Nouns that behave like the one in column (4) are called mass nouns (or non-count nouns). They typically refer to things that are viewed as a mass rather than individual units, or which have no precise shape or boundary. Mass nouns also can be either concrete (milk, wool, spaghetti, etc.) or abstract (happiness, communism, integrity). They cannot usually be made plural (*two wools), nor do they take the indefinite article (*a wool). If we want to count mass nouns, we must add a count noun to specify the quantity (two glasses of milk).
Count/Mass as a Function
Nouns like those in column (5) (brick, cake, paper, stone, etc.) can take all the determiners that count nouns can take, as well as all the determiners that mass nouns can take. There is, however, a distinction in meaning. With stone or some stone, the mass-noun uses, noun phrase refers to the material; with stones, the count-noun use, the noun phrase refers to individual items. The stone, which can be used for both mass and count nouns, is ambiguous: we may be thinking of either material or an item. Often, context will make it clear which use is intended:
(4) The stone used in this building comes from Italy
(5) The stone that broke the window was lying on the floor.
In sentence (4), stone is used as a mass noun; in sentence (5) it is used as a count noun. Additionally, some nouns that are typically either mass or count can be pressed into service the other way. For example, butter is typically a mass noun, and it seems strange to say two butters, but we can use it in a count sense in a sentence like the following:
(6) She likes butters from Wisconsin better than those from other states.
For this reason, we say that nouns are not inherently mass or count, but are rather used in mass or count functions.