Principia mathematica, by Alfred North Whitehead ... and Bertrand Russell.

*1. PRIMITIVE IDEAS AND PROPOSITIONS.

Since all definitions of terms are effected by means of other terms, every
system of definitions which is not circular must start from a certain apparatus
of undefined terms. It is to some extent optional what ideas we take as
undefined in mathematics; the motives guiding our choice will be (1) to
make the number of undefined ideas as small as possible, (2) as between two
systems in which the number is equal, to choose the one which seems the
simpler and easier. We know no way of proving that such and such a system
of undefined ideas contains as few as will give such and such results*. Hence
we can only say that such and such ideas are undefined in such and such
a system, not that they are indefinable. Following Peano, we shall call the
undefined ideas and the undemonstrated propositions primitive ideas and
primitive propositions respectively. The primitive ideas are explained by
means of descriptions intended to point out to the reader what is meant;
but the explanations do not constitute definitions, because they really involve
the ideas they explain.
In the present number, we shall first enumerate the primitive ideas
required in this section; then we shall define implication; and then we
shall enunciate the primitive propositions required in this section. Every
definition or proposition in the work has a number, for purposes of reference.
Following Peano, we use numbers having a decimal as well as an integral
part, in order to be able to insert new propositions between any two.
A change in the integral part of the number will be used to correspond
to a new chapter. Definitions will generally have numbers whose decimal
part is less than '1, and will be usually put at the beginning of chapters.
In references, the integral parts of the numbers of propositions will be
distinguished by being preceded by a star; thus "*1'01" will mean the
definition or proposition so numbered, and " 1" will mean the chapter in
which propositions have numbers whose integral part is 1, i.e. the present
chapter. Chapters will generally be called " numbers."
PRIMITIVE IDEAS.
(1) Elementary propositions. By an " elementary " proposition we mean
one which does not involve any variables, or, in other language, one which
does not involve such words as " all," "some," "the " or equivalents for such
words. A proposition such as "this is red," where " this " is something given
* The recognized methods of proving independence are not applicable, without reserve, to
fundamentals. Cf. Principles of Mathematics, ~ 17. What is there said concerning primitive
propositions applies with even greater force to primitive ideas.