of the Infinite is to the human intelligence what the sun is to physical nature. If in imagination we extinguish the sun, the world falls into chaos and darkness. So is it with the idea of the Infinite. Suppress it, and man dies intellectually. If phenomenal light be the vital agent of visible creation, the notion of the infinite, or of sovereign perfection, is the invisible light, the life of the spiritual creation.

At

Let us take the exact sciences as an illustration. the point of departure of arithmetic is found, not, as is vulgarly explained, number, but that which is at every point inverse, unity, which lies at the root of all numbers, but which none of them can arrive at and equal. The unit is not engendered; it does not multiply itself, it is always itself its own sum and product. Multiplied or divided by itself, it gives itself alone; it cannot be multiplied or divided.

What revealed this mystery to our intelligence? Everything in this world is an effect, issues from father and mother, results from some previous combination; everything is indefinitely multipliable, and subject to the law of division; all changes; consequently nothing in the visible world could have given us the idea of the unit.

The immutable, unengendered, immultipliable, and indivisible unit is the infinite Being: thus the unity of God is at the commencement of the exact sciences, as it is at the root of all equations. When the genius of man broke through the bounds in which numbers held him captive, he placed in the midst of them the infinite, and progress opened out to him an unlimited perspective.

Upon the idea of the infinite geometry rests; for the line, from which all its formulæ are derived, starts from a point, an indivisible unit, without length, breadth, or depth, and which produces all; the invisible measuring all that is

visible, the indefinite of the thought which cannot be seen or felt, but which defines and gives shape to all bodies. In fact, geometry is the science of the forms of matter, and the idea of form is synonymous with that of limit. Thus from the unlimited limitation proceeds.

Algebra is only generalized arithmetic, and one may say of this phase of the science of numbers what was said of arithmetic itself. But what if we speak of the infinitesimal calculus, that synthesis of mathematics which has enabled them to make such giant strides, and which lives upon the idea of the infinite, or rather, of the indefinite, which operates on it alone, reveals it everywhere present, between all numbers, above and below them, in the cypher and in the fraction, in the indefinitely great and in the indefinitely small, in all equations and in all their relations, and which might be called science calculating the indefinite every

where ?

Thus, in the sciences which are called exact, and with which men have laboured, and labour still, to dethrone the supra-sensible verity, they are unable to do without it any more than in the moral and religious and æsthetic sciences. Everything is limited in creation; but athwart all limits intelligence divines the Infinite. In the phenomenal world there is incessant flux, but the eternal verity remains; it is the immutable axis of all science. Everything in the motions and actions of man is bounded, and nevertheless everything within him aspires to and supposes the infinite as his supreme end.

What is all creation but an aspiration towards what it presupposes, the Infinite, from the atom to the globes that revolve in space, from the mineral to the man? It is an always progressive ascent of life, by overstepping limit after limit, from the narrower to the larger; it is Hegel's processus.

The mineral life is an escape from the limit which separates atoms, simple bodies; vegetable life assimilates by intussusceptation that which in the mineral was only juxtaposed; another boundary is overthrown; animal life breaks through the limitation of place which tied the plant to one spot, and obtains the faculty of motion; and man in his intellectual life follows the same law, spiring upwards, forming and breaking the moulds he makes as they become too strait for his spirit.

That to which all things tend is universal unity; the means is the sentiment of the indefinite, which is nothing else but the Ego, or human personality itself, having cognizance of its own life as a movement of aspiration without limits towards the beautiful, the good, and the true. what is this aspiration but the sentiment of perfection in all things?

Our senses are impressed by the beings that compose the world; we are infallibly certain that there exist between us and them constant relations; but we do not find in these creatures the basis of our appreciations, the reason of the laws which govern them, or the relations that unite them. Nor is our own personality the rule or criterium of our judgments, though it is within us. If we attend to the process within ourselves, we discover that there is a criterium which is not ourselves, and which approves or rejects our decisions. This tribunal is the sentiment of perfection, or conscience of what is good, beautiful, and true; in the order of good it is what is commonly called conscience; in the order of arts it is the sense of the beautiful; in the intellectual order it is the conviction of truth; in the practical order it is justice; in logic it is the base and criterium of our premisses for concluding from the finite to the infinite. Under all these aspects, this sentiment implies three things:

a type of absolute perfection by which one compares everything upon which one is called to judge; a relation between this prototype and the object or being which is compared with it; and an act which judges of the relation of perfection in which one stands to the other.

The living type of absolute perfection is God. “Not only," said Descartes, " do I know that I am an imperfect being, incomplete and dependent on another, who tend and aspire incessantly towards something greater and better than I am; but I know at the same time that He from whom I depend possesses in Himself all those great things to which I aspire, not indefinitely and potentially, alone, but actually and infinitely, and that thus He is God."1

The act which affirms the relation between the divine type of absolute perfection and us, is ourselves in our liberty and free-will judging according to our reason, our will, and our sentiment.

And what is the relation, the axis uniting the type with the antitype, the positive with the negative pole?

What is that relation which touches on one side the infinite and on the other the finite, the absolute and the limited, spirit and matter?

That is what we shall answer when we speak of the Incarnate Word.

The good, the true, and the beautiful, are three faces of the same ideal of perfection, the Infinite. The good is not separable from the true, nor the true from the beautiful. They are distinct, yet indissolubly one. That which is good is also true and beautiful. That which is false cannot be good, nor can it be beautiful. That which is beautiful must be true and good. It is impossible to scind these distinct aspects of perfection. The philosopher seeking truth errs

1 Méditations, i. p. 290.

if he attempts to oppose what is certain to what is goodly. The artist is mistaken if he seeks beauty apart from truth; and what pure act of virtue is not marvellous in its loveliness!

The three sciences, ethics, logic, æsthetics, based on these three aspects of the Infinite, are therefore not to be separated and opposed, for they complement one another and complete what would otherwise be fragmentary.

In ethics, the conscience judges, according to a sliding scale; what it judges at one time to be admissible and good, it decides, as its experience grows, or as circumstances alter, to be inadmissible and bad. That which was right one day is wrong the next, for as conscience grows, its perception strengthens, and it discriminates with greater acuteness; its powers of analysis increase, not for the purpose of dividing and opposing, but for the purpose of reducing what is divided and opposed to unity.

Evil is the rejection of the infinite for the finite, the declension from one pole to the other, and perversion of the moral sense. When the infinite is lost sight of, the sentiment of the indefinite loses its character, and the science of ethics is at an end. Morality is impossible without a sense of the indefinite, and the sense of the indefinite supposes the infinite source of good, or God. How can there be morality without a law, and how can there be law without a lawgiver.

If we pass from conscience to the world of reason, we find that the cause of all error in the science of God, man and the universe, consists in oblivion or an insufficient notion of one of these three terms. Psychologists and ontologists have not clearly seen that the co-ordination of these three terms is necessary for the attainment of certainty. All, starting from one of these terms, by method of division, have ended in abstraction. In placing man outside of unity, they have placed him outside of life. The first have de