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I'm learning articles and doing some exercises.

Here are my problem sentences:

A: What is a "capital city"?

B: Well, a "capital city" is the political center of a country.

My question is about 'the' in the second sentence. I'm don't see here any 'definiteness' of the center. From my point of view it is as indefinite as the country and city words.

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    A center is unique. A circle can have only one center: that's part of the very definition (and utility) of the concept center. By analogy, "the political center" of a country lies at the very heart of that country's power structure. Washington, D.C. is the political center of the United States. New York City is its financial center. L.A. is its (shudder) cultural center. And so on. – Dan Bron Aug 20 '14 at 22:24
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    @Dan LA is a cultural centre? Presumably you mean in the same sense as a bowl of yoghurt is a cultural centre? – Janus Bahs Jacquet Aug 20 '14 at 22:27
  • But the capital is unique too. I don't see here any differences. – Nosturion Aug 20 '14 at 22:29
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    @Nosturion The capital city of a country is unique. The notion of a city being capital is not unique—note how it says “capital city” in quotes. It's talking about the concept of a capital city (not of any specific country, but in general). It could just as well have said, “What is a ‘political centre’?” A capital city is a political centre. The capital city of the US is the political centre of the US. That means it's also a political centre. – Janus Bahs Jacquet Aug 20 '14 at 22:33
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    For each country, there is one, unique political center. So we use the when the context is a single country, because it's unique in that context. So London is a capital city, but it's the capital city of England. – Barmar Aug 21 '14 at 4:20
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We use the definite article the when we're referring to something specific or unique. While there are many political centers in general because there are many countries, the prepositional phrase of a country sets the context to being a single, although unspecified, country. For that country there's only one political center, so we use the rather than a.

As another example, we could say:

A nose is the organ in the center of a face.

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By using the instead of a, we can readily see that, in general, countries only have one* capital city.

Note that the definite article (i.e., the word "the") has several uses outside of "definiteness". Using "the" instead of "a" can indicate uniqueness, generalization, sufficiency, or members of a group. (I wrote more about this in my answer here.)


*Bolivia is sometimes said to be a noted exception, though some say that would be erroneous. (Nonetheless, this conversation is about grammar, not geography.)

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