IS
_Is_ has four perfectly distinct meanings in English, besides misuses of
the word. Among the misuses, perhaps the most important are those
referred to by De Morgan:[72] "... We say 'murder _is_ death to the
perpetrator' where the copula is _brings_; 'two and two _are_ four,' the
copula being 'have the value of,' etc."
Schroeder[73] quite satisfactorily pointed out the well-known distinction
between an _is_ where subject and predicate can be interchanged (such
as: "the class whose members are Shem, Ham and Japhet is the class of
the sons of Noah") and an _is_ or _are_ where they cannot (such as:
Englishmen are Britons), but failed to see[74] the more important
distinction (made by Peano) of is in the sense of "is a member of." If
Englishmen are Britons, and Britons are civilized people, it follows
that Englishmen are civilized people; but, though the _Harmsworth
Encyclopaedia_ is a member of the class Book (of one or more volumes),
and this class is the member of a class A of which it is the only
member, yet the _Harmsworth Encyclopaedia_ is not a member of A, for it
is not true that it is the whole class of books; and such a statement
would not even be made except possibly in the form of an advertisement.
The fourth meaning of _is_ is _exists_; it is in certain rare moods a
matter for regret that there are difficulties in the way of using one
word to denote four different things. For, if there were not, we might
prove the existence of any thing we please by making it the subject of a
proposition, and thereby earn the gratitude of theologians.
FOOTNOTES:
[72] _F. L._, p. 268.
[73] _A. d. L._, i. pp. 127 sqq.
[74] _Ibid._, vol. ii. pp. 461, 597.