but also, as we saw, of even the Third Conception of Being.
For if one asserts, as his account of the nature of Being, that certain ideas of possibilities of experience are valid, he is so far left with a world of objects upon his hands whose only character, so far as he yet defines the Being of these objects, is that these objects are in agreement with his ideas. Such a definition of Being constituted the whole outcome of the Third Conception. The mathematician’s ideas, as present to himself, take the form of observed symbols and diagrams. These, so far as they are observed, are contents of experience fulfilling purpose. They so far conform to our definition of what constitutes an idea, for they have internal meaning. But the existent objects concerning which the mathematician endeavors to teach us, are, by hypothesis, not the symbols, and not the diagrams, but valid truths to which these diagrams and symbols — these mathematician’s ideas — correspond. The existences of the mathematician’s realm are other than his mere finite ideas. Now that such objects have their place in reality, I myself thoroughly believe. But I point out that their reality, the true Being of these objects, is in no wise defined when you merely speak of the ideas as nothing but valid, because the assertion of validity is so far merely the assertion of a correspondence between a presupposed idea and its assumed object, without any account as yet either of the object, or of the truth of the idea. And bare correspondence, the mere possession of common characters in idea and in object not only fails to define, but, as we now see, can never lead us to define,
