What is a subject?
There's more than one theory of grammar, whether we're talking about English or Japanese, and you may find that the term subject has been defined multiple ways.
But some definitions are more adequate than others. How can we define subject in a useful way?
Let's start by looking at English, then move on to Japanese, and see we can find any useful parallels between these two very different languages.
Subjects in English
The definition you quoted is woefully inadequate. You wrote that a "subject is the noun, pronoun or set of words that performs the verb". But a verb is not an action that can be performed, it is a word that may or may not represent an action; and importantly, the subject does not always represent an entity that performs an action of any kind:
1. It's raining.
Here, the subject is it. This is what's called a dummy subject; in English, a grammatical subject is required in a (non-imperative) finite main clause. Since rain doesn't have a semantic subject, we have to insert the meaningless ("dummy") subject it.
This is called for any time we'd be left without a subject, for example in extraposition (example from The Cambridge Grammar of the English Language):
2a. [That it's a forgery] is clear.
2b. *＿＿ is clear [that it's a forgery].
2c. It is clear [that it's a forgery].
In example 2a, we have a canonical sentence with the subordinate clause that it's a forgery in a subject position. Note that this subject doesn't represent an entity, is clearly not performing an action of any kind, and the verb is doesn't represent an action.
This sort of sentence is usually extraposed, which means moving the subordinate clause out of subject position to the end of the sentence, as in example 2b. But that's ungrammatical because it leaves us without a subject, so we have to insert the meaningless (dummy) it, as in example 3b.
English has very clear grammatical rules for subjects, and this is one of them. But this is a purely grammatical rule. Even though the subordinate clause that it's a forgery has basically the same semantic role in both 2a and 2c, it's only a grammatical subject in 2a.
And extraposition isn't just an unusual exception where the semantic definition fails. There are lots of sentences used every day where it doesn't work. For example, almost every passive sentence:
3. The patient was murdered by his own doctor!
Here the subject represents an entity, but it isn't performing an action. His own doctor represents the agent in this sentence, but it's the object of the preposition by; grammatically speaking, it's not a subject.
We can't define a grammatical subject in semantic terms. It just doesn't work. What we can do is talk about what semantics a subject tends to or often has. If you'd like to say that subjects often represent entities which perform actions represented by verbs, I wouldn't argue. It's definitely true that we can find relationships between semantics and grammar; neither exists in a vacuum.
But the semantic definition is flat-out wrong as a definition of "subject". You can't come up with any semantic definition that all subjects satisfy. Instead, what we find are a number of grammatical attributes that a certain kind of constituent satisfies. And once we've identified those attributes in purely grammatical terms, we turn to semantics to figure out what to call it. We find that this kind of constituent typically represents the experiencer or agent in an active clause; and because that's true, we label this kind of constituent "subject".
But we have to come up with this sort of description on a language-particular basis. Although we can say that a subject in English is the constituent whose basic position is before the verb, which the verb agrees with in number and person, in which non-coordinate pronouns appear in nominative rather than accusative form (I rather than me), and so on, none of these rules apply to Japanese.
But what we can learn from this discussion of English is that each language has grammatical rules, and that it doesn't make sense to define grammatical functions purely in terms of semantics.
Subjects in Japanese
Again, the definition you've found is inadequate. Although が generally marks a subject, it's not true that all (or even most) subjects are marked with が. Nor is it true that a が-marked noun phrase represents an entity which performs an action; and predicates that take が-marked noun phrases as arguments don't necessarily represent actions. In fact, this sort of semantic definition fails in many of the same ways it fails in English, for example in passives.
First, let's look at the が-の alternation. In subordinate clauses, の often replaces が:
4a. 太郎が買った本 'the book Tarō bought'
4b. 太郎の買った本 'the book Tarō bought'
In both 4a and 4b, 太郎 is the subject of 買った, but it's been marked with two different particles! If you define "subject" as "marked by が", 太郎 can't be the subject in 4b. But since 太郎 has the other grammatical and semantic properties associated with a subject, that's an undesirable conclusion. To solve this problem, we'll want to introduce another layer of abstraction, separating grammatical case from grammatical function.
Particles like が and の are traditionally referred to as case particles (格助詞). The particle が is called a nominative case particle, and when you mark a noun phrase with が, we can say the noun phrase bears nominative case. We're going to be using a few more labels for cases below, so I'll lay them out here:
- が - nominative case particle
- を - accusative case particle
- の - genitive case particle
So what are these weird labels? Why do we call が "nominative"? Well, that's the traditional label for a case whose main purpose is marking a subject. But note that I wrote main purpose. I didn't say only purpose! Not all nominative noun phrases in Japanese are subjects, and not all subjects in Japanese are marked nominatively.
