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.
"Elementary Propositions and Independence." Notre Dame J. Formal Logic 37 (1) 112 - 124, Winter 1996. https://doi.org/10.1305/ndjfl/1040067320