Elementary Propositions and Independence

This paper is concerned with Wittgenstein's early doctrine of the independence of elementary propositions. Using the notion of a free generator for a logical calculus—a concept we claim was anticipated by Wittgenstein— we show precisely why certain difficulties associated with his doctrine cannot be overcome. We then show that Russell's version of logical atomism—with independent particulars instead of elementary propositions—avoids the same difficulties. We intend to discuss a basic notion of logical atomism: that of independence. Ele- mentary propositions are clearly central to Wittgenstein's atomism; their character- ization rests on the doctrine of their independence. And a central tenet of Russell's atomism is that the world is decomposable into independent components. Our aim is to elucidate these two uses of independence and the conceptions of elementary propo- sition to which they give rise.