*70. RELATIONS WHOSE CLASSES OF REFERENTS AND OF RELATA BELONG TO GIVEN CLASSES.
Project Gutenberg EPUB3 edition
Whitehead, Alfred North and Russell, Bertrand
Summary of *70.
If and are two given classes of classes, a relation is said to belong to the class if whenever , and whenever . If only one of these conditions is to be imposed, this result is secured by replacing the class involved in the other condition by "," since "" always holds, and so does "," and therefore neither imposes any limitation on . In the most important cases, and are either both cardinal numbers, or one is a cardinal number while the other is .
In virtue of *37·702·703, the conditions above mentioned as imposed upon by membership of are equivalent to
This form is used in the definition (*70·01).
The propositions of the present number are hardly ever used except in *71, where and are both replaced by or . The most useful propositions are
*70·1.
(This merely embodies the definition.)
*70·13.
*70·22.
*70·4.
*70·41.
*70·42.
*70·54.
with similar propositions for and .
*70·62.
with a similar proposition for .
*70·01.
*70·1.
*70·11.
*70·12.
*70·13.
Dem.
*70·14.
*70·15.
*70·16.
*70·17.
Dem.
*70·171.
*70·18.
*70·2.
Dem.
*70·21.
Dem.
*70·22.
Dem.
*70·3.
Dem.
*70·31.
Dem.
*70·32.