trouble was that mechanical repetition of Aristotle's formulae as matters of course inevitably led to loss of real insight into the meaning the formulae had borne for Aristotle. We may say, generally, that because Traditionalism is the death of sound thinking, the ages in which the prospects of advance in Philosophy are brightest are just those in which a powerful historical tradition has broken down and men feel themselves compelled to go back on their steps and raise once more the fundamental questions which their fathers had supposed to be disposed of once for all by a formula. This has happened twice since the downfall of the degenerate Scholasticism, Protestant and Roman, of the sixteenth century. In the seventeenth century the result was the great movement in Philosophy, Mathematics, and Physics, of which Descartes and Galileo are the principal figures. Towards the end of the eighteenth century, when the doctrines of Descartes had themselves been traditionalized, the same thing happened again, the leading actors in the drama being David Hume and Immanuel Kant; the result was first the revival of the 'critical' problem by Kant, and then the great, if over-hasty, attempt at a positive interpretation of the Universe which culminated in the philosophical system of Hegel. In our own age, it is mainly Kant and Hegel who have been traditionalized, and we seem to be living through the last stages of the discrediting of this third tradition with every prospect of a great advance if our own time can only find its Descartes. In what I am going on to say I must naturally speak of the disintegrating influences chiefly as we have seen them at work in our own country; but I should like, before I do so, to remark that on the Continent splendid work has been done in the requickening of genuine philosophical thought by an influence which has, so far, not made itself widely felt among ourselves. I mean the revival of Thomism so earnestly promoted in the academies of the Roman Church by Pope Leo XIII. Neo-Thomism, I am convinced, if its representatives will only maintain it at the high level characteristic, for example, of the Italian _Rivista Neo-Scolastica_, has a very great contribution to make to the Philosophy of the future, and is much more deserving of the serious attention of students in our own country than the much-advertised 'impressionism' of Pragmatists and Bergsonians. Indeed, I hardly know how much we may not hope from the movement if it should please Providence to send into the world a Neo-Thomist who is also a really qualified mathematician.