Giving up logical atomism? Some remarks on Wittgenstein’s Some remarks on logical form (1929)

Abstract

Elementary (atomic) and complex structures can be characterized with respect to its composition as well as to its decomposition. (a) The rules to (de-)compose elementary structures are non-recursive. (b) The rules to (de-)compose complex structures are usually conditioned and recursive. Using this differentiation four aspects of logical atomism with respect to Wittgenstein’s Tractatus are discussed: (atomic) facts, elementary propositions, objects/names and substitution rule. With respect to these aspects we investigate Wittgenstein’s modifications of his position towards logical atomism in Some Remarks on Logical Form. Against Wittgenstein’s position the consequences of using truth-functions within atomic propositions are checked. Finally we discuss analogies between the exclusion of atomic propositions on colour and the exclusion of atomic propositions describing positions of chess pieces on a board. The mutual exclusion of descriptions is related to the structure of the relevant logical space relative to the basic rules of the game. These considerations indicate one possible path to the concept of language games in Wittgenstein’s later philosophy.