The path I'm treading on these 'parts of speech' (verbs, nouns, adjectives) is that of avoiding trying to define them, but instead trying to assemble a list of things that such parts of speech 'do'. (In fact, it's always us who are doing the doing (!) not the words themselves. We should always remember that language, grammar, vocabulary - all of it - are devised by us, for our purposes. Language isn't some kind of self-regulated robot, doing its own thing!
So, we were on nouns.
What else do they do? How else do they function?
In English they combine with small words that immediately precede them. The two key ones are:
'a/an' and 'the'
But just as important is a nothing. (I'll come back to this)
In the same slot there is a range of other words we can use and which are often given a different name to describe them e.g.
any of the numbers (1,2,3 onwards) but also words indicating none e.g.
no, none of, not one of,
this, that, these, those, (in some non-standard dialects: them), both, both of, all, all of some, some of, any, any of, each, each of, , every, every one of,)
Some people would say that some of these words are 'adjectives' and I'm wrong to have lumped them in on the same list. A lot of grammar is about deciding on categories, arguing about it according to the function being served by that word in a particular place in a sentence.
So, though it sounds awkward to say it, another characteristic of nouns is that they are words which come after words like the ones I've just mentioned. In other words, that's one of the ways in which we make them work 'horizontally'. If this sounds odd, think of how a birdwatcher or a geologist might talk. They talk about characteristics appearing together and these help the observer spot what kind of bird or rock they are looking at. You can do the same thing with grammar.
You can also experiment with these words to see what word fits with another. So take 'this'.
You can put it easily in front of a lot of nouns: 'this car', 'this person'
But some are not so easy:
'this anger' - yes, you could, but it would be quite rare...'This anger I feel about the government today, is different from the anger I felt for the previous government' Hmmm, ok, but a bit forced.
How about: 'This France'. Again, difficult and rare. It seems as if 'car' is a different kind of noun from 'anger' and 'France'.
What about 'both'?
It seems to 'determine' that there are two things that are being referred to. This is more determining than 'the' which can apply to one, two or many things yet it's no more determining than 'a' which can only mean one thing or entity.
Now what about this 'nothing' ie when we use nouns with none of these kinds of words in front of them? Look at that sentence you've just read. It says, 'when we use nouns'. No 'a' or 'the' or 'this' in front of it. Why not?
Earlier, I wrote 'one of the ways', 'the observer', Why didn't I write, 'one of ways'; 'observer'.
In the same paragraph, I wrote 'a birdwatcher', 'a geologist'. Why didn't I write 'the birdwatcher', 'the geologist' or those two words without 'a' or 'the'?
I'm asking the question because there appear to be rules or conventions governing what to use and when. If you're a native speaker of English, none of this will present you with much of a problem. You will hardly ever hesitate when to use which word. For non-native speakers though, it seems to be very hard to 'sound right', ie to pick up on the rules, just by deducing them from listening to English being spoken. When I mark students' essays, it's the use of the words 'a', 'the' or the non-use of either, that is the quickest indicator to me that I'm reading something written by someone who is a non-native user of English.
I'm not going to run through all the rules or conventions now - I'm sure I don't know them all, anyway! More creative and useful for you is to see if you can deduce some yourselves.
Here are a few:
back with 'anger' and 'France' - they seem to be in a category where you very rarely use 'a' or 'the'.
'the' seems to have the advantage of suggesting that you've talked about, mentioned, written about the particular thing or entity before. Or that you're referring to something that is 'in the air'. 'This' and 'that' will do this job too of course and because they appear to 'demonstrate' (ie perform a gesture in writing, 'over here' and 'over there' as it were), they are sometimes called 'demonstratives').
'a/an' seems to be useful to indicate the opposite, I'm introducing a thing, concept or entity for the first time in this sequence of utterances (speech, writing).
The use of no 'a/an' or 'the' and a plural noun seems to help us be general or all-inclusive. It's as if we're saying 'all of these' without having to say 'all of these'.
If you're a teacher and you teach children who are learning English, you will hear and read them presenting nouns where the word immediately preceding it will sound or look wrong. As I've said, you will know intuitively what the right word is, (if you're a native speaker yourself). Your problem will be what to do about it. The traditional way is to 'correct' it. It's quite possible that this won't work because as fast as you correct one usage, it simply makes another usage wrong. How so? Because when we're told something is wrong in language, we can't stop ourselves making up a little rule for it. And the problem with that is that rule will almost certainly not fit all cases. Yes, we can say, 'a' will never become before a plural noun but in most cases, there will be exceptions to whatever rule, a text book will come up with. This is not some cruel trick. It's just that we invent language to suit millions of different circumstances. We didn't invent it so that it could be convenient for people who invent the rules!
So, today I've done a bit of vertical and horizontal. I've suggested that we can vary the slot in front of a noun (ie vertically) but what governs that variation are a host of horizontal rules or conventions.
What I didn't do (in order to avoid making it too complicated) is start slotting in adjectives (eg 'blue' or 'big') and seeing where 'a' and 'the' fit in. We'll do adjectives another day.
I think now though, we're in a position to put nouns and verbs together in the core bit of the grammar: the 'subject-verb' construction. Aha. For another day.
In the meantime, you might want to look up the terminology for 'the' 'a/an', 'each', 'both', 'this', 'that', 'any' etc. It's quite good fun to see if you agree with the categories that grammarians come up with for them.