in whom the real objects of science are open to the soul's contemplation. The soul must detach itself from the body and all material things, ascend by its love and contemplation to the empyreum it originally inhabited, and there contemplate in calm spiritual repose the first Good, the first True, and the first Fair. Or, in other words, the soul must enter into itself, and silently contemplate its own reminiscences of that ideal world from which it has been exiled. Setting aside the doctrine of reminiscence founded on Plato's doctrine of the pre-existence of souls, there is no doubt a shadow of truth in this; but it would then resolve the dialectic method into the contemplative, and assert that the object obtained is obtained by intuition, not by induction. M. Gratry must reject the doctrine of reminiscence, and therefore, it seems to us, must mean by the dialectic or inductive method, as distinguished from the syllogistic or deductive method, that of simple contemplation; in which case all he says of the infinitesimal calculus avails him nothing.

But contemplation of what? Of God? Then he must concede that we apprehend God intuitively, or at least apprehend intuitively that which is God. But this he seems to deny, or to be afraid to assert. Of the creature, or the finite, as he would seem to hold? Then he attains to a knowledge of God, if at all, by reasoning, and by reasoning which in no respect differs from the syllogistic or deductive reasoning, which he rejects. He says we dart at once from the finite to the infinite by mentally suppressing all conception. of bounds and limitations, as in the infinitesimal calculus; that is, by abstraction of the finite, and consequently by deduction, or syllogistic reasoning. But this is not all. If the author means by our darting at once to the infinite, that the infinite is immediately and simultaneously apprehended in the apprehension of the finite, we accept it, but the process is then intuitive, not dialectic. But if he means, as it would seem, that we attain to the infinite by a process, however rapid, of abstraction, his infinite is only an abstract infinite. Abstract from the finite its finiteness, or suppress mentally its bounds and limitations, and you suppress the finite altogether, annihilate the whole object, and there remains not the infinite, as supposed, but simply nothing.

M. Gratry professes to adopt the method of the geom

etricians, and says formally, that the process by which all men, learned and unlearned, philosophers and poets, attain to a knowledge of God, is precisely the method of which the infinitesimal calculus, invented by Leibnitz, is a special application. He labors at great length to prove that the demonstration of the existence of God is strictly geometrical. In this consists the original and novel part of his work. Others have indeed asserted it, but he is the first who has demonstrated it. But, with all deference to the learned and scientific author, we must say that the God he demonstrates by his geometrical process is simply zero. Mathematics is a mixed science, at once ideal and empirical. The mathematical infinities belong to the ideal, and the ideal is always God as the intelligible; for, as M. Gratry well maintains, the infinite is God, and there is no infinite separate or distinguishable from him. bottom of all your mathematical infinities, as the plane, so to speak, on which they are projected, is the intuition or conception of God, without whom they could not be conceived. Take away from the human mind the intuition of God, which accompanies all its conceptions as their ideal element, and the infinitesimal calculus would not only be an error, as Berkeley maintains that it is, but an impossible error; for there is and can be out of God no infinitely little or infinitely great, even in thought. St. Thomas, we believe, somewhere says, an atheist may be a geometrician, but without God there can be no geometry. We will add, that without the intuition of God as infinity no man can be a geometrician. Having through that intuition the conception of the infinite God, the conception of the infinitely real, we can speak of mathematical infinities, for in so doing we only make a special application of that conception. But these infinities are purely ideal, not empirical, and aside from their reality in the essence, wisdom, or power of God, not distinguishable from God himself, they are nothing, simply zero. But as we always have that conception, though we do not always take note that it is conception of God, we take it into our heads that mathematical infinities are something, and conceivable outside of God, which it is certain they are not. The suppression, empirically considered, of all bounds, limitations, or fixed, definite, or determinable quantity, gives us not infinity, but simply zero, which is nothing at all. Between

zero and a determinable number, between nothing and something, there is no medium. Zero multiplied or divided by zero gives simply zero, and hence, regarded in the concrete order, the infinitesimal calculus of Leibnitz, as the fluxions of Newton, is only a superb error, and harmless mathematically only where the error is equal on both sides, which is by no means always the case. Mathematicians do not detect its fallacy, because there is in their minds the intuition of the real infinite, in which their imaginary infinities have, so to speak, a basis or support.

