This has come up in this thread.
Take the following sentence:
“The book I’m talking about is in the bookshelf next to the desk.”
Quick! How many bookshelves are there next to the desk?
This is a poll of sorts.
-FrL-
One. There may be others in the room and that’s why you specify which one, or you may be giving directions to someone who doesn’t see a St Bernard until a ton of fur throws them to the floor, sits on them and starts licking their face and that’s why you specify where the only bookshelf is. But in any case, there is only one bookshelf next to the desk.
I would disagree.
I get a nonspecific number greater than 0. English “the” is a determiner (wikipedia it if you’re interested) which codes for specificity and definiteness. I’m going to butcher the definition by paraphrasing it without the predicate logic: basically, something is specific if it’s being singled out from a number of members of its class of meaning (shelves, desks, books). It’s definite if you can see and interact with it. Therefore 'the bookshelf next to the desk" tells us that at least one bookshelf definitely exists. Since the only numeric specification was non-zero as a consequence of being definite, however, there can be any number from one to infinity. At least in my english, which might be weird.
Omi no Kami, I believe you’re answering the wrong question, and the one you’re answering is this:
[spoiler]How many shelves are there (in the room)?
Both you and I agree in that, at least in the normal situation (i.e., no St Bernards involved), “next to the desk” is a specific identifier of the bookshelf in question. If there were two shelves next to the desk, then the identifier would be insufficient.
“The blonde woman” is one; if you’re using that description it’s because you identify which woman uniquely just by saying she was a blonde. If there had been a single woman in whatever situation you’re talking about, you’d only need to say “the woman”. “The bookshelf next to the desk” is one; it’s only that in this second case your adjective is a multi-word clause instead of a single word.[/spoiler]
I thought of that, but I don’t think spatial location is a mandatory consideration when it comes to definiteness in English. Strictly speaking ‘the’ indicates that you have a particular something in mind, which discourse will render obvious. If there are three apples on a table, I polish one, and say “the apple looks good,” discourse requires me to be referring to the apple I’ve polished. To do otherwise would trigger a presupposition failure. However, all “the” does in frylock’s example sentence is it presupposes that there already exists a bookshelf in discourse to which the speaker refers. I would argue that although it’s intuitive for “By the desk” to code a particular bookshelf in discourse, its actual role is to provide embellishment in the same manner as the prepositional phrase “on the plate” would in “the apple on the plate”.
As means of a more precise (if depressingly technobabble-y) argument, since the PP occupies CompDP in a +definite +specific -zero DP it can’t possibly be loading the semantic discourse unless there’s a trace of Comp that dominates D’, in which case we’re just seeing move-merge in action.
[spoiler] There is one bookshelf next to the desk.
There is at least one bookshelf in the room but there may be more in non-desk locations.[/spoiler]
There is one, and only one, bookshelf next to the desk. If there were more than one, the sentence would not make sense in English
Since the bulk of the responders seem to be judging that there’s one desk, I have to assume something is weird with my dialect or intuition. (I’m a linguist, by the by, so my grammatical intuition IS expected to be pretty bad.) If a desk had three bookshelves next to it, and I wanted to specify the one I was thinking about, I find “the bookshelf next to the desk” to be acceptable. It’s semantically weird, but it’s acceptable. Combine that with the fact that English ‘the’ doesn’t explicitly code for plural, and if the group consensus is that ‘one’ is the only reasonable answer, I have to assume that something in the PP is responsible for coding the number.
Are spoiler boxes really necessary?
[spoiler]Omi no Kami’s technical description (what the hell’s a PP) went over my head, but I think I get where he’s coming from. Let’s say there are three bookshelves next to the desk and I was challenged under oath for having lied about the book. I would defend myself saying, “The book I’m talking about IS in the bookshelf next to the desk.” That statement is both grammatically correct and true.
The sentence sucks, though, if I was asking someone to retrieve the book for me. The obvious response is, “Um, which bookshelf exactly? Could you be more specific?”[/spoiler]
No.
One. Although technically speaking I suppose one could say ‘none’ because the book would have to be ‘on’ the bookshelf, not ‘in’ it.
Omi No Kami, I’m not sure exactly what you’re saying, but I think it’s something like this. Use of “the” means in part just that there is at least one of something, but use of “the” in actual conversational contexts usually clearly implies that there’s exactly one of that thing.
