A second unit, added to the first, is in reality the beginning of all numeration and the foundation of arithmetic. As there are human races that have never gone further, we need not be surprised if animals stop there. But they do not stop there. They go on from this by successive additions, while we have reached the stage of multiplication, and have framed arbitrary systems of numeration, and have thus made of calculation an art founded on ideal notions. Animals, on the other hand, have a concrete notion of numbers more highly developed than we suppose, and perhaps more highly developed than it is with us, in proportion as abstraction is less easy with them. We need not suppose that the animal is destitute of all abstract notions and incapable of all generalization. Far from it; but the general notions being made of resemblances and the individual notions of differences, it is more struck than we are by individual characteristics. In this it again approaches the child and the savage, neither of whom has the generic notion of man. The child has the individual notion of its mother or its nurse, whom it distinguishes from all other persons around; but the generic notion, composed of all the common traits of the persons around, is of slow growth. The languages of savages are, for the most part, wanting in words for tree or animal, to comprehend the class, but have definite names for all the trees and animals that are useful to the tribe, or which they fear. We, therefore, may affirm that the dog has no generic idea of man, animal, or plant, but only ideas of particular men, particular women or children; and that every species, whether of animal or plant, is thought of by it as a representation of its individual figure, with all the differences that distinguish it from the others that it has seen. Our imagination by itself can not bring up the idea of an animal or plant which is not a particular animal or plant; and any effort we may make in this direction will end in there passing through the mind a succession of images of different animals and plants. If the use of generic names is taken from us, the general notion will go with it.
In the absence of articulate and descriptive language, and there being no object competent to serve us as a phonetic and auditive representation, we would think directly of things by a kind of precise interior view that permits no error or verbal sophism, and not as by a kind of internal audition that tends to replace things by their names, that makes us speak our thought within ourselves before speaking it aloud, and which we mistake as well as deceive others, when the interior definition which we give to the words does not correspond with the thing defined. It is especially difficult, in the absence of a common language between man and the animal, to make the latter comprehend what we require from it, and the object of the acts which we solicit it to perform. The
