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 previously given, an analysis of the formal law itself does not yield these elements. They belong to a certain class of values assigned it, not to the law itself; hence it is only when deity is conceived under the conditions of numerical oneness that the tripartite constitution of a whole number makes itself felt, and is applied to the divine nature. The essence of a logical unit is identity, of a mathematical, difference. The qualities of the latter are limitations--_so much of a thing_; those of the former are coincidences--_that kind of a thing_.