264. It is important to notice the difference between Extensive and
Intensive propositions; but this is not a division of propositions,
but a distinction as to our way of regarding them. Propositions may be
read either in extension or intension. Thus when we say 'All cows are
ruminants,' we may mean that the class, cow, is contained in the
larger class, ruminant. This is reading the proposition in
extension. Or we may mean that the attribute of chewing the cud is
contained in, or accompanies, the attributes which make up our idea of
'cow.' This is reading the proposition in intension. What, as a matter
of fact, we do mean, is a mixture of the two, namely, that the class,
cow, has the attribute of chewing the cud. For in the ordinary and
natural form of proposition the subject is used in extension, and the
predicate in intension, that is to say, when we use a subject, we are
thinking of certain objects, whereas when we use a predicate, we
indicate the possession of certain attributes. The predicate, however,
need not always be used in intension, e.g. in the proposition 'His
name is John' the predicate is not intended to convey the idea of any
attributes at all. What is meant to be asserted is that the name of
the person in question is that particular name, John, and not
Zacharias or Abinadab or any other name that might be given him.

265. Let it be noticed that when a proposition is read in extension,
the predicate contains the subject, whereas, when it is read in
intension, the subject contains the predicate.



_Exclusive Propositions._