 Hintikka (2006a: 73–77) takes the following to be among consequences of the novel insights made possible by (extended) IF first-order logic: reconstruction of normal mathematical reasoning on the first-order level, a novel perspective on the notion of truth in axiomatic set theory, insights into the nature of negation, and the formulation of a self-applied truth-predicate. A related topic of general interest is the phenomenon of informational independence in natural languages. The ideas related to negation and definability of truth have been discussed in Subsections 4.2 and 4.5, respectively. Let us consider here the remaining issues.