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>> Therefore, I would call the radicals an incomplete subset of the graphemes
>> of Chinese writing.
> So why is something that has "incomplete subsets" (whatever those are)
> (I can't see whatever you typed in Chinese) a useful bit of terminology
> or categorization?

Let me put it another way.
There are more basic units in Chinese writing than just the 214
Kanxi-radicals. But listing every single unit as a category on its own would
render any character dictionary useless, blowing it up unproportionally.
Those 214 radicals (there are by the way other Chinese character
dictionaries with a different number of radicals) are just a selection.
Some of those radicals are characters on their own. 耳 "ear" is also a
proper full-blown hanzi/kanji.

All of those radicals are graphemes. But there are more graphemes around,
more than just 214. Juergen Stalph gives a figure for the graphemes used in
Japanese, As far as I remember, it was more than 500. (cf. STALPH, Juergen
(1989): "Grundlagen einer Grammatik der sinojapanischen Schrift". Wiesbaden:

Describing it as features:
耳 (ear) = grapheme + radical + kanji
寺 (temple) = grapheme + kanji
[right half of] 構 denotes "structure" = only grapheme, *no* radical, *not*
used as an independent kanji.

>> The term "grapheme" is used by Japanologists and Sinologists a lot,
>> actually.
> They probably haven't read my articles.

There probably is yet another usage of this term, not identical to your
preferred definition ...
I just wanted to mention how this word is used among scholars of Japanese
and Chinese. It has a very narrow meaning - being restriced to Chinese
characters - and is not to be confused with the general term used in
grammatology (and your articles). Think of it as a different word.

>> Mind by the way that some of the graphemes can be further subdivided into
>> other graphemes, so graphically speaking, there are combinations of certain
>> graphemes which have a distinct meaning.
> Yet another way in which "graphemes" are not parallel to phonemes etc.

音 (sound) looks like 立 (to stand) on top of 日 (sun). But it makes sense
to consider "sound" as a unit on its own.
The same for 寺 (temple). It's 土 (earth) on top of 寸 (measure). But this
unit "temple" is part of many other characters.

If you want to compare it to phonology, you might find the sequence "oi" in
a word, let's take e.g. "coin", but it is a good idea not to treat it as a
combination of /o/ + /i/, but to treat it as a phoneme on its own, /oi/.
Although it looks strikingly similar on paper, it's just a different beast.

And similarly to allophones of the same phoneme, you can also find
allographs (I hope someone else has used this word before!) like the famous
"grass"-radical having three or four strokes (depending on your taste) but
still denoting the same.

>> P.S.: I wouldn't use the term when describing writing systems other than
>> Han, logographic cuneiform, hieroglyphics and the like.
> Well, what's the use of a linguistics (or semiotics) technical term with
> a meaning already covered by another term -- viz., logogram?

Which term is appropriate for Han characters is a problem on its own.
Ideographs, ideograms, logographs, sinograms .... there's something fishy
about all of them. Calling them morphographs (denoting morphemes) might be a
good idea, but then there will be someone pointing out the handful of
examples where one morpheme is written with more than one hanzi.
I just wanted to say, "grapheme" in the sinological and japanological sense
could also be applied to writing systems which work in a similar way.

And concerning your point, what's the use of using an existing word in a new
sense, apart from confusing everybody? - I'm afraid, this is a problem
innate to humans. Every alchemist needs his own gobbledygook, I suppose.