Abstract

In his posthumous book from 1914, “New foundations of logic, arithmetic andset theory”, Julius König develops his philosophy of mathematics. In a previous contribution, we attracted attention on the positive part of his “pure logic”: his “isology” being assimilated to mutual implication, it constitutes a genuine formalization of positive intuitionistic logic. König’s intention was to rebuild logic in such a way that the excluded third’s principle could no longer be logical. However, his treatment of truth and falsehood is purely classical. We explain here this discrepancy by the choice of the alleged more primitive notions to which the questioned notions of truth and falsehood have been reduced. Finaly, it turns out that the disjunctive and conjunctive forms of the principles of the excluded third and of contradiction have effectively been excluded, but none of their implicative forms.