The starting point of this work is the existence of historical paradoxes in the set theory. These are: Russell's paradox, applied to the set W, Cantor's, for the set U, and Burali-Forti's, of the set Omega. A systematic analysis aimed at the simplification and the refining of such paradoxes showed that: there exist at least eight contradictory expressions instead of three; another contradictory set is suggested by an extension of Burali-Forti's paradox; almost all of the contradictions apply to more than (...) one paradoxical set. (shrink)

The concept “truth under an interpretation” simply expresses the formal structure of truth assignations in any type of statement. In the particular case of empirical statements, interpretations consist of sets of material objects whose extent can only be determined by criteria of correspondence with facts. Such correspondence thus constitutes a substantive, non-formal aspect of empirical truth, outside the model theory. The existence of other types of truth also structured by the idea of “truth under an interpretation”, but outside the notion (...) of correspondence with facts, reinforces the existence of a line of demarcation between these two categories. (shrink)