But the antinomy thus effaced, another rises up under another form, and continues to exist indefinitely, as a series of equations always resolving into higher equations, incessantly approximating the total astronomical verity, towards which they tend interminably, without being able to reach it finally.

This is one of the manifestations of the infinite which we find everywhere. What man does in astronomy, he does in every aspect of life. He incessantly formulates himself in sentiments, thoughts and acts, which are so many diverse terms of the movement of his life, but which are never its extreme limit. For his life, incessantly gaining in activity by these progressive determinations, breaks successively the dead forms at the same moment that it assumes them, to emerge into new sentiments, ideas and acts, which it will again escape from in its unflagging and indefinite ascension.

Thus there opens out to man a magnificent prospect of advance in the acquisition of truth, beauty and goodness; for if these are three aspects of the Ideal, three indefinite realities never to be attained in their entirety, because by their nature they are infinite, the progress of man in science, art and virtue is without possible limit.

He can never arrive at the term of knowledge, never exhaust the circle of the sciences, he can never reach the boundary of the beautiful, but like the waves of the mighty sea, form after form of loveliness will break upon the shore of his perception, he will never attain the perfection of virtue, but goodness will present an infinite variety of modulations as the relations of men alter, so as to be always fresh, always new; the materials may be always the same, but the kaleidoscopic changes will be infinitely diversified. We say that science is in its infancy; it will never be

come decrepid, for if truth be infinite, there will always be new aspects of it to be discovered. Art cannot become worn out; from change to change it will alter its type, but each type will be beautiful, and none will be exhaustive. Goodness will be infinitely varied, as the social and political arrangements of men are permuted and afford openings for new varieties and combinations of goodness.

All this follows if we allow the Infinite, or God; if we do not allow Him, we fall into the bondage of the finite. But how are we to refuse to allow this, when we have within us the sentiment of the indefinite pointing to the infinite, and when without it, our existence becomes an enigma impossible of solution.

As I have said before, God's existence escapes demonstration; it is idle to ask reason to prove what is beyond its scope, for reason is the faculty of dealing with the finite. If we accept the existence of God, it will have to be as an axiom; but a necessary axiom, for the existence of the finite implies its contrary the infinite.

If the existence of the sentiment of the indefinite be objected to, I answer, have I not a sense of beauty, goodness and truth? can I not distinguish the beautiful from the ugly, the good from the evil, truth from falsehood? If I have, and no one can dispute this, then I have a second term leading to the third, the existence of God. From the finite I rise to the sense of the indefinite, and thence I arrive at the infinite which completes the problem. I have the opposite and the conciliatory "moments."

If I accept Hegel's hypothesis of the conciliation of antinomies, I cannot avoid the conclusion that God exists as the opposed pole to the world of finalities.

And what is more, without the idea of God, or the Infinite, science, art and morals are impossible. The sense

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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.

Let us take the exact sciences as an illustration. At 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 everywhere?

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 aesthetic 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. But 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: