A Scientific Revolution in Real Time. - Hintikka, Jaakko (Teorema, 2014)
Frege did not realize that the semantical job of quantifiers includes expressing, by their own formal dependencies on each other, actual dependencies between variables. This uncorrected mistake led to flawed first-order logic, set-theoretical paradoxes and inadequate grasp of higher-order logic. It began to be corrected only through the introduction of IF logic. This reform leads to a richer first-order logic, to a reduction of higher-order logic to first-order level, to a rejection of the usual first-order axiomatizations of set theory, to a new concept of probability, and to a re-evaluation of the incompleteness, indefinability, and unprovability results