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 Gità, 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 is made up of a definite one and an indefinite two (a μονας and an αοριστος δυας). 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 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.
To be sure it is no easy matter to free ourselves from the habit of confounding identity and individuality. We must cultivate a much greater familiarity with the forms of thought, and the character of universals, than every-day life requires of us, before the distinction grows facile. The individual, not the species, exists; our own personality, our thinking faculty is what we are most certain of. On it rests the reality of everything, the Unknown as well. But the rejection of a mathematical unity does not at all depreciate the force of such an argument. Individuality regarded as mathematical unity rests on the deeper law of logical identity from which the validity of numbers rises; it is not the least diminished, but intensified, in the conception of a Supreme Intelligence, as the font of truth, though the confinements and limitations of the mathematical unit fall away, and all contrasts disappear.
The reverse conception, however, has prevailed in religious systems, polytheistic or monotheistic. Man has projected on the cloudy unknown the magnified picture of his own individuality and shuddered with terror at the self-created plantasm, like the peasant frightened by the spectre of the Brocken, formed by the distorted image of himself. In his happier moments, with his hopes gratified, the same vice of thought, still active, prevented him from conceiving any higher ideal than his better self. “Everywhere the same tendency was observed; the gods, always exaggerations of human power and passions, became more and more personifications of what was most admirable and lovable in human nature, till in Christianity there emerged the avowed ideal man.” What could it end in but anthropomorphism, or pantheism, or, rejecting both, a Religion of Humanity, with a background of an imbecile Unknowable?
Is it necessary to point out how none of these conclusions can satisfy the enlightened religious sentiment? How anthropomorphism,which makes God in the image of man, instead of acknowledging that man is made in the image of God, belittles divinity to a creature of passions and caprices? How pantheism, increasing God at the expense of man, wipes out the fundamental difference of true and false, calls bad “good in the making,” and virtually extinguishes the sense of duty and the permanence of personality? And how the denial of all possible knowledge of the absolute digs away the only foundation on which sanity can establish a religion, and then palms off material comfort as the proper food for religious longing?