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.”

Mathematics seems to have a value for Mr. Russell akin to that of religion.  It affords a sanctuary to which to flee from the world, a heaven suffused with a serene radiance and full of a peculiar sweetness and consolation.  “Real life,” he writes, “is to most men a long second-best, a perpetual compromise between the ideal and the possible; but the world of pure reason knows no compromise, no practical limitations, no barrier to the creative activity embodying in splendid edifices the passionate aspiration after the perfect from which all great work springs.  Remote from human passions, remote even from the pitiful laws of nature, the generations have gradually created an ordered cosmos where pure thought can dwell as in its natural home, and where one, at least, of our nobler impulses can escape from the dreary exile of the actual world.”  This study is one of “those elements in human life which merit a place in heaven.”  “The true spirit of delight, the exaltation, the sense of being more than man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry.”

This enthusiastic language might have, I should think, an opposite effect upon some readers to that which Mr. Russell desires.  It might make them suspect that the claim to know an absolute ideal necessity, so satisfying to one of our passionate impulses, might be prompted by the same conceit, and subject to the same illusion, as the claim to know absolute truth in religion.  Beauty, when attributed to necessary relations between logical entities, casts a net of subjectivity over them; and at this net the omnivorous empiricist might be tempted to haul, until he fancied he had landed the whole miraculous draught of fishes.  The fish, however, would have slipped through the meshes; and it would be only his own vital emotion, projected for a moment into the mathematical world, that he would be able to draw back and hug to his bosom.  Eternal truth is as disconsolate as it is consoling, and as dreary as it is interesting:  these moral values are, in fact, values which the activity of contemplating that sort of truth has for different minds; and it is no congruous homage offered to ideal necessity, but merely a private endearment, to call