What is the difference between a radical and a part?

Question

I'm interested in the precise definition of the term "radical". The dictionaries I'm referencing do not always list all components of the character that could be a radical.

For example, 訓 contains 言 and 川, and I expected that both of those components would be considered radicals, but the dictionary listings below only consider the 言 a radical.

https://jisho.org/search/%E8%A8%93%20%23kanji

https://jitenon.com/kanji/%E8%A8%93

Here's another kanji, 万. This time, 一 is the radical, and the part below is not consider a radical.

https://jisho.org/search/%E4%B8%87%20%23kanji

https://jitenon.com/kanji/%E4%B8%87

What makes a component of a character a radical, and what distinguishes that from a "part"?

In my first example, 訓, both child components are used as radicals generally, but in the case of this specific character, it seems only the first component is considered a definitive radical for this character.

In my second example, 万, the first child component makes sense, but the second part does not correspond to any radical I know of that is used generally, so I suppose this time it makes sense that only the first component of this kanji is considered a radical -- I guess?

Answer 1

The difference lies in the original Japanese and Chinese terminology in Kanji studies. Radical corresponds to 部首{ぶしゅ}, whereas "part" roughly means 偏旁{へんぼう}. Your confusion apparently stems from the difference between 偏旁 and 部首.

The first thing you need to know is what 偏旁 is. There is no exactly English equivalent, at least within the realm of layman terminology. It is usually translated as "part" or "component" in English. A part or component, as the words themselves suggest, is what you get when you try and take apart a kanji. As per Wikipedia:

偏旁{へんぼう}とは、漢字の字体を構成する要素の一つで、左右上下内外の部分に分解できる要素をいう。偏や旁を総合して言う。冠と脚をあわせて偏旁冠脚{へんぼうかんきゃく}ともいう。

All the 偏旁 are well studied and usually well defined—although there have been historical changes, for example 肉->月, and cross-linguistic and regional variations among the kanji used in Japan, mainland China, Hong Kong, and Taiwan, but that's outside the scope of this question. So the "child components" you mentioned are all 偏旁. The study of 偏旁 is historically rooted and goes back centuries. As Wikipedia suggests, a comprehensive study of 偏旁 was done as early as 1716:

現在の偏旁冠脚は、基本的に『康煕字典』（1716年完成）を使っている。

部首 is coded so as to help dictionaries index kanji. Chinese dictionaries and Japanese kanji dictionaries list and index kanji by what's called 部首. If you are confused about radicals, 部首 is your guy. Wikipedia:

部首（ぶしゅ、英語: Radical）とは、漢字を分類する際に用いられる漢字の一部分である。また、それによる分類の、各グループである。部首による分類では、全ての漢字に一つの部首が割振られる。

部首, as used by dictionaries, is a modern thing and it is so designed that every kanji at least belongs to and falls under the category of one 部首, and because of that dictionaries can use 部首 to index all the kanji. 部首 as @sundowner explains is variously defined and coded in different dictionaries and different countries.

The reason that in a word you only see one radical is that's how it's designed, in order to avoid confusion and to follow the general rule that one kanji can only have one set radical 部首. A component may be a 部首 in one kanji, but a non-部首 component in another. Admittedly this categorization is not without randomness, arbitrariness, and contradiction. That's why you may see differences among different countries and different dictionaries.

Answer 2

In my understanding of the Wikipedia article, it is ultimately arbitrary what is a radical of a character (as long as it is a part of the character).

The purpose of radicals is to provide indexes to Chinese characters in a dictionary. What is defined to be the index for a particular character is its radical. As such, a radical of a character can be different from dictionary to dictionary.

For example, a Chinese dictionary 康煕字典 and a Japanese Kanji dictionary 新字源 differ in what is the radical of 飲. The former lists 飲 as 食部4画 and the latter as 欠部8画 (the Wikipedia article lists some more).

So for your question,

What makes a component of a character a radical, and what distinguishes that from a "part"?

It is dictionary editors' decision that makes a component a radical. The difference is only that it is defined to be a radical.