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I think it's clear that the following two sentences are grammatical:

Is that a cup I see?

Are those cups I see?

However, what if you seek to inquire as to how many cups you can see?

Is that one cup or two cups I see?

Are those one cup or two cups I see?

Which of the above two sentences is correct?

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    I think this is based on the initial assumption/perception of the speaker, but I'd like to know what others think. I like this question. – shin Jan 16 '18 at 7:55
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    Consider the case where you're preparing a sugary coffee for someone, and either forgot or misheard them. You would say 'Was that one lump or two?' Any other permutation would just sound awkward. – Strawberry Jan 16 '18 at 13:25
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For the first pair of questions, we know how many things we are looking at, and are simply querying what the individual items are. For this reason, the question can, and must, reflect the number.

For the second pair of questions, we know that they are cups but not how many. The way we deal with this, when we don't know how many items, is to talk about it as the whole scene or ensemble, which is one item: this works regardless of whether there is one cup or two cups.

Is that one cup or two cups I see?

In this sentence, that is the scene or ensemble.

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    Taking things a little farther, I'd probably also say "Is that two cups or three?" for exactly the reason you describe. – David Richerby Jan 16 '18 at 19:45
  • @DavidRicherby you wouldn't say "Are there two cups or three?" – Robert Grant Jan 16 '18 at 20:45
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    @RobertGrant In some cases, yes. But, for example, if I offered a cup of coffee to everyone in the room, two people said "yes" and one mumbled, it would definitely be "Is that two cups or three?" (or "Fred, did you say yes?") rather than "Are there..." Likewise, if I was peering into the distance, not sure what I was seeing, "Is that two cows or three?" ("Are there..." sounds like it's a question about cows in general, rather than the specific situation.) – David Richerby Jan 16 '18 at 22:19
  • Fair enough, although I think your first example isn't quite the same thing - my understanding is that there "it" refers to the order, not the collection of cups. – Robert Grant Jan 16 '18 at 22:35
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I think your last example is awkward, although I'd hesitate to say it's wrong.

I agree it's necessary to ask what "that" is referring to, but this is not an easy question to answer. It could refer to a group of things which are seen collectively as one group, or a scene/ensemble as JavaLatte has said, but there might be other possibilities. I've had a look online but can't find much except a rather obscure entry in the OED.

c. Used with a plural n. or numeral, instead of those: now only with plurals treated as singulars (e.g. means, pains) or taken in a collective sense.

Anyway, I don't have a grammar jargon answer to this, and I suspect it's a colloquial construction, and not formal. I should imagine in a formal piece, the writer would just avoid the problem and use different wording. However, the construction works regardless of the numbers involved (or the grammar).

Examples:

Is that one cup or two cups I see?

Is that two cups or four?

That's four cups, not two! (this usage is definitely colloquial)

Is that four zebras or five?

Is that two moons around Saturn I see? (if this is OK for Reuters, I'd say it's good enough for anyone).

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"That which I can see there is two cups."

What's represented by "that" is "what you see", not the number of objects which "what you see" contains. So, "that" is either singular or uncountable, not sure which, but it's certainly not plural. I'm thinking uncountable because it's like saying "that stuff..." but skipping the word "stuff".

"Those two which I can see there are cups."

I'm sure that by now you can see how the position of "two" changes what you're talking about from the singular perception of what you see to the (potentially) plural number of objects perceived.

Let's keep going by re-introducing the ambiguity of how many cups there are.

"That which I can see there is one or two cups." Correct.

"Those one or two which I can see there are cups." Also correct, if awkward.

So, your second example, of "Are those one cup or two cups I see?" is not correct. Your first example which says "Is that..." is correct.

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    I can't imagine anybody ever saying "That which I can see there is two cups" so it's hard to really see how that fits into an answer. It's extremely clunky. – David Richerby Jan 16 '18 at 19:46
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    I find a lot of irony in your comment reading "Also correct, if awkward." I think everything you've suggested here is very awkward. – J.R. Jan 16 '18 at 20:23
  • I didn't give them as examples of what to say, I gave them as thought experiments so that it's easier to see why one of the OP's choices is correct and the other isn't. That was the question,after all - not "give me a whole different thing to say". If that had been the question, I'd have given "How many cups are there?" – Beanluc Jan 17 '18 at 17:45

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