我之前在電郵中寫過，文法具有「遞迴性 recursive」這特徵：也就是說，整個文法系統是一個完整的系統，當中有不同層次。如果某東西在其中一個層次會發生，同樣的東西也會在其他所有層次中發生——不會因為層次不同而被不同的規律規範。
這就是「系統性文法」的定義。
兩星期前，在一封談文法「遞迴性 recursiveness」的電郵裡，我以「完成式體貌 perfect aspect」為例：既然英文動詞的「完成式體貌」（即顯示那動作是「已完成」的那字形）是透過加入輔助動詞「have」，再加主要動詞的固定 past participle 字形來表現，那麼這個系統性規律也會出現在子句每一個層次中。
這聽起來好像複雜，但其實只要用簡單例子，就能再次清楚看見：
I have done this.
我已做了這事
I want to have done this.
我想已做了這事
Having done this, I moved on.
在已做完了這事的背景下，我繼續向前
重點是：在英文文法中，只要是要表現「完成式體貌」的動詞字形，都會有「have」作輔助動詞（依照該詞組確實需要的字形來變），後接主要動詞的 past participle 字形。
不論那個要變「完成式」的動詞是整個子句層次中的限定動詞（例如第一句 I have done it 裡的 have done），還是其他非限定動詞（例如第二句中的 to have done it 或第三句中的 having done it），只要是「完成式」的字形，都一樣會有「have」作輔助動詞（相應字形）加主要動詞的 past participle 字形。
這就能顯示文法的「遞迴性」。如果你知道 I have done it 裡的 have done 是如何有完成式體貌的字形，那麼你也應該知道，在像 to have done it 或 having done it 這些非限定動詞字形中，呈現完成式體貌的邏輯是相同的，只是套用到子句中不同層次而已。
此外，這三個句子也展示了另一個「遞迴性」的例子：既然這些動詞組，雖然在各自的結構層次中扮演不同文法角色，但它們都在表達同一個動作（「做了這事」），都一樣有一個 this 作賓語。
在 I have done this 裡，this 是限定動詞「have done」的賓語；而在 to have done this 或 having done this 這些非限定詞組中，this 也是該詞組層次裡，非限定動詞「to have done」和「having done」的內部賓語。
這同樣是遞迴性的例子：當一個動詞需要賓語才能完整呈現某個特定意思時，不會因為它是在整個子句層次、還是在其他詞組層次而改變 —— 它在所有層次裡都需要該賓語。
現在回到我一開始想寫這封電郵的原因：在另一封談到我與一般英文教學 「paradigm」的差異時，我提到有一位學生最近指責我從來沒有提過「complement」這個術語。
我之所以刻意不在我的教學 paradigm 裡使用這個術語，是因為它是典型的「功能行先」的用語；這種方向往往會把學生鎖死在把句子看成一堆被任意定義的「功能」，而不是從系統性的基本組件與邏輯，去看英文句子（任何句子和任何層次）是如何一層層遞迴地建構起來的。
（完整解釋可見標題為「因為『paradigm mismatch』（教學框架和理念不對應）帶來的誤會😫」那封電郵。）
今天這組例子，其實正好示範了其中一個原因，為什麼我認為「complement」這個術語並不能幫助學生理解文法的系統性與遞迴性。（而幫助學生理解這兩點正是我用語言學概念教英文的主要目的。）
這原因是，在一般教學裡，通常極力要把 I have done this 中的 this 標為 complement。
名詞 this 在這句裡的確有「完成」 I have done（做了什麼？）的功能，好 —— 這裡把「this」標籤為 complement，當然沒問題。
問題在於：在同一個架構的一般教學中，雖然會把「I have done this」的「this」標籤為 complement，但通常不會（或幾乎不會）在 to have done this 和 having done this 這些「下一層次」的詞組中，也把 this 標籤為內部 complement。
但在這兩個非限定詞組裡，this 的功能是完全一樣的：它一樣是在完成 to have done 和 having done 的動作意思，去表達「做了這事」。
完成「to have done」和「having done」意思的「this」同樣是這些非限定動詞的complement —— 只是它完成的是非限定動詞意思，而不是像在「I have done this」中那樣，在完成整個子句的限定動詞（核心動作）「have done」的意思。
一般教學裡像 object complement 這類標籤，多半只會用於描述整個子句層次（例如 I have done this）。而且常常還會搭配把整句硬定義成某個「句子功能／意義類型」。
我的教學目標，如我在另一封電郵中詳細說明的，是完全相反的：我希望學生先看見英文文法如何作為一個完整系統運作，再把這個系統與功能／意思連結起來。
我不使用「complement」這個術語，是因為我不希望學生困在逐句貼上功能標籤，而看不到所有句子背後真正的系統性運作方式。
我也不希望學生只能停留在整個子句層次思考 —— 因為如上所示，文法在所有層次上都有遞迴性，而真正的文法理解取決於能否看見這一點。
即使一般教學中會用到 complement 這樣的功能標籤，它的使用方式也不會跨層次一致，反而遮住了文法的「遞迴性」。
因此，即使我在我的教學 paradigm 的確會不斷加入更好的系統 → 功能討論（包括 complement 的功能），這些都必須放在同一個前提下進行：讓學生清楚看見句子各層次是如何系統性、遞迴性地連結在一起的。
我的教學 paradigm 一直在持續打磨，但核心理念與方向始終沒有改變。☺️
I wrote in previous emails that grammar is “recursive” -- that is, it operates as an entire system, but in layers. If something happens in one layer of the system, it also happens in all other layers -- there are not different rules for different layers. That is the definition of systematic grammar.
