the existence of qualities in things, but what determines is the real substance of what exists, so that each thing is essentially just its having in it unity, duality, as also their antithesis and connection. Aristotle (Met. I. 5, 6) puts it clearly thus: “It is characteristic of the Pythagoreans that they did not maintain the finite and the infinite and the One, to be, like fire, earth, &c., different natures or to have another reality than things; for the Infinite and the abstract One are to them, the substance of the things of which they are predicated. Hence too, they said, Number is the essence of all things. Thus they do not separate numbers from things, but consider them to be things themselves. Number to them is the principle and matter of things, as also their qualities and forces;” hence it is thought as substance, or the thing as it is in the reality of thought. These abstract determinations then became more concretely determined, especially by the later philosophers, in their speculations regarding God. We may instance Iamblichus, for example, in the work _θεολογούμενα ἀριθμητικῆς_, ascribed to him by Porphyry and Nicomachus. Those philosophers sought to raise the character of popular religion, for they inserted such thought-determinations as these into religious conceptions. By Monas they understood nothing other than God; they also call it Mind, the Hermaphrodite (which contains both determinations, odd as well as even), and likewise substance, reason, chaos (because it is undetermined), Tartarus, Jupiter, and Form. They called the duad by similar names, such as matter, and then the principle of the unlike, strife, that which begets, Isis, &c.