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 propositions 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.
- ↑ In the above remarks I am making use of unpublished work by my friend Ludwig Wittgenstein.
