Subject/Complement Agreement. How to describe problem with "The thing is the objects."

Question

In https://ell.stackexchange.com/questions/29140/is-or-are-the-only-thing-that-i-want-you-to-hit-right-now-is-are-the-books/29170#29170, I provided the following, problematic, wording (especially bold italic), and I need help to better understand this issue so I can fix my answer:¹

The thing is the books. (Reduced form of Sentence 2.a)

Fundamentally, Sentence 2.a (the so-called "correct" answer), is grammatically defective. Recall there is another grammatical rule: the subject and subject's complement should match in number. The reduced sentence makes the disagreement between the subject's and complement's plurality obvious. What is one to do? Language is linear and we know "The thing is X" is better than "The thing are X", so we go with the former, which is the subject-verb agreement rule. But what is "the books" then? It must be thought of as a collective noun, even if it doesn't look or feel like one. Forcing something to be a collective noun is related to the idea of notional agreement.

Others noted that grammatically defective is too strongly worded. There is no such "grammatical rule" for subject/complement agreement. Please help me understand/improve upon my line of thought here. I'm stating that Sentence 2.1 presents a fundamental "conflict" or "error" (however one might define error) at some level (morphological, syntax, grammatical, semantic):

The thing is the books. (Or, "The thing is the objects.")

Based on the "obvious" morphosyntactic plurality conflict, the above sentence feels so wrong that I think many native speakers would think it "simply" grammatically incorrect. However, @F.E. gives counter examples:

And here are some more grammatical examples, where the number of subject and predicative complement don't agree: "They were a problem to us all", "That so-called work of art is simply four pieces of driftwood glued together" (CGEL, page 254-5). As CGEL says: "What is required is semantic compatibility, not syntactic agreement . . .". There are more examples on page 512: "The only thing we need now is some new curtains", "The major asset of the team is its world-class opening bowlers", "Our neighbors are a nuisance", "This gadget is five different tools in one".

I think all the examples given above can be explained as notional agreement.

Question 1: If we explain this phenomena in terms of notional vs syntactic agreement, where does "grammatically correct/incorrect" fit in?

Question 2: Can a simple sentence such as "The thing is the objects." be grammatically incorrect while more complex sentences such as "The thing is four pieces of driftwood glued together." be grammatically correct? (The answer, in my mind, must be no; this is my conundrum.)

Question 3: Would it be better to say that Sentence 2.a has a low level of (linguistic) grammaticality?

Question 4: How about a low level of gradient well-formedness and that it's semantically difficult to be (linguistically) acceptable?

Question 5: Do we simply draw a hard line and say "The thing is the objects." is 100% grammatically correct? I didn't particularly like this option based on intuitive notions of "grammatically correct".

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^{1. Please help me and be kind; I'm trying to improve my understanding. I'm looking for cool, objective advice on how to look at this.}

^{I numbered my questions so they can be easily referenced, if desired. My preference is the final answer would sufficiently answer all the questions, but of course that can be done explicitly or implicitly.}

Answer 1

The question addresses an aspect of English syntax that is still somewhat in flux. The mechanism known as copular inversion should be part of the answer.

The direct answer to the question(s) is that acceptability judgments exist on a cline. There is more than one principle that influences the choice of subject. When these principles conflict, acceptability is degraded to a greater or lesser degree. Consider the following datum from German:

 Was wir brauchen sind/*ist neue Vorhaenge.
 'What we need are/*is new curtains'

In German, plural generally trumps singular when it comes to choosing the subject. Thus in this example, neue Vorhange 'new curtains' is indisputably the subject of the sentence, a fact that makes was wir brauchen 'what we need' the predicative NP. A related observation occurs in the following case:

 Der Klempner bin/*ist ich.
 'The plumber am/*is I.'

The first person pronoun ich is indisputably the subject in this sentence. First person pronouns trump third person NPs when it comes to choosing the subject (second person pronouns also trump third person NPs).

English cannot rely on morphological markers to identify the subject, since it lacks the inflectional richness of German (and many other languages). English relies much on word order instead. There is thus a very strong tendency to take the NP that immediately precedes the finite verb to be the subject, regardless of the factors that influence subject choice in a language like German (singular vs. plural, first or second person vs. third person, definiteness). But English and German are closely related, which means the principles of subject choice in German are not entirely dead in English; they survive in a weakened state and are influencing our sense of acceptability. They are responsible for the awkwardness of the sentence

 The problem is the books.

In German, subject-verb agreement for a sentence like this obtains with the plural NP:

 Das Problem sind/*ist die Buecher.
 'The problem are/*is the books.'

Another factor that is influencing how these sentences are interpreted is the mechanism of copular inversion. Consider the following sentences:

 1a. The discussions were tedious.

 1b. Tedious were the discussions.

Sentence 1b is strongly marked; it needs a quite special context for it to occur, but given this context, it can be acceptable. It involves copular inversion; the subject NP has inverted to the other side of the finite verb, forcing the predicative adjective to appear in first position. Copular inversion in English is a remnant of the V2 principle of Germanic languages. Now with examples 1a-b in mind, consider the following sentences:

 2a. The discussions were a problem.

 2b. ??A problem were the discussions.

Based on an analyis in terms of copular inversion along the lines in 1b, one could argue that copular inversion has occurred in 2b as well, which would make the discussions the subject. But 2b is strongly marginal at best. The tendency for the NP that immediately precedes the finite verb to be granted subject status is too strong in English. But the acceptability judgments are not robust in such cases, since the V2 principle is not entirely dead in English; it is still influencing our sense of acceptability, if only to a minor extent.

In sum, acceptability judgments are often not black-and-white, but rather two or more principles of subject choice can be in competition, reducing acceptability to a greater or lesser extent. Someone who has mastered the language knows how to avoid the competition by using alternative formulations or how to use it to his or her advantage in order to create the desired effect of unusual or marginal language.