Every proposition has a content and a form. We get the picture of the pure form if we abstract from the meaning of the single words, or symbols (so far as they have independent meanings). That is to say, if we substitute variables for the constants of the proposition. The rules of syntax which applied to the constants must apply to the variables also. By syntax in this general sense of the word I mean the rules which tell us in which connections only a word gives sense, thus excluding nonsensical structures. The syntax of ordinary language, as is well known, is not quite adequate for this purpose. It does not in all cases prevent the construction of nonsensical pseudopropositions (constructions such as "red is higher than green" or "the Real, though it is an in itself, must also be able to become a for myself", etc.).
If we try to analyze any given propositions we shall find in general that they are logical sums, products or other truthfunctions of simpler propositions. But our analysis, if carried far enough, must come to the point where it reaches propositional forms which are not themselves composed of simpler propositional forms. We must eventually reach the ultimate connection of the terms, the immediate connection which cannot be broken without (163) destroying the propositional form as such. The propositions which represent this ultimate connexion of terms I call, after B. Russell, atomic propositions. They, then, are the kernels of every proposition, they contain the material, and all the rest is only a development of this material. It is to them we have to look for the subject matter of propositions. It is the task of the theory of knowledge to find them and to understand their construction out of the words or symbols. This task is very difficult, and Philosophy has hardly yet begun to tackle it at some points. What method have we for tackling it? The idea is to express in an appropriate symbolism what in ordinary language leads to endless misunderstandings. That is to say, where ordinary language disguises logical structure, where it allows the formation of pseudopropositions, where