In fact, most aren't. On a main clause subject, the nominative case particle が is generally replaced with は unless the speaker has a specific reason to use が (e.g. the "exhaustive listing" implicature). And in familiar speech, the nominative case particle is often dropped entirely, with no particle in its place!
So with that in mind, let's take another look at our examples:
4a. 太郎が買った本 'the book Tarō bought'
4b. 太郎の買った本 'the book Tarō bought'
In 4a, we can say we have a nominative subject, that is, a subject marked by が. In 4b, we can say we have a genitive subject, that is, a subject marked by の. That allows us to say that they're both subjects, even though only one has が.
But why? What do we gain by abstracting "nominative case" from "subject function"? In order for this to make sense, we need to be able to identify grammatical and semantic characteristics that subjects have in Japanese, and so far, the only one we've really talked about is being marked by が!
In chapter six of The Oxford Handbook of Japanese Linguistics, Masatoshi Koizumi lays out some of the grammatical characteristics subjects and objects have, showing why we need to separate grammatical case (nominative, accusative) from grammatical function (subject, object). I'll borrow the following examples from Professor Koizumi:
Subjects undergo subject honorification, while objects do not:
5a. 千草先生が 学生たちを お呼びになった。
5b. ＃学生たちが 千草先生を お呼びになった。
In example 5a, the subject 千草先生 triggers subject honorification, replacing the simple verb form 呼んだ with the honorific construction お呼びになった. But sentence 5b doesn't work; 千草先生 can only trigger this sort of honorification in subject position.
Now let's try the same thing with transitive adjective 好き(だ):
6a. 千草先生が 学生たちが お好きだ。
6b. ＃学生たちが 千草先生が お好きだ。
Even though this is a non-canonical sentence where both arguments are marked with が, instead of one being marked with が and the other を, we find the same thing. It's as though the second が-marked constituent is behaving like an object, not a subject; for this reason, Koizumi refers to it as a nominative object.
The reflexive 自分 binds to subjects, but not to objects:
7. 正美が 裕美が 自分のクラスで 一番好きだ。
Although there are two noun phrases marked with が, the reflexive 自分 refers back to the subject 正美, not to the nominative object 裕美.
Subjects cannot be marked with の plus the formal noun こと:
8a. ジョンが マリーを 騙した。 'John deceived Mary.'
We can add 〜のこと to the object マリー, but not the subject ジョン:
8b. ジョンが マリーのことを 騙した。
8c. ＊ジョンのことが マリーを 騙した。
Now let's try that again with the non-canonical predicator 好き(だ), whose second object is (traditionally) marked with が rather than を:
9a. ジョンが マリーが 好きだ。
We find the same thing:
9b. ジョンが マリーのことが 好きだ。
9c. ＊ジョンのことが マリーが 好きだ。
The second argument here is marked with が, but it doesn't have the grammatical or semantic traits a subject typically has. It's not a subject; it's a nominative object.
The chapter provides further examples which you may be interested in reading, but I'll stop there. I think this is sufficient to demonstrate that we can abstract grammatical case from grammatical function.
So what is a subject in Japanese?
- It is the constituent which typically represents the experiencer or agent in an active clause, or the theme or patient in a passive clause.
- It is the constituent reflexive 自分 typically binds to.
- It is the constituent which triggers subject honorification.
- Its basic position is near the beginning of the clause, typically before the object if one is present. It can be moved out of this position, as Japanese word order is flexible, but this increases processing time.
- Its basic case marking is nominative (with が), though it very often appears without nominative marking, sometimes with another case particle instead (such as の or に, depending on the construction).
But unlike English:
- It can be readily omitted even from main clauses, as long as it's not focused and can be understood from context, particularly in familiar speech.
- It does not trigger subject-verb agreement.
- Its position is not nearly as rigid in the sentence.
- A different set of syntactic processes affect the subject; there is no subject-auxiliary inversion in main clause interrogatives, no extraposition of non-finite clauses as subjects, and so on.
So I'm afraid it's not as simple as "something marked with が is a subject", nor is it as simple as "the subject is the doer of the verb". You'll find definitions like these used quite often, but they're not really adequate; to come up with an accurate description, you'll have to dig a bit deeper.
In this answer:
* or ＊ marks a sentence as ungrammatical.
# or ＃ marks a sentence as semantically anomalous.