Two weeks ago, in my latest email about the “recursiveness” of grammar, I gave the example that, since the “perfect aspect” of verbs (grammatical state showing that verb’s action as “completed”) is shown in English by adding the auxiliary verb “have” and turning the main verb into its fixed past participle form, this happens across every layer of sentences in English.
This sounds complicated in words, but we can just use a simple example to illustrate this clearly again:
I have done this.
我已做了這事
I want to have done this.
我想已做了這事
Having done this, I moved on.
在已做完了這事的背景下，我繼續向前
The point is that, in English grammar, verbs in perfect aspect are formed by having the auxiliary verb “have” and the past participle form of the main verb.
It does not matter whether the verb in a particular clause is the finite verb (like “have done” in “I have done it”) or a type of non-finite verb (like in the phrases “to have done it” or “having done it”) -- if we want to form a verb form showing perfect aspect, we need to have the verb “have,” in its relevant form for each type of phrase, followed by the past participle form of the main verb in question.
This is what “recursiveness” means in grammar. If you know how to form the perfect aspect finite verb “have done” in “I have done it” -- you should also know that, even in non-finite verb phrases like “to have done it” or “having done it,” the logic of showing the perfect aspect is the same, just correspondingly applied.
Now, another thing that these three examples show about “recursiveness” is that, since all of these verb phrases, despite their different grammatical roles in their respective clauses, are expressing the same action (“做了這事”), they not only show the same aspect but also all have the same direct object “this.”
The clause “I have done this” has “this” as a direct object, and the non-finite verb phrases “to have done this” and “having done this” also have “this” as a direct object within their phrase layers.
This is also an example of “recursiveness.” When a verb requires a direct object to express a certain meaning, it would have that object whether it is playing the role of the finite verb in a clause (the core action of the clause) or in other non-finite verb phrases playing other roles.
Now, this brings me to the point I started this email wanting to make. In another email about the differences between my “paradigm” and the mainstream teaching paradigm, I mentioned that a student recently accused me of not mentioning “complements.”
I deliberately chose to leave this term out of my paradigm because it is a typical “functions-first” term that often locks students in thinking about sentences as having arbitrarily defined “functions” rather than as infinitive iterations from the systematic building blocks and logic.
(You can find my full explanation in that email, titled “因為「paradigm mismatch」（教 學框架和理念不對應）帶來的誤會😫.”)
The examples I gave today offer one illustrative reason why I think this term does not help students’ understanding of the systematic and recursive nature of grammar (which is my entire goal in teaching English).
That reason is that, in mainstream teaching, the term “complement” would often be used insistently to label the “this” in the first sentence, “I have done this.”
The noun “this” has the “function,” in this particular sentence, of being the object completing the meaning of “I have done” -- “I have done what?” “I have done this.” It is therefore a “complement.”
That is all well and good.
The problem is, in mainstream teaching, the same term “complement” would not (or would rarely!) be applied or mentioned at all in the case of the phrases “to have done this” and “having done this.”
Inside the phrases “to have done this” and “having done this,” the noun “this” is also acting as a “complement” to the non-finite verbs “to have done” and “having done.”
The “function” of “this” in the phrases “to have done this” and “having done this” is exactly the same as that in “I have done this.” It is also a “complement” -- just that it is a complement completing the meaning of a non-finite verb instead of the finite (core) verb.
In mainstream teaching, when functional labels like “object complement” are used, they are often used only on the level of the whole clause -- like in “I have done this.” Very often, this is done in conjunction with labeling the “whole sentence” as being “a particular pattern of function or meaning.”
My goal in teaching from a Linguistics perspective, as I have explained at length in that other email, is to do the reverse -- to show students how the entire architecture of English grammar works as a whole system before linking that systematic framework to functions and meanings.
I don’t use the term “complement” because I don’t want students to get bogged down in labeling the arbitrary “functions” of different parts of a clause in each arbitrary example without understanding how all sentences are formed systematically.
I also don’t want students to get trapped in thinking only on the clause/sentence level — when, as I said, seeing grammar as recursive across all structural layers in sentences is very important to true grammatical understanding.
Even when a term like “complement” is used in mainstream teaching, it is not used systematically across all sentence levels. Rather, it is used in a way that mars rather than shows that grammar is recursive.
As such, even if there is a case for me to improve the treatment and explanation of functions (including the function of “complements”) in my paradigm (which I think there is, after 8 years of experience doing this) -- it would still need to be done in the context of highlighting to students how different layers of sentences all fit together systematically and recursively.
My teaching paradigm is constantly being refined — but the core premise and philosophy have not changed. ☺