4. POSITIVE EXPOSITION OF THE DOCTRINE OF IDEAS.—Ideas may be defined according to the different sides of their historical connection, as the common in the manifold, the universal in the particular, the one in the many, or the constant and abiding in the changing. Subjectively they are principles of knowing which cannot be derived from experience they are the intuitively certain and innate regulators of our knowledge. Objectively they are the immutable principles of being and of the phenomenal world, incorporeal and simple unities which have no relation to space, and which may be predicated of every independent thing. The doctrine of ideas grew originally out of the desire to give a definite conception to the inner essence of things, and make the real world conceivable as a harmoniously connected intellectual world. This desire of scientific knowledge Aristotle cites expressly as the motive to the Platonic doctrine of ideas. “Plato,” he says (_Metaph._ XIII. 4), “came to the doctrine of ideas because he was convinced of the truth of the Heraclitic view which regarded the sensible world as a ceaseless flowing and changing. His conclusion from this was, that if there be a science of any thing there must be, besides the sensible, other substances which have a permanence, for there can be no science of the fleeting.” It is, therefore, the idea of science which demands the reality of ideas, a demand which cannot be granted unless an idea or conception is also the ground of all being. This is the case with Plato. According to him there can be neither a true knowing nor a true being without ideas and conceptions which have an independent reality.