whichever is/are the higher

Hi, Raymond,

@raymondaliasapollyon posted:

Pensions should be increased annually in line with earnings or prices, whichever is/are the higher.

I think that both are correct. However, the singular seems to be more usual. The plural form will be required when the preceding nouns are at a higher syntactic level (being object to a preposition is not high enough in the syntactic hierarchy). See, for example, these examples I found on the Internet (there are many similar ones):

- [The objectives are] To minimize order costs or carrying costs, whichever are higher. ("order costs or carrying costs" is the direct object)
- Individual access rights of the user or universal access rights (whichever are higher) are granted. ("Individual access rights ... universal access rights" is the subject)

Being inside an adjunct of manner, "earnings" and "prices" are somewhat hidden for "whichever (are) higher" to refer directly to them. Instead, "whichever is higher" refers more clearly to the idea of the annual increase of pensions being smaller or larger depending on whether earnings or prices are taken as a basis for their calculation (the increase to be established will be the larger one). "Is" would then refer to the result of applying one or another variable. Therefore, I see that "whichever" as a sentential relative.

@raymondaliasapollyon posted:

In the following sentence, which verb form is okay?

Pensions should be increased annually in line with earnings or prices, whichever is/are the higher.

Hi, Ray and Gustavo—Well, this has been a head-scratcher for me. My first inclination was to pounce on the use of "the" in "the higher" as unidiomatic in that construction. But I now see that Ray's use of "the higher" offers convenient rationale for using the singular verb ("is"). The "whichever" clause may be said to involve inversion and to take the noun phrase "the higher" as subject.

whichever is the higher = whichever the higher is
"Pensions should be increased annually in line with earnings or prices, whichever the higher is."

As to the relationship of the "whichever"-clause to the rest of the sentence, I find Gustavo's sentential-relative analysis interesting. I myself incline towards analyzing it as being in apposition to the disjunction, "earnings or prices." I take their reversibility to be an indicator of apposition:

• Pensions should be increased annually in line with whichever is the higher, earnings or prices.

In case anyone reading this enjoys (and can follow) a Reed–Kellogg diagram, which I think may be more intuitively pleasing than a syntax tree in a case like this, I have diagrammed my parsing below.

To justify the apposition, I will borrow two concepts from formal syntax. The first is that the "whichever"-clause has the status of an NP. The second is that the phrasal node comprising the coördination of NPs (or DPs) is itself an NP.

Thus, the higher NP of the coördinate structure could stand in apposition to a noun phrase outside the coördinate structure, even one realized by a "whichever"-clause.

@David, Moderator posted:

I myself incline towards analyzing it as being in apposition to the disjunction, "earnings or prices." I take their reversibility to be an indicator of apposition:

• Pensions should be increased annually in line with whichever is the higher, earnings or prices.

Yes, that sounds very reasonable. In this case, the singular would be justified by the fact that one variable is earnings, and the other variable is prices: ... in line with whichever is the higher between these two variables: earnings or prices.

Thank you, David and Gustavo.

Is the following okay, with "the" removed from the comparative?

Pensions should be increased annually in line with earnings or prices, whichever is higher.

@raymondaliasapollyon posted:

Pensions should be increased annually in line with earnings or prices, whichever is higher.

Yes, that is correct. Actually, the absence of the article is much more usual than its presence. From Ngram Viewer:

Like Gustavo, I favor the singular verb, whether or not "the" is used. I would argue that the singular is superior from a semantic standpoint. My argument works in tandem with Gustavo's analysis in terms of variables.

Building upon the apposition analysis I gave above, I would say that "whichever is higher" is the properly the first term of the appositive pair: "They should be increased in line with whichever is higher, earnings or prices."

I don't mean to say that "whichever is higher" is improperly placed when placed at the end—only that the appositive should be understood as if it preceded "earnings or prices."

It is NOT that pensions should be increased in line with earnings or prices regardless of whether earnings or pensions are higher. The "whichever"-clause does NOT mean "It doesn't matter whether earnings or prices are higher."

The meaning is that pensions should be increased annually in line with the higher of two variables—earnings or prices. They should be increased in line with the higher one, and it can't be stated in advance what that higher one is.

In sum, I think (a) both the singular verb and the plural verb are syntactically defensible, (b) the meaning is different in each case, and (c) the meaning with the singular is the meaning that would be intended in a normal context.

@Gustavo, Co-Moderator posted:

Hi, Raymond,

I think that both are correct. However, the singular seems to be more usual. The plural form will be required when the preceding nouns are at a higher syntactic level (being object to a preposition is not high enough in the syntactic hierarchy).

Does the following sentence call for "are"?

John will bring cookies or chocolates, whichever are/is more popular with the kids.

@raymondaliasapollyon posted:

Does the following sentence call for "are"?

John will bring cookies or chocolates, whichever are/is more popular with the kids.

Both "are" and "is" are possible there, but each, technically, has a different meaning. With "are," the meaning is that John will bring cookies or chocolates regardless of whether cookies or chocolates are more popular with the kids. With "is," the meaning is that John will bring that which, between cookies and chocolates, is more popular with the kids. See the analysis in my last post.

Thank you, David, for that interesting difference.

I've found the following sentence, and I'm wondering how an apposition-based analysis could handle it.

@raymondaliasapollyon posted:

Thank you, David, for that interesting difference.

Indeed!

Curiously, we can also have this altogether different sentence if we change the position of "whichever":

- John will bring whichever cookies or chocolates are more popular with the kids. (Meaning: those cookies or chocolates which are more popular among kids.)

@raymondaliasapollyon posted:

You may leave at 4:00 or when you've finished the job, whichever comes first.

I think a possible, albeit awkward, paraphrase would be:

- You may leave at whichever time comes first, 4:00 or when you've finished the job.

@Gustavo, Co-Moderator posted:

I think a possible, albeit awkward, paraphrase would be:

- You may leave at whichever time comes first, 4:00 or when you've finished the job.

Thank you, Gustavo, for providing the paraphrase.

I see "whichever time comes first" can serve as the object of the preposition "at." The same goes for "4:00."  This is expected of elements standing in apposition.

But "when you've finished the job" is different. Can it be the object of "at"?

?  You may leave at when you've finished the job.

@raymondaliasapollyon posted:

But "when you've finished the job" is different. Can it be the object of "at"?

?  You may leave at when you've finished the job.

No, it cannot. However, "when" can be understood as "at the time at which" (please note that this is not idiomatic but is merely provided for you to understand the appositive value of the "whichever"-clause by applying the test David cleverly suggested):

- You may leave at 4:00 or when you've finished the job, whichever comes first ⇒ You may leave at whichever time comes first, at 4:00 or at the time at which you've finished the job.

Thank you, Gustavo, for your paraphrase. The analysis, along with the paraphrase, requires treating the adverbials (a prepositional phrase and a subordinate clause like the when-clause) as standing in apposition, a reasonable assumption in itself.

How do we analyze the following sentence under the apposition-based approach?

Yes, we'll have to use a "light" verb:

- We will gladly do whichever you prefer, exchange your goods or refund your money.

I think an apposition-based analysis helps us gain an understanding of the meaning of the said construction. The remaining issue is that the analysis of cases invovling verb phrases and prepositions and conjucntions is not so straightforward as of noun phrases, with additional elements having to be inserted.  Still, it suffices for practical and pedagogical purposes.