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For example, we know "cat" or "student" are countable nouns, they are only marked as countable in the Longman Dictionary of Contemporary English as well. But are "cat" and "student" still countable when they are used in sentences like "We need cat food." and "Please forgive my student loan"? In sentences like these, I think the countable noun is used as a modifier which means a certain category (mass meaning?) instead of entities or objects. This is all very confusing to me...

Christopher W
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Adjectives are not nouns - countable or otherwise

The "cat" in "cat food" and the "student" in "student loans" are being used as adjectives and not nouns. They are descriptions of the food and the loan respectively.

Incidentally, food is a non-countable noun and loan is a countable noun.

Dale M
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For example, we know "cat" or "student" are countable nouns

These are known as attributive nouns and function as adjectives:

Cat food = food associated in some way with cats/a cat.

Cat foods = foods associated in some way with cats/a cat

Student loan = a loan associated in some way with students/a student.

Student loans = loans associated in some way with students/a student.

You will note that the indefinite article (a student/ a cat) is being indefinite (as opposed to meaning “one”.) Cat and Student can be a class noun or mean “an example of a cat/student.”

Likewise with both beer and bottle in Beer bottle shape = a shape associated in some way with a bottle that is itself associated in some way with beer.

As an attributive/adjective the noun is not inflected for gender or number – the attribute cannot be plural. Consider:

The red ball

*The reds balls.

However…

What do we make of a trouser press, or a scissor sharpener? Well, we know trousers and scissors are a plural concept, but here – acting adjectivally – the inflection is lost.

Then there are

A goods vehicle (A vehicle for carrying goods) and a clothes dryer (an appliance for drying clothes) – In English goods (in this sense) and clothes do not appear in the singular – they are plural only: the ‘s’ is part of the noun, not an inflection.

Rather than say “attributive nouns are uncountable, it is probably better to say “Attributive nouns are not inflected.”

If you are looking for a hard and fast rule to help you with this, you are wasting your time - hard and fast rules do not exist in English:

Consider

The language department of the university -> the department of the university associated in some way with language (uncountable)

The modern languages department of the university -> the department of the university associated in some way with modern languages (countable)

(The modern language department of the university might imply there is now a new building that replaced the old one.)

Greybeard
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    They don't function as adjectives but as modifiers. Adjective is not a function but a word class (POS) like noun, verb, preposition etc. Functions are Subject, Object, Modifier, Complement etc. Thus in the NPs "cat food" and "student loan" "cat" and "student" are nouns functioning as modifiers. – BillJ Nov 07 '22 at 12:24
  • I am surprised - You seem to be confusing the verb "to function" with the noun "function" (I have not used the latter) -- OED: 1.b. intransitive. With as. To perform a particular function; to do the work of or serve as something 2000 Nature 18 May 291/2 The protein..could be made to function as an enzyme. – Greybeard Nov 07 '22 at 13:38
  • Sorry if you can't understand that. Just get rid of the word 'adjective'; it's a misnomer. "Cat" and "student" are not adjectives, nor do they "function" as ones. They are nouns and they function here as modifiers. That's why we distinguish the function "modifier of" from the category (or word class) "adjective". Btw. not my downvote. – BillJ Nov 07 '22 at 18:07