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I have edited the question for those nitpicking. It is a simple question.

The premise: "Many/a lot of" are multal degree quantifiers. "Not many/not a lot of" are their negatives. It follows that they correspond to some paucal degree quantifiers. If you think the premise is wrong, feel free to explain how.

The question (in 2 parts):

(1) Which paucal degree quantifiers do "not many/not a lot of" correspond to? That is, what can they be replaced with in

[Not many] things were done. [Not a lot of] work was done.

(2) When (in what context) does one use "not many/not a lot of" and when does one use paucal degree quantifiers?

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    It might help if you look at it like this: A few things were done means Not many things were done. But Few things were done means Hardly any things were done.
    – Tinfoil Hat
    Mar 13 at 1:55
  • You eliminated shades of meaning and ask about subtle differences?
    – Yosef Baskin
    Mar 13 at 16:26
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    It is misleading to call words like 'many' quantifiers. Their numerical significance is context dependent, like 'big' and 'little'. And, like 'big' and 'little', their negations are effectively turning them into their antonyms. If you want to get round that, you have to qualify them by saying "Not many, by quite a few."..' or something like that. Still, they do not 'quantify'; they are not even estimates. There are ways around this, such as "not many but quite a few", and "not few, but not many either," or "not all that many"; or, conversely, "not many, but not all that few."
    – Tuffy
    Mar 13 at 23:18
  • @Tuffy They are called quantifiers by modern grammars (Huddleston and Pullum), cognitive grammar (Langacker) and language teachers (Larsen-Freeman). In my search, I even saw one or two logic papers calling them quantifiers.
    – user473438
    Mar 14 at 18:21

1 Answer 1

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The Cambridge page you cite isn't actually claiming that "not many" means "almost none." Instead, it's saying that "few" can mean either "not many" or "almost none." Likewise, it's saying that "little" can mean either "not much" or "almost nothing."

Of course, one could argue about whether Cambridge is correct on this point, but that seems to address your main source of confusion.

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    In part, the attitude of the informant affects the word choice. "A few things were done." is more supportive than the critical "Not much was done." Euphemism often serves to soften criticism, so "You didn't accomplish a lot." is less confrontational than "You failed to accomplish anything."
    – Dave Tamblyn
    Mar 13 at 21:40

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