The logical faculties are invariably those which in man are developed the most slowly and with the greatest difficulty. But they are also those which constitute the intellectual power of great nations. Without Aristotle, Plato, and Socrates, what had been ancient Hellas? Without Bacon, Locke, Newton, and Stuart Mill, what were modern England? Or Italy, without Galileo? And France, without Pascal, Descartes, Diderot, and Montesquieu? And Germany, without Fichte, Hegel, Kant, and Schlegel? The savage, however, possesses these faculties in a purely rudimentary condition. Analysis, synthesis, abstraction, generalization, are mental achievements which they cannot accomplish. They show themselves incapable, in fact, of the simplest calculations, of resolving easy arithmetical problems which are no mystery to the infants in our European infant-schools. Their numeration never goes beyond the safe and certain limit of their ten fingers; often they cannot compute above five, three, and even two. The Guarinis employ the expression "one hand" and "two hands" to designate _five_ and _ten_; other American tribes say "two men" instead of _forty_, because each man has twenty toes and fingers. Among most of the African negroes, numeration is quinary; it is ternary, or even binary, among the Australian aborigines. The savage knows nothing of art, nor of that feeling for beauty which is the essence of art. If he cultivates music, it is of so discordant a character, and so incongruous a medley of sounds, that no European can listen to it with patience. The gods which they fashion out of wood or clay, and to which they frequently offer human sacrifices, are of the utmost hideousness; and it is with difficulty the spectator can recognize in their rude outlines any likeness, however imperfect, to the models in man or beast which the sculptor has pretended to imitate. The want, or rather the depravation of taste, is shown in the choice of the ornaments with which they decorate their persons; in the tatooings with which they bespatter their bodies; in the unbecoming ornaments of every kind which they suspend to the nose, the lips, the ears, and which render monstrous the visage already ugly enough by nature.