the number of words it may contain. Thus, fibrillate, rain cats and dogs, and come in are all lexemes, as are elephant, jog, cholesterol, happiness, put up with, face the music, and hundreds of thousands of other meaningful items in English. The headwords in a dictionary are all lexemes." (David Crystal, The Cambridge Encyclopedia of the English Language, 2nd ed. Cambridge University Press, 2003) )

The fact that is equal to etc can readily be substituted by equals etc strongly supports the multi-word single-lexeme analysis. It then becomes arguable whether it is helpful to try to analyse within the fixed expression (along the lines: is equal more closely bound to the 'verb' or the 'preposition'? if the 'adjective'-'preposition' binding is tight, is to better analysed as a particle?).

Of course, the verb-form is not invariant: So, the left-hand side must be equal to the right-hand side.

Also, be equal to meaning measure up to (the demands of) is not synonymous with equal:

Do you think he is equal to the task?

*Do you think he equals the task?

Answer 2

The word "equal" has three parts of speech: noun, verb, and adjective.

1. four plus two equals six

   In your first example sentence, "equal" is being used as a verb in the third person singular form: equals.

2. four plus two is equal to six

   In your second example, "equal" is being used as an adjective, and so it needs to employ a linking verb (in this case, "be" or "is") before it. The "to" after it is a preposition.

3. four plus two is six

   Finally, here "is" is again a linking verb in an S + LV + C pattern (Subject + Linking Verb + Complement).

Answer 3

I'm not entirely sure what the question or questions are, but in the sentence X is equal to Y, is is a lexical, not an auxiliary, verb. Equal is an adjective acting as the subject predicative. To Y is a prepositional phrase acting as the complement to equal.

Answer 4

The entire phrase "is equal to" is a predicate, not any part of it. A predicate describes a relationship between two things; in this case, that the first thing ("4 + 2") is related to the second thing ("6") by the first being equal to the second. A predicate describes a static truth, while a verb describes (loosely speaking) an action in progress.

Math makes this distinction especially confusing because math uses practical language to describe abstractions. An example that makes the difference clearer is:

(1) George tends the garden.
(2) George is the tender of the garden.

(1) describes something George does, while (2) describes something George is.

Answer 5

(bold means a verb, italic means a noun, parentheses mean a prepositional phrase, strikethrough means an adjective).

"Four (plus two) is equal (to six)" N-LV-A
"Four (plus two) is six." N-LV-N
"Four (plus two) equals six". N-LV-N

In the first sentence, "is" is a linking verb or copula. Here "equal" is an adjective, and the predicate of the sentence. The word "six" is the object of the prepositional phrase "to six", which functions as an adverb, modifying the word "equal".

In the second sentence, "is" is still a linking verb, but instead of an adjective, "six" is now the predicate of the sentence, which circumvents the necessity for a prepositional phrase.

Finally, the third sentence does not use "is" at all, but instead uses "equals" as its linking verb. It is more or less identical to the second sentence, but replaces "is" with a more colorful, more descriptive linking verb.

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As a somewhat loose follower of the E-Prime philosophy--which in its strictest form mandates the omission of the verb "to be" and all of its conjugations--I would be most inclined to use sentence 3. A quote from the Wikipedia article on the use of "equals" rather than "is":

Replacing statements including "to be" with those using becomes, remains and equals divides perception of, and expressions about, time more operationally into actual cognitive categories that humans know how to act upon.

To claim that one thing equals another is a claim only about the present with no reference to the future or the past—it can be disproved by direct testing.

Answer 6

Finally, could you please provide another example that is useful if one needs an extra syllable?

Well, it’s actually two syllables –– len(“is equal to”)–len(“equals”) = 4–2 = 2.

An example:

Two bees or not two bees, that is the question;
        To risk a sting to get their sweet confection;
But do not add a dozen to the scene;
        As twelve plus two is equal to fourteen.

Nonsense?  You bet it’s nonsense.  But most modern poetry is –– am I right?