Mathematics requires, so far as I know, only two other primitive
propositions, the one that material implication is a relation, the other that ∈ (the relation
of a term to a class to which it belongs) is a relation^{[24]}. We can now develop
the whole of mathematics without further assumptions or indefinables. Certain
propositions in the logic of relations deserve to be mentioned, since they are
important, and it might be doubted whether they were capable of formal proof. If
`u`, `v` be any two classes, there is a relation `R`
the assertion of which between any two terms `x` and `y` is
equivalent to the assertion that `x` belongs to `u` and
`y` to `v`. If `u` be any class which is not null,
there is a relation which all of its terms have to it, and which holds for no
other pairs of terms. If `R` be any relation, and `u` be any
class contained in the class of referents with respet to `R`, there is
a relation which has `u` for the class of its referents, and is
equivalent to `R` throughout that class; this relation is the same as
`R` where it holds, but has a more restricted domain. (I use
*domain* as synonymous with *class of referents*.) From this point
onwards, the development of the subject is technical: special types of relations
are considered, and special branches of mathematics result.(§ 30 ¶ 1)

§ 30 n. 1. There is a difficulty in regard to this primitive proposition, discussed in §§ 53, 94 below. ↩

The Principles of Mathematics was written by Bertrand Russell, and published in in 1903. It is now available in the Public Domain.