[.Presented to the Texas Academy of Science May 1, 1896.'] 
THE ESSENCE OF NUMBER. 
BY DR. GEORGE BRUCE HALSTED. 
Numbei' is primarily a quality of an artificial individual. By artificial 
is meant “ of human make.” The characteristic of these artificial indi¬ 
viduals is that each, though made an individual, is conceived as con¬ 
sisting of other individuals. In language the designations for artificial 
individuals so characterized usually contain other connotation. Exam¬ 
ples are a flock, a herd, a bevy, a covey, a throw, a flight, a swarm, a 
school, a pack, a bunch, a cluster, a drove, a company, a brood, a group, 
etc. To any such artificial individual pertains an important quality, its 
“Anzahl,” which may agree or differ among such artificial individuals, 
as may their color. But something like color is made and recognized by 
insects and animals, so that color is not so highly artificial as number, 
but will serve for an illustration. Just as the color of a bunch of grapes 
might be identified by use of a card of standard colors, and so a partic¬ 
ular descriptive color name attached to the bunch, in the same way by a 
well-known process of identification its “Anzahl” may be determined 
and the proper descriptive name attached. This particular process of 
identification is called counting, and used originally the standard set of 
artificial individuals makable from the fingers. 
The creation of artificial individuals having this numeric quality, 
“Anzahl,” the creation of number of necessity preceded counting, which 
is only a subsequent process for identification, for finding the “Anzahl” 
where it is already known to be. 
Number is so peculiarly human a creation that it might be used as an 
argument for the unity of mankind. Man has found it advantageous 
to perceive in nature distinct things, the primitive individuals. Each 
distinct thing is a whole by itself, a unit. The primitive individual 
thing is the only whole or distinct object in nature. But the human 
mind takes primitive individuals together and makes of them a single 
whole, an artificial individual, and names it. These are artificial units, 
discrete magnitudes. The unity is wholly in the concept, not in nature. 
It is of human make. 
From the contemplation of the primitive individual in relation to the 
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