-Thank you probus. I totally agree with you. In fact several native speakers including teachers of English have pointed it out to me so far. I agreed with them each time because they are right.
However, I'm not a lover of a logical or mathematical thinking, because logic (and mathematics) seemed to me to impair something heartful or delicate in a language and in life as well. I used to be a lover of English and American literature, which I majored in in the university.
Before starting to teach English, I'm not so interested in English grammar: also I disliked language theories like Chomsky's or structuralists',
But my attitude changed after I became a teacher of English. As you know, the Japanese language is so far from the English language in many ways, particularly in an article system, which doesn't exist in a Japanese language system and too difficult for Japanese teachers let alone students.
Some teachers try to master articles and teach them to their students, but knowing an article system has something illogical in it and understanding it requires years of experience, not just linguistic experience but also cultural experience, end up giving up teaching articles. (Japanese students, except for few who are lucky enough to have years of experience of staying or studying in English speaking countries, don't have such experience. And they aren't under the condition that they cannot live on if they don't mater English.)
Only a few teachers teach articles. They don't provide a logical explanation and instead use the word "social convention", which is a convenient phrase for them. However, the students never master articles particularly in the case of an exophoric use. For them there are too many cases requiring rules of thumb, which apply to each individual case, and don't have high versatility.
As a result, most Japanese students have rarely been taught articles, and even if they are taught articles, they hardly understand. That's a shame, but it can't be helped.
I wondered I could come up with a breakthrough solution. Nothing, nothing as long as the teaching of articles definitely requires years of linguistic and cultural experience. To make the matters worse, the time allowed for teaching articles to the students is sadly small. But we Japanese teachers want our students to speak and write correct English.
One day, came to me an idea:
Native speakers make appropriate choices as to which article to take based on rules of thumb. Almost everyone makes an appropriate choice, but what on earth makes it possible? Probably they, when choosing articles by experience, share the identical psychological tendency. When each person's psychological tendency is the same, it should be thought, there is some extent of logic in it. What kind of logic then? Only God knows. However, it just seems to me to be as reasonable as possible.
Now when I teach the reason for "the" being added to, say, "meter", as in "The cloth is sold by the meter in that shop.", I provide 4 explanations:
One is that the standard "meter" must be only one meter recognized by people.
Another is that generally a unit of measurement is the only socially accepted one.
Still another is that the meter is chosen by the shopkeeper, not the yard or not the inch.
(The meter is in contrast with other units of measurement.)
Still another is that the meter is the generalized concept of meters, which is only one thing.
Which of the four is correct? Only God knows. Also it is possible there isn't a correct idea among the 4. I tell my students that nobody can judge which one is correct, because nobody knows which idea native speakers had in the days "the meter" was first used, and tell them there might be influences from foreign languages (say, French), and from that on there might be historic changes. And so I let my students choose whichever they like, and tell them the point is whether they come to choose appropriate articles, regardless of its trueness of the chosen idea.
As for me, I try to provide plural ideas my students can refer to in their choice of articles. And I tell them I cannot provide a correct idea but can provide a reasonable and valid one. Also I tell particularly to the students wishing to be an English teacher to remember what they are taught by me now isn't a definite truth but rather just a reasonable idea.
(Of course, in th case of anaphora use and cataphora one, I teach in a logical way.)
As for my questions to you native teachers, I'd like you to make a judgement as to which explanation is reasonable, not which is correct. I just use the word "correct" for convenience. The words "Am I right?" mean in my mind "Is my explanation reasonable enough for my students to understand?" or "Is it useful for their choice of articles?"
If I should be an English teacher in English speaking countries, I would probably take (much) the same way as you do. As it is, I'm an English teacher in a country of which the language system is the farthest from your countries'
Anyway so much for the argument. I talked too much. Thank you for your sincere advice.