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having abandoned the abstractions of pure Realism and pure Mysticism, we went on, at the last time, to the study of a Third Conception of Being. We saw at all events how vain it is for any one to assume that, if you doubt metaphysical Realism, if you question whether the world can be real independently of knowledge, of ideas, and of definition, you must necessarily be a mere sceptic, and believe in no authority whatever, and in no world at all. On the contrary, as we saw, even ordinary conversation is full of assertions that objects have genuine Being which are explicitly not objects independent of experience, or of definition, or of ideas. Such supposed genuine beings, which are still not realistic entities, we found exemplified by the prices, debts, and credits of the commercial world, by analogous facts in the world of valid social estimates, and by the moral law. And then, passing from common sense to science, we pointed out the still more marvellous types of existence that people the eternal fairyland of mathematical construction. We saw how the mathematical entities appear to have all the variety, the stubbornness, and the frequently unexpected characters which, in the ordinary world, are said to belong to real beings. The mathematician’s realm is in one