A mere semantic observation of the articles in English, i.e. the definite article the and the indefinite article an, at once discloses not two, but three meaningful characterizations of the nounal referent achieved by their correlative functioning, namely: one rendered by the definite article, one rendered by the indefinite article, and one rendered by the absence (or non-use) of the article. Let us examine them separately.
The definite article expresses the identification or individualization of the referent of the noun: the use of this article shows that the object denoted is taken in its concrete, individual quality. This meaning can be brought to explicit exposition by a substitution test. The test consists in replacing the article used in a construction by a demonstrative word, e.g. a demonstrative determiner, without causing a principal change in the general implication of the construction. Of course, such an "equivalent" substitution should be understood in fact as nothing else but analogy: the difference in meaning between a determiner and an article admits of no argument. Still, the replacements of words as a special diagnostic procedure, which is applied with the necessary reservations and according to a planned scheme of research, is quite permissible. In this case it undoubtedly shows a direct relationship in the meanings of the determiner and the article, the relationship in which the determiner is semantically the more explicit element of the two.
Cf.: But look at the apple-tree!-* But look at this apple-tree!
The town lay still in the Indian summer sun.- That town lay still in the Indian summer sun.
The water is horribly hot.- This water is horribly hot.
It's the girls who are to blame.- It's those girls who are to blame.
The indefinite article, as different from the definite article, is commonly interpreted as referring the object denoted by the noun to a certain class of similar objects; in other words, the indefinite article expresses a classifying generalization of the nounal referent, or takes it in a relatively general sense. To prove its relatively generalizing functional meaning, we may use the diagnostic insertions of specifying-classifying phrases into the construction in question; we may also employ the transformation of implicit comparative constructions with the indefinite article into the corresponding explicit comparative constructions.
Cf.: We passed a water-mill. -We passed a certain water-mill.
It is a very young country, isn't it?- It is a very young kind of country, isn't it?
What an arrangement! -What sort of arrangement!
This child is a positive nightmare. -- This child is positively like a nightmare.
The procedure of a classifying contrast employed in practical text-books exposes the generalizing nature of the indefinite article most clearly in many cases of its use.
E.g.: A door opened in the wall. - A door (not a window) opened in the wall.
We saw a flower under the bush.-* We saw a flower (not a strawberry) under