 With the work of Gödel and Tarski, paradoxical arguments were reshaped into fixed point results, while the semantic conception of truth, the formalization of semantics and the arithmetization of syntax yielded firm grounds for systematic metamathematical investigations. In addition, an effort was made to elaborate new grand logics as a reaction to the logic of Principia Mathematica. Conceptually, the notions of (self-applicable) function-in-intension/operation and property/ predicate were accepted as primitive, and the very mechanism of definition/combination of concepts was studied. This line of thought gave impulse to the elaboration of syntactical methods within combinatory logic and to the rise of recursion theory. The diagnosis of the paradoxes was further enriched by a subtler analysis of purely logical features of paradoxical reasoning: this is especially true for negation and the crucial role of contraction and duplication properties built into the laws of standard implication. Three valued logic was applied to naïve comprehension.