Are they proper nouns (cases like "physical education" in "She teaches physical education")?

[Lycidas]

A recent thread here caused me to wonder whether phrases like "physical education," "special education," etc., are proper nouns in sentences like these:

(1) She teaches physical education.
(2) She teaches special education.

It was agreed that it won't do to say:

(3) *She teaches education.

And the thread was closed after it was observed that modifying the adjective preceding "education" is absurd in sentences like (1) and (2).

(1') *! She teaches metaphysical education / partly physical education.
(2') *! She teaches very special education.

These two facts suggest that "physical education" and "special education" do not behave like normal noun phrases in such sentences, where they refer to subjects that can be taught. It seems to me that they may be proper nouns. My question here is whether they are.

It occurs to me that we can even put attributive nouns before the adjective in such cases. We can't do this in noun phrases formed with common nouns:

(4) She teaches grade-school physical education.
(5) *She likes apple delicious pie.

If they proper nouns, should they not be capitalized? Are there any other proper nouns, apart from the names of some eccentrics, that are not capitalized? Yes, the names of school subjects are not normally capitalized. But, absent context, how can we know to what "physical education" refers in the following sentence?

(6) Physical education appeals to me more than online education does.

Does that mean that I like P.E. more than I like taking classes on the Internet, or that I prefer in-person education to online education?

 

[jutfrank]

I don't think it needs to be capitalised unless it's the name of a particular P.E. course, at a particular institution.

It's the same with other subjects:

She teaches mathematics.

We don't need a capital there. Why? Is it because mathematics does not refer to a subject that can be taught?

(6) Physical education appeals to me more than online education does.

Does that mean that I like P.E. more than I like taking classes on the Internet, or that I prefer in-person education to online education?

It could be either, just as with my 'mathematics' example, but given the context of the sentence I think the latter is more likely.

Semantically, what's long interested me is how the verb teach can have two completely different arguments. You can 'teach somebody' (a person receiving instruction) and you can equally 'teach something' (a procedure of some kind). What does this tell us about the meaning of the verb? Is it fair to say that when we say She teaches mathematics, it's really just an ellipted way to say She teaches [people how to do] mathematics?

 

[emsr2d2]

I'm on the fence with this one. There might be absolutely no grammatical basis for what I write but here it is anyway.

How did you do in the history exam? (Not capitalised)
What grade did you get for History? (Capitalised)
I've got double maths this afternoon. (Not capitalised)
If you don't pass Maths, I'm going to ground you. (Capitalised)

 

[jutfrank]

How did you do in the history exam? (Not capitalised)
What grade did you get for History? (Capitalised)
I've got double maths this afternoon. (Not capitalised)
If you don't pass Maths, I'm going to ground you. (Capitalised)

I agree with those and they all accord with what I'm saying about capitalising the name of a course, not a subject (as with the first example), and not a lesson (as with the third).

 

[5jj]

I'm grateful I didn't have to worry about such hair-splitting things in the UK. I taught French and German!