“You have appropriated to yourself a place in the Infinite of Number; you have fitted it to your own proportions by creating (if indeed you did create) arithmetic, the basis on which all things rest, even your societies.  Just as Number—­the only thing in which your self-styled atheists believe—­organized physical creations, so arithmetic, in the employ of Number, organized the moral world.  This numeration must be absolute, like all else that is true in itself; but it is purely relative, it does not exist absolutely, and no proof can be given of its reality.  In the first place, though Numeration is able to take account of organized substances, it is powerless in relation to unorganized forces, the ones being finite and the others infinite.  The man who can conceive the Infinite by his intelligence cannot deal with it in its entirety; if he could, he would be God.  Your Numeration, applying to things finite and not to the Infinite, is therefore true in relation to the details which you are able to perceive, and false in relation to the Whole, which you are unable to perceive.  Though Nature is like unto herself in the organizing force or in her principles which are infinite, she is not so in her finite effects.  Thus you will never find in Nature two objects identically alike.  In the Natural Order two and two never make four; to do so, four exactly similar units must be had, and you know how impossible it is to find two leaves alike on the same tree, or two trees alike of the same species.  This axiom of your numeration, false in visible nature, is equally false in the invisible universe of your abstractions, where the same variance takes place in your ideas, which are the things of the visible world extended by means of their relations; so that the variations here are even more marked than elsewhere.  In fact, all being relative to the temperament, strength, habits, and customs of individuals, who never resemble each other, the smallest objects take the color of personal feelings.  For instance, man has been able to create units and to give an equal weight and value to bits of gold.  Well, take the ducat of the rich man and the ducat of the poor man to a money-changer and they are rated exactly equal, but to the mind of the thinker one is of greater importance than the other; one represents a month of comfort, the other an ephemeral caprice.  Two and two, therefore, only make four through a false conception.

“Again:  fraction does not exist in Nature, where what you call a fragment is a finished whole.  Does it not often happen (have you not many proofs of it?) that the hundredth part of a substance is stronger than what you term the whole of it?  If fraction does not exist in the Natural Order, still less shall we find it in the Moral Order, where ideas and sentiments may be as varied as the species of the Vegetable kingdom and yet be always whole.  The theory of fractions is therefore another signal instance of the servility of your mind.