Adjective is a category (parts of speech) and not a function.

Adjective is a part of speech, but it is also a function in that other words and phrases can be used in the place of an adjective, as in this case. I'm not sure what you're trying to say or how it helps answer the question.

@geekahedron my point is an adjective can be used as many ways. These ways are called functions. So when you say that a particular word is used as an adjective, it doesn't say explicitly what way that is used or more precisely what function that word play there. Well, an word or phrase can however be placed in place of an adjective. And an adjective is not a function. My whole point is that please keep the category and function apart. Don't mix it up. It's not good for learners and future readers and not for the OP as well. You however can do some more research before editing your answer.

@Austin sorry for late reply. I wouldn't consider "to live" there as correct. Rather I would use "to have lived". Or "the first human being lived...". And "the first human being living..." is also not wrong.

@geekahedron let's take this analogy. It's a bold one :) consider a paper (think that it's a category) and it came be used either as a wrapper or something to put the words down. These uses are called functions of the paper. Now the category or parts of speech is adjective. It can be used either a modifier or a complement. The use of adjective as a complement or a modifier is its function. So if we say something used used as an adjective (category) we can think that it can be used either as a modifier or a complement or both. It is not very clear, right. Even sometimes this is wrong.

@Man_From_India Your analogy is more broken than it is bold. What does that have to do with this answer? If we accept the analogy, however, adjective is both a category ("blue is an adjective") and a function ("In the phrase 'microwave oven,' the noun 'microwave' is being used as an adjective").

For example if something is used in a a sentence as a modifier and not a complement, and we say that it is used as an adjective, one might think that it is used as a complement. So it is wrong to say it that way. I hope I could make it clear :)

@Man_From_India Sorry, but it is not wrong to say that a phrase or a word that is normally a different part of speech are being used as an adjective. It's a very normal usage, in fact, and more specific than simply saying "modifier" which can refer to either adjective phrases or adverbial phrases, for example. Do you have any source which backs up the distinction you are drawing or your claim that my terminology is incorrect? Nearly if not every dictionary and grammar resource uses that type of phrasing ubiquitously.

@geekahedron yes I do have. But you actually answered your own question. See, a modifier can be an adjective or an adverb. Or anything else. So if you say the noun phrase "this way" is used as an adjective in "he did it this way", will it say that this noun phrase is actually a modifier? I don't think so. And it is a noun phrase and not a adjective. So this noun phrase is used as a modifier there. This is much clear statement.

The only questions I have raised are what this contributes to the answer and what sources you have to back up your opinion. I do not think I have answered either of those questions for myself.

Well there are modern grammar that make the modification to the traditional grammar. And one such modification is not mixing up the category and function. You have used category for function in your answer, and it is not something good, not for OP and not for anyone else (you included). Basically such things should be better left out.

Incidentally, there are two ways to interpret "he did it this way". "I asked him to paint the room with horizontal stripes. He did it this way." In this case, "this way" refers to the method and acts as an adverb, modifying "did." "I did not think he should paint while he was tired. He did it this way." In the second case, "this way" refers to "tired" and modifies "he," acting as an adjective. In both instances, the phrase is used as a modifier, but saying just that is not clear.

Again, please provide a source for the distinction you are trying to enforce. This is the first time I've seen anyone trying to argue that saying "this phrase acts as an adjective" is poor form, let alone a reputable source or cogent argument to that end.

Well I am not into any argument. No matter how constructive this is, partly because I have no time for that :(

Example:

> he is very tired.

This adverb very modifies another adjective. Correct?

So when you say that "this way" can be used as an adverb, will you also mean that it can be used to modify an adjective? Like very?

> this way tired.

Or can you give any better example?

Any modern English grammar like Oxford Modern English Grammar by Bas Aarts

It's a rather disingenuous straw man argument to say that "this phrase is used as an adjective" necessitates "literally anywhere you can use an adverb, you can insert this phase." A noun phrase acting as an adjunct adverbial can only be used as a pre-head adjunct in the absence of a determiner ("this" is a determiner, so "this way" can only used as a post-head adjunct).

OMEG has a very strict style which treats functions, and the word function itself, in a precise manner for absolute clarity and internal consistency. This is fine, but it's also completely absurd to try and enforce that style anywhere outside of the context of that specific resource.

Worse, to drop in a comment such as "an adjective is not a function" with no context or explanation whatsoever, only muddies the waters of what I still think is a very clear and straightforward answer to a simple question.

More to the point, as I stated earlier, every single online grammar resource or dictionary states that infinitive phrases "can be used as" or "function as" nouns, adjective, or adverbs. That being the phrasing with which you seem to take issue, I suggest that the scope of your argument is much larger than just this one answer.