Is that what you’re saying?
What, IYO, is the diff in meaning between the sentence in question and the sentence “The book I’m talking about is in a bookshelf next to the desk”? (“A” instead of “The.”) And why does the former imply (without meaning, strictly speaking) that there’s exactly one, while the latter does not?
-FrL-
“The” implies specificity as described by ‘next to my desk’. ‘The’ has to mean one because the noun it refers to is ‘bookshelf’ not ‘bookshelves’. One could say ‘in one of the bookshelves’ in which case there are obviously more than one. In fact, there may be many bookshelves in the room but ‘the bookshelf (no ‘s’) next to my desk’ is what implies only one. ‘A’ bookshelf is less specific but no more implies that there are many bookshelves than ‘the’ does. In both cases there could be many bookshelves but in the latter, there could be more than one next to the desk and the person looking would need to check however many bookshelves next to the desk there might be.
This has gotten too technical.
Any normal native speaker of English would understand “the bookshelf next to the desk” to imply there being only one such bookshelf. If there happened to be more than one bookshelf there, the statement would be considered incomplete and inaccurate in not specifying precisely which bookshelf. It would be poor communication.
Now, while the statement would normally imply there’s only one such bookshelf, it does not explicitly state so. So, how many bookshelves are next to the desk? One, if the speaker is carefully and accurately making his statement in a normal fashion. If he’s not, who knows?
There’s no bookshelf - the book is on the floor under the bed where he shoved it after his mother yelled “I mean it this time mister! No computer until that room is clean!” The whole bookshelf/desk thing was a ploy to cover that he doesn’t remember the book, got it home from the library without any conscious knowledge of the book, and frankly doesn’t intend to read the thing before the report is due anyway.
I would say that, taking the question to mean “How many bookcases near the desk would there have to be for a native speaker of English to have produced this sentence naturally?” – in other words, not a trick question – there is probably only one bookcase by the desk, but there might be more than one bookcase by the desk, if it were clear to the speaker and listener which bookcase was meant.
For example, say there are three bookcases in the room: two by the desk, and one on the other side of the room. If one of the two bookcases by the desk were empty, I might well say “the book’s in the the bookcase by the desk,” as it is clear which one is meant. Or say one of the bookcases is usually by the desk and the other one is being stored there temporarily, or so forth.
Or as another example, suppose I refer to “the rug in my mom’s living room.” Now, it so happens she has two rugs in her living room; a huge, gorgeous rug that my dad brought back from Pakistan, and a little rug in front of the fireplace. I might well say “the rug in my mom’s living room” even though, strictly speaking, that has two referents; it would be reasonably clear that I mean the huge rug, although I would probably want to be clearer about it if it were important (say, telling the delivery person which rug I want to have cleaned).
Now that I think about it, it sort of comes to a phenomenon in semantics called a prototype. What this means is that certain members of a class of things are thought of as being “better” exemplars of that class. For example, if you’re asked to imagine “a bird,” you’re most likely to imagine a sparrow or a robin, less likely to imagine an eagle or a duck, and still less likely to imagine an ostrich or a turkey – even though those are all familiar to you as members of the class of “birds.” Likewise, even if there are more than one “bookcase by the desk,” if one of those were for some reason particularly salient, or the others were not good exemplars of that class, you might well say “the bookcase by the desk” and mean, and be understood to mean, only one of several.
My take on it is that there is one bookshelf next to the desk, and at least one other bookshelf in the room. If there was only one bookshelf in the room then the “next to the desk” clarifier would not be necessary, and the fact that “next to the desk” is sufficient to locate the book means that there is only one bookshelf next to the desk.
But then, if Mrs Geek had uttered the sentence in the OP, then all bets are off. She’s famous for locating things with insufficient info, such as last night when my daughter asked where the paper was with the info for how to get her homework assignment. Mrs Geek’s response? “Over there.” (no pointing, no info about which direction “over there” indicated, no nothing). Mrs Geek is also fond of saying things like “Go get me the thing” to which I’ll respond “What thing?” and receive an answer from here like “You know, the thing that goes on the thing.”
This would also be my understanding.
(Question: How do you interpret the “the” in the thread title? 
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The locution could be British – don’t they say “the house in Downing Street,” rather than “on”?
I’m not a cunning linguist, so I’m just asking is all.