Nietzsche's so-called "real world" is one ideal among many others. It is as much subjective as the ideals of other mortals,--of men who seek happiness in wealth, or in pleasures, or in fame, or in scholarship, or in a religious life--all of them imagine that the world of their thoughts is real and the goal which they endeavor to reach is the only thing that possesses genuine worth. In Nietzsche's opinion all are dreamers catching at shadows, but the shadow of his own fancy appeared to him as real. According to Nietzsche the universe is not a cosmos but a chaos. He says (_La Gaya Scienza_, German edition, p. 148): "The astral order in which we live is an exception. This order and the relative stability which is thereby caused, made the exception' of exceptions possible,--the formation of organisms. The character-total of the world is into all eternity chaos, not in the sense of a missing necessity, but of missing order, articulation, form, beauty, wisdom, and as all our æsthetic humanities may be called." In agreement with this conception of order, Nietzsche says of man, the rational animal: "I fear that animals look upon man as a being of their own kind, which in a most dangerous way has lost the sound animal-sense,--as a lunatic animal, a laughing animal, a crying animal, a miserable animal." (_La Gaya Scienza_, German edition, p. 196.) If reason is an aberration, the brute must be superior to man and instinct must range higher than logical thought. Man's reason, according to this consistent nominalist view, is purely subjective and has no prototype in the objective world. This is a feature common to all nominalistic philosophies. John Stuart Mill regards the theorems of logic and mathematics, not only not as truths, but as positive untruths. He says: "The points, lines, circles, and squares, which any one has in his mind, are (I apprehend) simply copies of the points, lines, circles, and squares which he has known in his experience. Our idea of a point, I apprehend to be simply our idea of the _minimum visibile_, the smallest portion of surface which we can see. A line, as defined by geometers, is wholly inconceivable. We can reason about a line as if it had no breadth; because we have a power, which is the foundation of all the control we can exercise over the operations of our minds; the power, when a perception is present to our senses, or a conception to our intellects, of attending to a part only of that perception or conception, instead of the whole. But we cannot conceive a line without breadth; we can form no mental picture of such a line: all the lines which we have in our minds are lines possessing breadth."