from experience, had validity for the whole universe, independent of the boundaries of our experience. Mill, himself, thought, as is well known, that even the propositions of algebra and of geometry, whose empiric origin he endeavored to establish, could only be sure of a limited dominion. He extolled to me the little book "Essays by a Barrister," from which he himself quoted a few sentences. The barrister finds it quite conceivable that our multiplication-table, as well as our Euclid, may be utterly valueless in another solar system. "The question is," he says, "whether our certainty of the truth of the multiplication table arises from experience or from a transcendental conviction, excited by experience, but anterior to and formative of it." To illustrate the former of these views he presents a few striking examples:-- "There is a world in which, whenever two pairs of things are either placed in proximity or are contemplated together, a fifth thing is immediately created, and brought within the contemplation of the mind engaged in putting two and two together. This is surely neither inconceivable, for we can readily conceive the result by thinking of common puzzle tricks, nor can it be said to be beyond the power of Omnipotence, yet, in such a world, surely two and two may be five; that is, the result to the mind of contemplating two twos would be to count five. This shows that it is not inconceivable that two and two might make five; but, on the other hand, it is perfectly easy to see why in this world we are absolutely certain that two and two make four. There is probably not an instant of our lives, in which we are not experiencing the fact. We see it whenever we count four books, four tables or chairs, four men in the street, or the four comers of a paving stone, and we feel more sure of it than of the rising of the sun to-morrow, because our experience upon the subject is so much wider, and applies to such an infinitely greater number of cases. Nor is it true that every one who has once been brought to see it is equally sure of it. A boy who has just learned the multiplication table is pretty sure that twice two are four, but is often extremely doubtful whether or not seven times nine are sixty-three. If his teacher told him that twice two made five, his certainty would be greatly impaired.