Maech 27, 1896.] 



SCIENCE. 



471 



card of standard colors, and so a particular 

 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 iden- 

 tification is called counting, and used ori- 

 gLually the standard set of artificial indi- 

 viduals makable from the fingers. 



The creation of artificial individuals hav- 

 ing this numeric quality, 'Anzahl', the crea- 

 tion of number of necessity preceded count- 

 ing, 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 artificial in- 

 dividual spring the related ideas ' one ' and 

 ' many.' A unit thought of in contrast to 

 ' many ' as hot-many gives us the idea one 

 or ' a one.' A ' many ' composed of ' a one ' 

 and another ' one ' is characterized as ' two'. 

 A many composed of ' a one ' and the 

 special many ' a two ' is characterized as 

 ' three. ' And so on, at first absolutely with- 

 out counting, in fact before the invention 

 of that patent process of identification now 

 called counting. The 'Anzahl ' of a group 

 is wholly abstract, in that it represents all 

 at once the primitive individuals or ele- 

 ments of the group or artificial individual, 

 and' nothing more. There never was and 



never will be a concrete number or any- 

 thing concrete about number. 



The number in the sense of 'Anzahl ' of a 

 group is a selective photograph of the group, 

 ,a numeric picture which takes or rep- 

 resents only one quality of the group, 

 but takes that all at once. This picture 

 process only applies primarily to those 

 particular artificial wholes which may be 

 called discrete aggregates. But these are 

 of inestimable importance for human life. 



This overwhelming importance of the 

 number-picture after centuries led to a 

 human invention as clearly a device of man 

 for himself as is the telephone. This was a 

 device for making a primitive individual 

 thinkable as a recognizable and recoverable 

 artificial individual of the kind having the 

 numeric quality. This is the recondite de- 

 vice called measurement. 



Measurement is an artifice for making a 

 primitive individual conceivable as an arti- 

 ficial individual of the group kind, and so 

 having an ' Anzahl,' a number picture. 



It may be likened to dyeing cotton 

 with analine dyes. This will give the 

 cotton a color which may then be identified 

 by comparison with the set of standard 

 colors. 



The height of a horse, by use of the arti- 

 ficial unit, a ' hand,' is thinkable as a dis- 

 crete aggregate and so has a number- picture 

 identifiable by comparison with the stand- 

 ard set of pictures, that is by counting, as 

 say 16. But to argue from this the implicit 

 presence of the measurement idea in every 

 number is the analogue of maintaining the 

 implicit presence of the process-of-dyeing 

 idea in every color. 



George Bruce Halsted. 



Austin, Texas. 



ROBERT EDWARD EARLL. 

 Mr. Eobert Edward Earll, who died on 

 March 18th, at ' Chevy Chase,' near Wash- 

 ington, was one of the oldest and most 



