I'm confused because I see a contradiction in your reasoning. At first, you replied, "The former yes, the latter, no," confirming that "the amount of work he did yesterday" allows for both readings. But then you said, "b) is right but a) isn't," which means that "the amount of work" doesn't allow for both readings. What am I missing?
I'm not sure. It seems one or both of us have misunderstood something. I think it may be that I misunderstood what you meant here:
a) "The amount of work he did yesterday" = yesterday's part (Is it grammatical?) of all the work.
b) "The amount of the work he did yesterday" = all the work.
The construction of a house, for example, always includes a specific set of actions/events. If I said about a builder, "It's hard to estimate the amount of work he did yesterday," I certainly wouldn't mean some abstract idea. That's why I'm trying to figure out the difference between "the amount of work" and "the amount of the work".
Okay, you're rejecting my explanation. That's fine. I accept it is difficult to understand this, so I'll try to convince you one more time.
When a speaker says
It's hard to estimate the amount of work he did yesterday, he probably has lots of different thoughts and pictures in his mind as he speaks, but the 'main' thought at the forefront of his mind is revealed by the language he uses to express it.
From the words and structure of the sentence he uses, we can hear that the focus of his mind is something about a quantity. This could well be a number (I imagine an employer talking about a worker, while doing payroll, for example). In any case, even though he's probably imagining the worker actually doing specific events, his mind is focused on 'the amount' in whatever way that may be represented mentally, numerical or otherwise. He uses
the amount with a definite article because he's making specific reference to it. He could have chosen to say
It's hard to estimate how much work he did yesterday, but he didn't, and there's a reason for that.
He also could have said
It's hard to estimate how much of the work he did yesterday. If he had done that, he would thereby be making specific reference to 'work', for some reason. Normally, when a speaker uses a definite article, it is because he is confident that the listener will know what he's referring to. A likely interpretation is that the speaker and listener here both have the idea that
the work refers to, say, a building project, where there's a total amount of work that must be done, and 'he' did an inestimable part of it yesterday. The use of the definite article shows that the speaker wants to 'point out' this total amount to the listener. By doing this, he's defining the abstract notion of 'work' by limiting it only to work done on this project. Another way to say that is that he's specifying the way that the abstract concept of work is applied to this particular situation, at this time and in this place, realised through this particular set of events.
I think you'll do well to keep in mind the idea that every time a speaker uses
the, it's as if he's literally pointing with his finger to the concept represented by the word that follows. That's what's called 'reference' in academic terms. With concrete nouns, which represent physical objects, it's quite easy to imagine someone pointing to them, but with abstract nouns, like 'work', it's not so easy, but it's still the same thing—the speaker is pointing to the concept in his mind.
So when a speaker decides to use a zero article, it is because he does not want or need to make reference to the concept. It exists only as a generalisation in his mind, whether that's essentially a singular idea (as with uncountable nouns) or a plural idea (as with plural nouns). By using a zero article, the speaker in our sentence does not wish to specify his concept of work. He's too busy focusing on a specific amount of a generalised idea. There's no particular work he wants to 'point to'.
Let's consider the following contexts:
x) Our man has been building a house for three days = It's the entire amount of work.
x-1) It's hard to estimate the amount of work he did yesterday.
x-2) It's hard to estimate the amount of the work he did yesterday.
I tend to choose x-2) because of all of the work, we're trying to estimate only the amount of yesterday's part. There's an implied contrast between the entire work and yesterday's part.
Yes, that's right. By using
the work, he's referring to the entirety of the work, and by using
the amount, he's referring to a specific proportion.
y) Our man was building a house all day yesterday = It's the entire amount of work.
y-1) It's hard to estimate the amount of work he did yesterday.
y-2) It's hard to estimate the amount of the work he did yesterday.
I tend to choose y-1) because the work being estimated is all of the work.
Yes, but it's still possible the speaker could have used y-2, if he wants to specify the entirety of the work. But yes, it is easier to imagine that he doesn't need to. He's just talking about work in general. Even though there is of course some part of his mind entertaining the specificities of this particular building job, the part of his mind/brain responsible for speech (in academic terms called the 'mind-language interface') is using only the generalised concept. We can tell that by the language he uses.
I wrote this comment in an hour and a half.:roll:
Lucky there's not much to do outside, right?
To me, the best ones are: 
