The smallest parts are the words of the sentence. What shall we take to be the meanings of words? In the case of a proper name, it seems intuitively right to regard its meaning as being that individual in the world to which the name refers. The meaning of `Trafalgar Square', for example, will be just that square in London. But this cannot be quite right: consider that some individuals can be referred to by more than one name, but that we would not want to say that the names `mean the same thing'. Consider the expressions `Saint Peter' and `the first Pope', both of which refer to the same person. The two expressions can not mean the same thing, for otherwise the sentence ``Saint Peter was the first Pope'' would be an uninformative tautology -- which it obviously is not. Frege therefore distinguished between the reference (nowadays more commonly called the extension) of an expression, and its sense (or intension) -- roughly, whatever it is that we need to know about an object to identify it. What the Automated Tourist Guide knows about Trafalgar Square is in fact given in its database:
[[trafalgar square] isa [square]]
The intension, or internal representation, of the expression is what connects that expression to an object in the world, and might thus be considered the meaning of the sentence.
Arguably, the database represents `knowledge' rather than `meanings'. In our simplified treatment of semantics, however, we shall not distinguish between the two, and permit ourselves the liberty of talking about database facts as though we were talking about meanings. What the intension of an expression is will vary from account to account according to the theoretical bias of the author and to how formal the semantics is. In Sowa's (1984) theory of conceptual graphs, for example, the intension of a word is a representation in semantic memory, something like a dictionary definition; thus the intension of `mammal', for example, might be ``warm-blooded animal, vertibrate, having hair and secreting milk for nourishing its young'' (Sowa, 1984, pp. 10-11). In more mainstream formal semantics, the ``intension of an expression is a function giving the reference of that expression in any world'' (McCawley, 1981, p. 401). In the world of a science fiction novel, for example, the first Pope on Twin Earth might be Saint Thomas, in which case `the first Pope' and `Saint Peter' would not have the same referent. The intension of an expression, then, will contain an index that links it with particular individuals in particular worlds.
What about common nouns? The question at the beginning of the chapter made reference to the `square'. As there are many squares in London, we could have been referring to any one of them. So let us say that the word `square' simply picks out the set of all squares (its extension), and that the meaning of `square' is the internal representation that allows the Tourist Guide to decide what is a member of that set and what is not. A fragment of the meaning of `square' might then be
[[trafalgar square] isa [square]]
[[russell square] isa [square]]
[[berkeley square] isa [square]]
[[leicester square] isa [square]]
...etc.
In general, we may say that a common noun stands for the set of all those individuals that satisfy the description, and that to know the meaning of a noun is to know what things it can be used to refer to. We shall assume that the Tourist Guide knows about only one `possible world', which is the London of this book. The intension is therefore simply a pointer to all the things in London that are squares.