can attach to the word fact, and how ill those appreciate truth who suppose an object disposed of by relegating it to the world of “pure ideas.” An important elementary lesson in metaphysics comes when we liberalize somewhat our notions of what it is to be, not only by examining the various senses in which the word has been used, but by following these senses into the various sorts of examples which make their variety first really appreciated.
Nor are the foregoing the only marks of an ontological, or, so to speak, substantial character about the world of mathematical fact. A very extended, but recently very rapidly growing, series of developments in this mathematical realm tends constantly afresh to show the marvellous character of the world of validity by revealing unexpected unities and connections amongst those of its facts and laws which have been the result of seemingly quite independent definition, and which have been reached in the course of researches that originally had no connection whatever.
VII
By this long series of instances of our third type of real beings, I have meant to show that there are reasons why a philosophical conception, specially planned to meet such cases, should be attempted as a conception of the meaning of the ontological predicate. The obvious contrast between beings of this type and the beings of technical realism proper, in our former sense of that word, is that the entities of the metaphysical realist are supposed to be what they are quite independently of any knowledge, actual, or even possible, which may be supposed,
