208 SCIENTIFIC METHOD IN PHILOSOPHY 



If the theory that classes are merely symbolic is accepted, 

 it follows that numbers are not actual entities, but that 

 propositions in which numbers verbally occur have not 

 really any constituents corresponding to numbers, but 

 only a certain logical form which is not a part of pro- 

 positions having this form. This is in fact the case with 

 all the apparent objects of logic and mathematics. Such 

 words as or, not, if, there is, identity, greater, plus, nothing, 

 everything, function, and so on, are not names of definite 

 objects, like "John' or "Jones," but are words which 

 require a context in order to have meaning. All of them 

 are formal, that is to say, their occurrence indicates a 

 certain form of proposition, not a certain constituent. 

 " Logical constants," in short, are not entities ; the 

 words expressing them are not names, and cannot 

 significantly be made into logical subjects except when it 

 is the words themselves, as opposed to their meanings, 

 that are being discussed. 1 This fact has a very important 

 bearing on all logic and philosophy, since it shows how 

 they differ from the special sciences. But the questions 

 raised are so large and so difficult that it is impossible to 

 pursue them further on this occasion. 



1 In the above remarks I am making use of unpublished work by my 

 friend Ludwig Wittgenstein. 



