Some Difficulties in Proposing a Mathematical Isomorphism to Interpret Wittgenstein’s Tractatus

Abstract

Here I present some arguments against an alleged mathematical isomorphic relation between elementary propositions and states of affairs in the Tractatus. This is a standard proposal to understand the world-language relation in Wittgenstein’s early philosophy. I advocate that the application of this type of isomorphism in the Tractarian conceptual framework conflicts with some of its philosophical peculiarities. This technical approach especially overlooks some crucial Tractarian tenets, such as a sharp modal distinction between form and structure and Wittgenstein’s rejection of a priori true propositions.