The sentences:

The subjects we study at school can be divided roughly into two groups: the sciences and the arts. The purpose of education is to fit us for life in a civilized community, and it seems to follow from the subjects we study that the two most important things in civilized life are Art and Science.
About "the arts/Art", does that mean anything artistic only, like music and painting?

My book says "yes", but I don't think so; it includes all humanities like psychology, sociology, philosophy...whatever.

Well, my dictionary says when it means humanities, it has to be art"s". But then, what about the singular form with capital A?
You're right, and the arts include English too!

I think in the case of 'Art', the author does mean the fine arts, and is (slightly illogically) selecting them from among the arts (the humanties) to stand as his example in his conclusion about the 'two most important things'.
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So you mean to the author the fine arts are especially important among the humanities? Or is it that the fine arts are tyipical (to the authour) of the humanities?
What I am suggesting is that the author changed his mind-set slightly between talking about the school curricula (arts and sciences) and talking about the most important things of life (Art and Science). He didn't carry the precise concept over from one consideration to the other when he set up his conclusion. Perhaps as you say he considered Art typical of the arts for this purpose.
I see.

If I were the author and brought the essay to a writing lab, which I used to use very often when I was in the U.S, I guess the tutor would say "Taka, you need to revise it. Be consistent." ^_^
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