what is animal and fundamental in it, else we shall give a false place, and too loud an emphasis, to our definitions of the ideal. However, it would be much worse not to reach the ideal at all, or to confuse it for want of courage and sincerity in uttering our true mind; and it is in uttering our true mind that Mr. Russell can help us, even if our true mind should not always coincide with his. In the following pages I do not attempt to cover all Mr. Russell's doctrine (the deeper mathematical purls of it being beyond my comprehension), and the reader will find some speculations of my own interspersed in what I report of his. I merely traverse after him three subjects that seem of imaginative interest, to indicate the inspiration and the imprudence, as I think them, of this young philosophy. II. THE STUDY OF ESSENCE "The solution of the difficulties which formerly surrounded the mathematical infinite is probably," says Mr. Russell, "the greatest achievement of which our own age has to boast.... It was assumed as self-evident, until Cantor and Dedekind established the opposite, that if, from any collection of things, some were taken away, the number of things left must always be less than the original number of things. This assumption, as a matter of fact, holds only of finite collections; and the rejection of it, where the infinite is concerned, has been shown to remove all the difficulties that hitherto baffled human reason in this matter." And he adds in another place: "To reconcile us, by the exhibition of its awful beauty, to the reign of Fate ... is the task of tragedy. But mathematics takes us still further from what is human, into the region of absolute necessity, to which not only the actual world, but every possible world, must conform; and even here it builds a habitation, or rather finds a habitation eternally standing, where our ideals are fully satisfied and our best hopes are not thwarted. It is only when we thoroughly understand the entire independence of ourselves, which belongs to this world that reason finds, that we can adequately realise the profound importance of its beauty."