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On page 17 of 发展汉语，高级口语（I）in 课文 09 there's this a discussion about homeschooling. The first sentence is:
孩子在家接受教育存在不足。
It literally translates to something like:
Kids [孩子] at [在] home [家] receive [接受] education [教育] exists [存在] insufficient [不足].
So it likely means "homeschooling is lacking". I'm not sure why 存在 is used here.
Question: What exists (存在) in the sentence 孩子在家接受教育存在不足?
I'm guessing what exists is "insufficiency", but I'm not sure.
孩子在家接受教育存在不足。
It is a [topic] + [comment/ opinion sentence]
[孩子在家接受教育] (children receive education at home) is the topic
[存在不足] (insufficiency exist ) is the comment/ opinion
孩子在家接受教育存在不足 means "insufficiency exist in children home schooling "
To make it clear, let's expand the sentence
不足處 (insufficient areas)
存在於 (exist in)
孩子在家接受教育 (children receive education at home)
的系統 (the system of)
之中 within
不足處存在於孩子在家接受教育的系統之中 = insufficient areas exist in the system of children receive education at home (home schooling children)
Back to the original sentence
存在不足 = insufficiency exist/ have insufficiency
存在 (exist/ have) is a verb here
It is an odd way to use 存在 without a preposition in a Chinese sentence.
The typical way of using 存在 is with a preposition
Example:
[不足處 (subject)] [存在 (verb)][於 (preposition)] [孩子在家接受教育的系統 object][之中 (preposition)]
[雙方(subject)] [之間 (preposition)][存在著 (verb in continuous/ progressive tense)] [矛盾 (object)]
不足 here means disadvantage, weakness, shortcomings. 存在: exist.
孩子在家接受教育存在不足 means there exists disadvantage for homeschooling.
孩子在家接受教育存在不足。
Kids at home receive education have lack
Kids who (only) receive home education lack something.
It depend on context, since you only provide this sentence, I perceive the sentence this way. There is(存在) isufficiency(不足) for kids(孩子) who receive(接受) education(教育) at home(在家). I think maybe this sentence means that they gain less from education at home.
To express objective facts compares to 是, which could be an opinion, I thought it is lacking, but maybe you don't think so.
But please don't take 存在 as an irrefutable word to overuse it. Because of most of the time, what you said is just your opinion, people hate that cold face that thought what he said is the truth that can only be agreed with.
And this sentence structure, XX存在不足 always appears in the official news. I said nothing.
