1. He goes to an academy to study math and English.
[Is 'an academy' in generic use? Or Does 'an' mean 'one'?]
2. He goes to academies to study math and English.
[Is the word 'academies' in generic use?]
3. He goes to the academy to study math and English.
[Does 'the academy' mean the specific academy? Or is 'the academy' in generic use?]
In all those sentences, academy/academies is generic, of course. If it were the name of the school, it would read something like this: The Math and Science Academy.
When you put a/an in front of a word, yes, you're indicating one, although perhaps not a particular one.
Thank you for your help.
4. He goes to academies to study math and English after school.
5. He goes to an academy to study math and English after school.
6. He goes to academy to study math and English after school.
[Then, you mean we can use both 4 and 5. In #4 'academies' are in generic use. In #5, is 'an academy' in generic use? In #6, is 'goes to academy' ungrammatical?]
That's right. You can use 4 and 5, but 6 shouldn't be used as it's written.
If the word "academy" is the name of the school, Academy, it is a proper noun and should be capitalized. As a common noun, you really need "an" or "the".
Thank you for your help. By the way, do you mean that 'an academy' is in generic use?
Yes.
1. In the sentence "He goes to an academy to study math and English," "an academy" is not in generic use. "An" is an indefinite article that indicates one of many academies. It means that he goes to one, unspecified academy to study math and English.
2. In the sentence "He goes to academies to study math and English," "academies" is in generic use. "Academies" is the plural form of "academy," and it refers to multiple institutions where he studies math and English. It implies that he goes to various academies or different ones on different occasions.
3. In the sentence "He goes to the academy to study math and English," "the academy" refers to a specific academy. "The" is a definite article that indicates a particular noun. It suggests that there is a specific academy that he attends to study math and English, perhaps a well-known or known-to-the-speaker institution.