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.”
Schröder[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 Encyclopædia 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 Encyclopædia 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.
[72] F. L., p. 268.
[73] A. d. L., i. pp. 127 sqq.
[74] Ibid., vol. ii. pp. 461, 597.
CHAPTER XXVII
AND AND OR
When, with Boole, alternatives (A, B) are considered as mutually exclusive, logical addition may be described as the process of taking A and B or A or B. It is a great and rare convenience to have two terms for denoting the same thing: commonly, people denote several things by the same term, and only the Germans have the privilege of referring to, say, continuity as Stetigkeit or Kontinuierlichkeit. But Jevons[75] quoted Milton, Shakespeare, and Darwin to prove that alternatives are not exclusive, and so attained first to recognized views by arguments which were plainly irrelevant.
Of course, and is often used as the sign of logical addition: thus one may speak of one’s brothers and sisters, without being understood to mean the null-class (as should be the case), or pray for one’s “relations and friends,” without being sure that one’s prayer would be answered,—as it certainly would if one meant to pray for the null-class, this being the class indicated. And a word like while is often used for a logical addition, when exclusiveness of the alternatives is almost implied. Thus, a reviewer in Mind,[76] noticing the translation of Mach’s Popular Scientific Lectures into American, said of the lectures that: “Most of them will be familiar ... to epistemologists and experimental psychologists: while the remainder, which deal with physical questions, are well worth reading.” The reader has the impression, probably given unintentionally, that Professor Mach’s epistemological and psychological lectures are not, in the reviewer’s opinion, worth reading.
[75] Pure Logic ..., London, 1864, pp. 76-9. Cf. Venn, S. L., 2nd ed., pp. 40-8.
[76] N. S., vol. iv. p. 261.