Definite and indefinite articles with uncountable and countable nouns

Question

I am talking about using definite and indefinite articles with uncountable nouns and also in of-phrases. I would be very grateful if anyone could explain it to me.

These two examples I found on the internet they refer to the usage of articles with uncountable nouns:

The position requires a knowledge of German. The knowledge of computer software is very useful nowadays.

I am not sure why the first sentence uses the indefinite article while the second one the definite one.

When it comes to of-phrases (I apologize for calling them this way, I don't know the proper name for this type of constructions).

For example:

A chapter of a book. / The chapter of a book.

I found an article, which says that if the noun is followed by a prepositional phrase (of/in/to…), it is made definite and takes the definite article. Does it mean that the first noun always require the definite article even if it is the first mention of a noun? The chapter of a book. The name of a movie. etc.

Answer 1

As I'm sure you know, the definite article is for something unique, the indefinite article for something not unique. With something abstract like knowledge, either could be used in different contexts.

For example, you could have knowledge of computer software that covers a certain set of basic applications, whereas I could have knowledge of a completely different set. We both have a knowledge of computer software. With this example, the definite article seems wrong - the knowledge of computer software would imply that it is possible to have a single, all-encompassing knowledge of this subject. The same goes for languages - most people would say, of a second language, that they have a knowledge of it - some may know more, some may know less.

However, you could use the definite article with "knowledge" in other contexts. For example, "I have the knowledge required for this job", would mean that you have the specific knowledge required. Also, you could use it without any article and say, for example, "I have knowledge of computer software".

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Your other examples of book chapters are unusual.

"A chapter of a book" is perfectly grammatical, but it would refer to a nonspecific chapter of a nonspecific book. I suppose you could say "I read a chapter of a book yesterday" if your purpose was to say how much you read, and what you read was not important.

"The chapter of a book" is more unusual, as it refers to a specific chapter in an unspecified book. I can't imagine a context where you would benefit by being specific about something that is part of something you do not name.

More likely would be "I read a chapter of the book", which would imply that you have already named the book you are reading, and you are noting that you read a chapter of it, but what particular chapter does not matter.

Answer 2

X of Y might make X countable, since X of Y can express a specific X of the set Y to which X belongs or is otherwise associated. We're pulling 1 thing out of a set. Therefore, countable and also eligible for article usage.

The position requires a knowledge of German.

Other "things" of the set "German" might be "history", "etymology", "speakers", etc.