90 
TRANSACTIONS OF THE TEXAS ACADEMY OF SCIENCE. 
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 natural individual in relation to the 
artificial individual spring the related ideas “ one” and “ many.” 
A unit thought of in contrast to “many,” as not-many, gives us the 
idea one. A “ many” composed of “one” and another “ one” is char¬ 
acterized as two. A many composed of “one” and the special many 
“ two” is characterized as “ three.” But the young mind is very slow 
to pass from the knowledge of one and two on to the distinct recognition of 
the quality three. If I should judge from my two little boys, who 
should hereditarily be not inapt, their ancestors for four generations be¬ 
ing Princeton graduates, I would not be surprised if it took a year to 
pass naturally from a distinct recognition of one, two, and many, on to 
the equally distinct recognitiqn of three. 
Numerals applied thus each to a special kind of discrete magnitude are 
called cardinal numbers. Their names are easily learned by a child. He 
may repeat the names readily up to ten and beyond, long before he 
knows the quality three. 
Then teaching him to count, or pair each name with a natural unit of 
the specific artificial unit to be counted, we teach him to transfer to the 
artificial unit that name at which the count ends. 
Ordinals are these numeral words modified in form or sound and ap¬ 
plied successively each to a natural unit of the artificial unit. An or¬ 
dinal will designate a natural unit among the arranged natural units of 
an artificial unit or group. 
Number is a creation of the human mind, and only applies primarily 
to the artificial wholes created by the human mind—discrete aggregates. 
The numerical symbols are first pictures of all groupshaving the desig¬ 
nated quality; the freer from other qualities the better the symbol, since 
it is to symbolize something wholly abstract; it needs to represent the 
individual existence of the elements of the group, and nothing more; to 
that alone the numerical quality pertains. 
Just as a woman buying a ribbon, in order to convey the desired color, 
would produce a scrap having that color, so a savage would hold up 
three fingers in describing a group of bears he had seen. Such pictorial 
reproductions are the primitive numerals I, II, III, IIII, V. The numeral 
words are the names of the hand-pictures used in conveying the abstract 
numeric quality. 
In Eskimo “hand me” is tarn ut'che, “shake hands” is tal lalue, 
“bracelet” is tale gow'ruk, “five” is talema. 
Our word five is cognate with the Latin quinque, Greek pente , San¬ 
scrit pankan, Persian pendji; and in Persian penjeh or pentcha means 
an outspread hand. 
