The articles the and a(n) are determinatives, words which mainly function as determiners:
Thedeterminative : determiner Poincarenoun : attributive conjecturenoun : head
Thedeterminative : determiner Higgsnoun : attributive bosonnoun : head
Each of these noun phrases has:
- A determinative functioning as a determiner: the.
- A proper noun functioning attributively: Poincare, Higgs.
- A noun functioning as head: conjecture, boson.
But the determiner slot can also be filled by a genitive noun phrase:
Locke'sgenitive noun : determiner argumentnoun : head
Tolstoy'sgenitive noun : determiner booksnoun : head
John'sgenitive noun : determiner propertynoun : head
There's nothing in attributive position, although we could put something there, like an adjective:
Locke'sgenitive noun : determiner brilliantadjective : attributive argumentnoun : head
Tolstoy'sgenitive noun : determiner longestadjective : attributive booksnoun : head
John'sgenitive noun : determiner stolenadjective : attributive propertynoun : head
And we could put determinatives in the determiner slot, if we wanted:
adeterminative : determiner brilliantadjective : attributive argumentnoun : head
thedeterminative : determiner longestadjective : attributive booksnoun : head
∅determinative : determiner stolenadjective : attributive propertynoun : head
In the last example, the determiner slot can't be filled by a or the because property isn't countable in this sense. If you prefer, you could say it's filled by a "zero article", which would then be a type of determinative; I've marked this with the ∅ symbol.
What's important here is that we can't fill the determiner slot with two different things at the same time. Generally speaking, you can fill the determiner slot with a determinative or a genitive noun phrase, but not with both at the same time. Your example *"the Locke's argument" is ungrammatical for this reason.
In your last example, the determiner slot is empty. It can't be filled by an article:
∅determinative : determiner Steinbecknoun : attributive countrynoun : head
That's because country in this sense is uncountable. This is sense 4 in Macmillan, "an area that is known for a particular product, activity, person, etc.", which includes the following example:
East of here is mostly [ farming country ].
A non-genitive noun like farming generally can't fill the determiner slot. It's being used attributively, much like an adjective:
∅determinative : determiner farmingnoun : attributive countrynoun : head
But the determiner slot can be filled:
America'sgenitive noun : determiner winenoun : attributive countrynoun : head
Just not by an article.
Not a rigorous explanation, but the's in the Poincare's conjecture, the Higgs boson, and the Locke's argument are for conjecture, boson, and argument. The use of the for these words are basically the same to the use of the in general, i.e. to be specific about which conjecture, which boson, and which argument. (Compare: we are not very specific about which book or which property in Tolstoy's books or John's property) – Damkerng T. – 2013-12-11T08:50:29.320
@DamkerngT.: But the books written by Tolstoy is an exact group of books, not all books in general, why am I not supposed to say "The Tolstoy's books." ? – Graduate – 2013-12-11T08:53:46.063
I suppose that Tolstoy must have written many books, and when someone says Tolstoy's books, she simply is talking about books in general, which happened to be written by Tolstoy. Actually, I believe that she can even say a Tolstoy's book too, if she wants to refer to some (but not sure which one) book written by Tolstoy. – Damkerng T. – 2013-12-11T08:59:48.400
I just got an idea, potentially a very useful one. To see if you really need to use the, try replacing the with some, if the meaning doesn't change, it means that you don't need (and shouldn't use?) that the. For example, I read some Tolstoy's books makes sense, but she studies some Poincare's conjecture doesn't. – Damkerng T. – 2013-12-11T09:04:39.177
1It's not a question of exact group versus not exact group, but rather of the rule that we do not use an article with a proper name. If I say, "I gave the book to Bob Smith", "Bob Smith" is a very exact group -- one specific person -- but I still don't use "the" because of the proper name rule. But as I say in my answer below, when a proper name is used as an adjective, without a possessive, it loses this "special exemption" from needing an article. I can see how this rule may be confusing to people learning English as a second language. All I can say is, that's the convention. – Jay – 2013-12-11T18:28:30.913