42 SCIENTIFIC METHOD IN PHILOSOPHY 



theory of number, which we shall deal with in Lecture 

 VII. j but the whole theory of physical concepts which 

 will be outlined in our next two lectures, is inspired by 

 mathematical logic, and could never have been imagined 

 without it. 



In both these cases, and in many others, we shall 

 appeal to a certain principle called "the principle of 

 abstraction." This principle, which might equally well 

 be called " the principle which dispenses with abstraction," 

 and is one which clears away incredible accumulations of 

 metaphysical lumber, was directly suggested by mathe- 

 matical logic, and could hardly have been proved or 

 practically used without its help. The principle will be 

 explained in our fourth lecture, but its use may be briefly 

 indicated in advance. When a group of objects have 

 that kind of similarity which we are inclined to attribute 

 to possession of a common quality, the principle in 

 question shows that membership of the group will serve 

 all the purposes of the supposed common quality, and 

 that therefore, unless some common quality is actually 

 known, the group or class of similar objects may be used 

 to replace the common quality, which need not be assumed 

 to exist. In this and other ways, the indirect uses of 

 even the later parts of mathematical logic are very great ; 

 but it is now time to turn our attention to its philosophical 

 foundations. 



In every proposition and in every inference there is, 

 besides the particular subject-matter concerned, a certain 

 form, a way in which the constituents of the proposition or 

 inference are put together. If I say, " Socrates is mortal," 

 " Jones is angry," " The sun is hot," there is some- 

 thing in common in these three cases, something indicated 

 by the word " is." What is in common is the form of the 

 proposition, not an actual constituent. If I say a number 



