Linguistics Encyclopedia.pdf

These, and the gradable binary antonyms can be modelled as being situated at opposite
ends of a continuum. As far as their effect on sentences in which they occur in predicates
is concerned, they behave like the members of sets of mutually exclusive or
incompatible terms, terms from semantic fields like ‘days of the week’, ‘months of the
year’, ‘animals’, and so on. They differ in their effects on sentences from binary
antonyms in that we cannot infer from the falsehood of a sentence containing one of the
predicates from a field the truth of another sentence differing from the first only in
containing one of the other predicates. We cannot infer from the fact that It is Monday is
false the truth of any particular one of the other possibilities—though we will, of course,
know that one of them must be true; the point is that we do not know which one. We can,
of course, infer from the truth of any one of the sentences, say, It is Sunday, the falsehood
of all the others.
So far, we have confined discussion to one-place predicates (see SET THEORY), and
thus to sentences containing one predicate and one referring term. When we start looking
at two-place predicates, we shall be dealing with sentences containing one predicate and
two referring terms. It is then possible to identify some properties that such predicates
have, by looking at the forms of relationship between the referring terms that are set up
by means of the predicate which links them. Some two-place predicates, for example, are
symmetric; we know that if
then
a is married to b
b is married to a
We shall say of any predicate, R, which satisfies the formulation (see FORMAL LOGIC
AND MODAL LOGIC),
that is, ‘for all x and for all y if x stands in relation R to y, then y stands in relation R to
x’, that it is symmetric.
Other predicates are transitive. We know that if
and
then
a is in front of b
b is in front of c
a is in front of c
A-Z 527
We shall say of any predicate that satisfies the formulation