P. HISTORY OF ' AATHEMATICAL - School of Mathematics

MATHEMATICAL LOGIC
305
the composite property: n[Pj, viz., the property of having every
property P of the class [Pj of properties. . . . ."1
"From a class: [Pj, of properties of elements arises by disjunction
the disjunctive property: U[P], viz., the property of having at least
one of the properties P of the class [Pj of properties. The notation is
so chosen that the class of all elements having the disjunctive property
U[Pj is the class U[~], viz., the least common superclass of the classes
'.\3 of the corresponding class ['.\3j of classes of elements.l"
"We may write the definitions as follows:
viz., an element x having the composite property Pi . . . . P" is by
definition (==) an element z such that (~) for every integer i having the
property: 1 ~i~n, it is true that (.:::) o)x has the property Pi;
x ncPl: ==:x ~ PCP] 0:::) .x p ,
viz., an element z has the composite property n[Pj in case for every
property P belonging to the class [Pj it is true that z has the property
r,
viz., an element x has the disjunctive property P 1 - 0 •• 0 "P.. in case
there exists an (~) integer i having the property: 1 ~i;;;an, such that s
has the property Pi;
XUIP] 0 == -z ~ ~ PIP] ~ xP ,
viz., an element x has the disjunctive property U[Pj in case there
exists a property P belonging to the class [Pj such that x has the
property P."·
695. Signs of Whitehead and Russell.-The Principia maihemaiica
of Alfred North Whitehead and Bertrand Russell, the first volume of
which appeared in 1910 at Cambridge, England, is a continuation of
the path laid out in recent years mainly by Frege and Peano. Whitehead
and Russell state in their Preface: "In the matter of notation, we
have as far as possible followed Peano, supplementing his notation,
when necessary, by that of Frege or by that of Schroder. A great deal
of symbolism, however, has had to be new, not so much through dissatisfaction
with the symbolism of others, as through the fact that
1 E. H. Moore, Introduction toa Form of General AnalyBia (1910), p, 18.
20p. cit., p. 19.
aE. H. Moore, op. cit.• p. 19,20.