258 THE POPULAR SCIENCE MONTHLY. 



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 sur- 

 prised 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 com- 

 mon traits of the persons around, is of slow growth. The lan- 

 guages 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 indi- 

 vidual 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 aud 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 soph- 

 ism, 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 



