REMAINING LAWS OF NATURE. 165 



What, then, is that which is connoted by a name 

 of number ? Of course some property belonging to 

 the agglomeration of things which we call by the 

 name ; and that property is, the characteristic manner 

 in which the agglomeration is made up of, and may 

 be separated into, parts. We will endeavour to make 

 this more intelligible by a few explanations. 



When we call a collection of objects two, three, or 

 four, they are not two, three, or four in the abstract ; 

 they are two, three, or four things of some particular 

 kind; pebbles, horses, inches, pounds weight. What 

 the name of number connotes is, the manner in which 

 single objects of the given kind must be put together, 

 in order to produce that particular aggregate. If the 

 aggregate be of pebbles, and we call it two, the name 

 implies that to compose the aggregate, one pebble must 

 be joined to one pebble. If we call it three, we mean 

 that one and one and one pebble must be brought 

 together to produce it, or else that one pebble must 

 be joined to an aggregate of the kind called two, 

 already existing. The aggregate which we call four 

 has a still greater number of characteristic modes of 

 formation. One and one and one and one pebble may 

 be brought together ; or two aggregates of the kind 

 called two may be united ; or one pebble may be 

 added to an aggregate of the kind called three. Every 

 succeeding number in the ascending series, may be 

 formed by the junction of smaller numbers in a 

 progressively greater variety of ways. Even limiting 

 the parts to two, the number may be formed, and 

 consequently may be divided, in as many different 

 ways as there are numbers smaller than itself; and, if 

 we admit of threes, fours, &c., in a still greater variety. 

 Other modes of arriving at the same aggregate present 

 themselves, not by the union of smaller, but by the 



