Logical Dependence and Independence in the Tractatus

Abstract

A central Tractarian thesis is that of the logical independence of the elementary
propositions, the atoms. The aim of this paper is threefold. First, I will make
precise what the thesis is, and show that Wittgenstein endorses it (section 1).
Second, I will identify a concept of logical dependence in terms of which logical
independence can be defined (section 2). And finally, I will show that these notions
of logical dependence and independence fail to capture certain explanatory links
between propositions, and I will then try to refine the previous definitions in order
to end up with concepts which do capture such links (section 3). Part of these
matters have been dealt with by (Simons, 1981). But as I will show, Simons'
investigation is mistaken on independence, and-as a consequence-incomplete on
dependence.