THE POSITIVE THEORY OF INFINITY 201 



similarity between number and colour ; but this does not 

 consist in the fact that both are sensibly perceptible in 

 external things, but in the fact that both are objective ' 



(P- 34)- 



"I distinguish the objective," he continues, "from the 



palpable, the spatial, the actual. The earth's axis, the 

 centre of mass of the solar system, are objective, but I 

 should not call them actual, like the earth itself" (p. 35). 

 He concludes that number is neither spatial and physical, 

 nor subjective, but non-sensible and objective. This 

 conclusion is important, since it applies to all the subject- 

 matter of mathematics and logic. Most philosophers 

 have thought that the physical and the mental between 

 them exhausted the world of being. Some have argued 

 that the objects of mathematics were obviously not sub- 

 jective, and therefore must be physical and empirical ; 

 others have argued that they were obviously not physical, 

 and therefore must be subjective and mental. Both sides 

 were right in what they denied, and wrong in what they 

 asserted ; Frege has the merit of accepting both denials, 

 and rinding a third assertion by recognising the world 

 of logic, which is neither mental nor physical. 



The fact is, as Frege points out, that no number, not 

 even 1, is applicable to physical things, but only to general 

 terms or descriptions, such as " man," " satellite of the 

 earth," "satellite of Venus." The general term "man' 

 is applicable to a certain number of objects : there are in 

 the world so and so many men. The unity which philo- 

 sophers rightly feel to be necessary for the assertion of a 

 number is the unity of the general term, and it is the 

 general term which is the proper subject of number. 

 And this applies equally when there is one object or none 

 which falls under the general term. " Satellite of the 

 earth ' is a term only applicable to one object, namely, 



