202 SCIENTIFIC METHOD IN PHILOSOPHY 



the moon. But " one " is not a property of the moon 

 itself, which may equally well be regarded as many 

 molecules : it is a property of the general term " earth's 

 satellite." Similarly, o is a property of the general term 

 " satellite of Venus," because Venus has no satellite. 

 Here at last we have an intelligible theory of the 

 number o. This was impossible if numbers applied to 

 physical objects, because obviously no physical object 

 could have the number o. Thus, in seeking our definition 

 of number we have arrived so far at the result that 

 numbers are properties of general terms or general de- 

 scriptions, not of physical things or of mental occurrences. 

 Instead of speaking of a general term, such as " man," 

 as the subject of which a number can be asserted, we may, 

 without making any serious change, take the subject as 

 the class or collection of objects i.e. "mankind" in the 

 above instance to which the general term in question is 

 applicable. Two general terms, such as " man " and 

 " featherless biped," which are applicable to the same 

 collection of objects, will obviously have the same number 

 of instances ; thus the number depends upon the class, 

 not upon the selection of this or that general term to 

 describe it, provided several general terms can be found 

 to describe the same class. But some general term is 

 always necessary in order to describe a class. Even when 

 the terms are enumerated, as " this and that and the 

 other," the collection is constituted by the general pro- 

 perty of being either this, or that, or the other, and only so 

 acquires the unity which enables us to speak of it as one 

 collection. And in the case of an infinite class, enumera- 

 tion is impossible, so that description by a general charac- 

 teristic common and peculiar to the members of the class 

 is the only possible description. Here, as we see, the 

 theory of number to which Frege was led by purely logical 



