It is a belief in one god as
distinct from the belief in several gods. In other words, it applies to
God the mathematical concept of unity, a concept which can only come
into cognition by virtue of contrasts and determinations, and which
forces therefore the believer either to Pantheism or anthropomorphism to
reconcile his belief with his reason. No other resource is left him.
With monotheism there must always be the idea of numerical separateness,
which is incompatible with universal conceptions.

Let him, however, clear his mind of the current admiration for
monotheisms, and impress upon himself that he who would form a
conception of supreme intelligence must do so under the rules of pure
thought, not numerical relation. The logical, not the mathematical,
unity of the divine is the perfection of theological reasoning. Logical
unity does not demand a determination by contrasts; it conveys only the
idea of identity with self. As the logical attainment of truth is the
recognition of identities in apparent diversity, thus leading from the
logically many to the logically one, the assumption of the latter is
eminently justified. Every act of reasoning is an additional proof of
it.[188-1]

Nor does the duality of nature and thought, to which I have alluded, in
any wise contradict this. In pure thought we must understand the
dichotomic process to be the distinction of a positive by a privative,
both logical elements of the same thought, as I have elsewhere shown.
The opposites or contraries referred to as giving rise to the dualistic
conceptions of divinity are thus readily harmonized with the conception
of logical unity. This was recognized by the Hindoo sage who composed
the Bhagavad Gita, early in our era. Krishna, the Holy One, addressing
the King Ardjuna says: "All beings fall into error as to the nature of
creation, O Bharata, by reason of that delusion of natural opposites
which springs from liking and disliking, oh thou tormentor of thy
foes!"[189-1]

The substitution of the conception of mathematical for logical unity in
this connection has left curious traces in both philosophy and religion.
It has led to a belief in the triplicate nature of the supreme Being,
and to those philosophical triads which have often attracted thinkers,
from Pythagoras and Heraclitus down to Hegel and Ghiberti.

Pythagoras, who had thought profoundly on numbers and their relations,
is credited with the obscure maxim that every thought