But M. Gratry cannot have so much as this, for he professes to dart from the finite to the infinite without a previous intuition of the infinite, by simply suppressing or disregarding in the finite apprehended its bounds, limitations, or determinable quantity. But this is a complete abstraction of the finite, and the remainder is simply zero, not only empirically but even ideally; for the very conception of the finite is the conception of a fixed or definite quantity. Remove that conception, and nothing remains; for, according to the hypothesis, there is no previous or concomitant intuition of the infinite which, as in mathematics, survives, so to speak, the suppression, in thought, of the finite or determinable quantity. M. Gratry, then, by his process, that of abstracting the finite or disregarding the determinable, attains for his God simply zero, das nichtseyn, and, strangely enough, finds himself in perfect accord with Hegel, whom he ridicules without mercy. It would perhaps not be difficult to show that his dialectic method is at bottom identically the constructive method of the Hegelians. We must say, therefore, and we do so with profound respect, that we do not think he has added anything valuable to philosophy or theodicy by his geometrical demonstration, for the alleged demonstration, strictly taken, is an error even in geometry, inasmuch as it starts with the assumption that zero is not nothing, but something.

It may be our own blindness and stupidity, but we confess that we do not understand how there are or can be two distinct methods of reasoning, and we have never yet been able to see wherein Aristotle erred when he termed induction an imperfect syllogism. Reason has two very distinct modes of operation, which we term intuition and reasoning or ratiocination. It is intuitive and discursive. But all discursion, all reasoning, is, as far as we are able

to understand it, syllogistic; and all induction, in so far as it is a logical process at all, may be reduced to a regular syllogism, as all the old masters of logic have taught. We agree entirely with M. Gratry, that we do not and cannot obtain our principles by syllogistic reasoning, for the principles must be given prior to reasoning. The office of the syllogism is not to discover new principles, or to extend science to new matter, but to clear up, systematize, and confirm what in some form is already held by the mind. Principles, or the matter from which and on which the syllogism operates, must be furnished prior to and independent of it. These, according to Plato, the soul brings with it, and are reminiscences of its knowledge in its pre-existing state, or previous life; according to us, they are furnished objectively by intuition, and reach us through simple intuitive apprehension. To extend our knowledge in this direction, Plato recommended silence and recollection. We recommend tranquil contemplation, or observation. Beyond these two methods, which differ from one another only as seeing or beholding differs from remembering, we are unable to conceive any other. A dialectic or inductive method, which is neither intuitive nor syllogistic, we cannot understand, and a logical process distinguishable from intuition, by which the reason can be furnished with principles, is to us inconceivable. M. Gratry is frequently on the verge of the truth, but seems either not to apprehend it, or to fear to assert it. What he wants is, to perceive that what he calls dialectic is, so far as distinguishable from the syllogistic, intuitive, and that the infinite is affirmed to us in direct intuition; not attained by a logical process, or by way of abstraction of the finite. He is probably afraid to do this, because our theologians have, as it were, appropriated the term intuition of God to express the beatific vision of the Blest, the vision of God in his essence, or as he is in himself, which is not naturally possible, and is attainable only by the supernatural light of glory. He fears, most likely, that, were he to say that we have intuition of God here, he would fall into a condemned heresy, and be thought to teach that we are naturally capable of the beatific vision, and may even naturally enjoy it on earth. But we think this fear is groundless. To have intuition of God as the ideal, the intelligible, is, in our judgment, something very different

from having intuition of him as he is in himself, or in his essence, and we think may be asserted without danger to faith; for it is asserted by St. Augustine, St. Bonaventura, Père Thomassin, and Cardinal Gerdil, and implied by St. Thomas, and in reality by M. Gratry himself.

Nevertheless, M. Gratry is not, as a matter of fact, deceived in supposing that, after suppressing the finite, he has not zero, but the infinite, present to his apprehension. His mistake lies in supposing that he in that way obtains it, or attains to a conception of it. The fact is, in every intuition we have direct and immediate intuition of both the infinite and the finite, of the necessary and the contingent, of God and the creature, and by disregarding or mentally suppressing the finite we only detach the infinite from the finite presented along with it in the same intuition, and turn our minds to its direct and distinct consideration. We do not thus obtain it originally, but we thus obtain it as a distinct conception. If we suppose the mind destitute of all intuition of the infinite, the method proposed by our author would give us simply zero, as we have said, not the infinite, for the infinite is not deducible from the finite; but since we really have all along the intuition, as a matter of fact the infinite by the suppression of the finite remains present to the mind, and is, what it was not before, distinctly apprehended. The fact is as the author asserts, but his account of it is not correct, for the idea is not obtained in the way he supposes. It is not obtained by his dialectical process; it is only made an object of distinct recognition and contemplation.

M. Gratry will permit us, however, to say, that he seems to us, throughout his work, to confound two things which in our judgment are very distinct; namely, the process by which we know that God is, with that by which we learn what he is. That God is, we know intuitively, in that we have direct and immediate intuition, of real and necessary being, which is God; but what he is, what are his moral attributes, and what are our relations to him, we learn only by a process similar to that which he calls the dialectic. His work is less a demonstration of the existence of God to those who deny it, than a discourse to advance in the knowledge and love of God those who, though they deny not that he is, have no lively sense of his existence, and seek their beatitude, not in loving and serving him, but in