Seventeenth International Conference on New Directions in the Humanities

Abstract

The main purpose of this session is to refine the exercise of philosophy today by considering an exposition about Russell’s paradox where it can be seen as a necessary paradox to the Cantor Sets Theory, since it should not be censored merely for being contradictory, for the paradox still relevant from both syntactic and semantic points of view. Also, to get to philosophical conclusions, it will take observations about the use of propositional variables in Gödel’s first theorem, which states, in the theorem, that if a proposition can be a formula its negation must also be a formula. However, it is a rule that renders any proposition undecidable, in a closed system, although even more criteria for validation of these propositions can be entered. These episodes on the history of logic influenced the conception of the first computers, just as they subjected the scientific community to a special way of thinking. The indeterminations that both the paradox and the incompleteness theorems suggested to the eternal search for universal truth are brought to this article with the objective to discuss post modernity today.