Sobre contradições no Middle Wittgenstein

Abstract

In classical logic, a theory becomes inconsistent if we can derive a contradiction from it; likewise, it becomes trivial if we can deduce any formula that is underlying to it. The mere presence of a contradiction signifies the destruction of a logical calculus. At the end of the 19th century, the logical society found itself bombarded by various inconsistencies in its main theories of mathematical logic. Such occurrences seemed to demand not only a certain necessity in avoiding these contradictions but also finding an effective method to combat them. However, in 1929, we find Middle Wittgenstein displaying great flexibility regarding contradictions in formal systems. In several passages surrounding this period, the author offers harsh criticism on how mathematicians feared contradictions. Now, if contradictions are so problematic, why is Wittgenstein so permissive about them? Our work aims to clarify the controversial writings of the author on contradiction in his intermediate period. In doing so, we would like to highlight not only the significance but also the wide scope of this theme in the context of other lines of argumentation.