THE most noteworthy reformation of recent years in logic is the discovery and development by Mr. Bertrand Russell of the fact that the paradoxes-of Burali-Forti, Russell, Konig, Richard, and others-which have appeared of late years in the mathematical theory of aggregates and have just been referred to, are of an entirely logical nature, and that their avoidance requires us to take account of a principle which has been hitherto unrecognized, and which renders invalid several well-known arguments in refutation of scepticism, agnosticism, and the statement of a man that he asserts nothing.