CHAPTER IL
CONSISTENCE.
1-3. The field of observation or universe and its specification by symbols—
4. Derivation of complex from simple relations by specifying the
universe—>5-6. Consistence—7-10. Conditions of consistence for one
and for two attributes—11-14. Conditions of consistence for three
attributes.
I. Any statistical inquiry is necessarily confined to a certain
time, space, or material. An investigation on the prevalence of
insanity, for instance, may be limited to England, to England in
1901, to English males in 1901, or even to English males over 60
years of age in 1901, and so on.
For actual work on any given subject, no term is required to
denote the material to which the work is so confined: the limits
are specified, and that is sufficient. But for theoretical purposes
some term is almost essential to avoid circumlocution. The expression
 the universe of discourse, or simply the universe, used
in this sense by writers on logic, may be adopted as familiar and
convenient.
2. The universe, like any class, may be considered as specified
by an enumeration of the attributes common to all its members,
e.g. to take the illustration of § 1, those implied by the predicates
English, male, over 60 years of age, living tn 1901. It is not, in
general, necessary to introduce a special letter into the classsymbols
 to denote the attributes common to all members of the
universe. We know that such attributes must exist, and the
common symbol can be understood.
In strictness, however, the symbol ought to be written : if, say,
U denote the combination of attributes, English—male—over 60
—Iliving in 1901, 4 insanity, B blindness, we should strictly use
the symbols—
(U) =Number of English males over 60 living in 1901,
(U4) = 23 insane English males over 60 living in 1901,
(UB) = PP) blind ” » »
(U4B)= 5 blind and insane English males over 60 living in 1901,
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