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

*12. THE HIERARCHY OF TYPES AND THE AXIOM OF REDUCIBILITY.
The primitive idea " (x). Ox" has been explained to mean " fx is always
true," i.e. "all values of Ox are true." But whatever function 4 may be,
there will be arguments x with which Ox is meaningless, i.e. with which as
arguments q does not have any value. The arguments with which Ox has
values form what we will call the " range of significance " of Ox. A " type "
is defined as the range of significance of some function. In virtue of *9 14,
if Ox, Oy, and frx are significant, i.e. either true or false, so is fry. From
this it follows that two types which have a common member coincide, and
that two different types are mutually exclusive. Any proposition of the
form (x). Ox, i.e. any proposition containing an apparent variable, determines
some type as the range of the apparent variable, the type being fixed by the
function (.
The division of objects into types is necessitated by the vicious-circle
fallacies which otherwise arise*. These fallacies show that there must be
no totalities which, if legitimate, would contain members defined in terms of
themselves. Hence any expression containing an apparent variable must not
be in the range of that variable, i.e. must belong to a different type. Thus
the apparent variables contained or presupposed in an expression are what
determines its type. This is the guiding principle in what follows.
As explained in *9, propositions containing variables are generated from
propositional functions which do not contain these apparent variables, by the
process of asserting all or some values of such functions. Suppose fa is a
proposition containing a; we will give the name of generalization to the
process which turns fa into (x). Ox or (3x). Ox, and we will give the name
of generalized propositions to all such as contain apparent variables. It is
plain that propositions containing apparent variables presuppose others not
containing apparent variables, from which they can be derived by generalization. Propositions which contain no apparent variables we call elementary
propositionst, and the terms of such propositions, other than functions, we call
individuals. Then individuals form the first type.
* Cf. Introduction, Chapter II.
+ Cf. pp. 95, 96.