is made up of a
definite one and an indefinite two (a ~monas~ and an ~aoristos duas~).
Some of his commentators have added to rather than lessened the darkness
of this saying. But applied to concrete number, it seems clear enough.
Take any number, ten, for example, and it is ten by virtue of being a
_one_, one ten, and because on either side counting upward or downward,
a different number appears, which two are its logical determinants, but,
as not expressed, make up an _indefinite two_.

So the number one, thought as concrete unity, is really a trinity, made
up of its definite self and its indefinite next greater and lesser
determinants. The obscure consciousness of this has made itself felt in
many religions when they have progressed to a certain plane of thought.
The ancient Egyptian gods were nearly all triune; Phanes, in the Orphic
hymns the first principle of things, was tripartite; the Indian
trinities are well known; the Celtic triads applied to divine as well as
human existence; the Jews distinguished between Jehovah, his Wisdom and
his Word; and in Christian religion and philosophy the doctrine of the
trinity, though nowhere taught by Christ, has found a lasting foothold,
and often presents itself as an actual tritheism.[190-1]

The triplicate nature of number, thus alluded to by Pythagoras, springs
from the third law of thought, and holds true of all concrete notions.
Every such notion stands in necessary relation to its privative, and to
the logical concept of next greater extension, _i. e._, that which
includes the notion and its privative, as I explained in the first
chapter. This was noted by the early Platonists, who describe a certain
concrete expression of it as "the intelligential triad;" and it has been
repeatedly commented upon by later philosophers, some of whom avowedly
derive from it the proof of the trinitarian dogma as formulated by
Athanasius. Even modern mathematical investigations have been supposed
to point to a _Deus triformis_, though of course quite another one from
that which ancient Rome honored. A late work of much ability makes the
statement: "The doctrine of the Trinity, or something analogous to it,
forms, as it were, the avenue through which the universe itself leads us
up to the conception of the Infinite and Eternal One."[191-1] The
explanation of this notion is the same as that of the "Trinity of the
Gentiles," always hitherto a puzzling mythological concept.

For reasons pre