Bruce Aune On the Complexity of Avowals
Black, Max · 2014
The pagination of the German in the Oxford editions is the same as in the original. With the writings on the philosophy of mathematics of Frege&s;s predecessors even with such great philosophers as Kant without concluding that Frege&s;s work represents an enormous advance in clarity and rigour. Dummett suggests that taking an equivalence relation of entities of one kind as a criterion of identity for entities of a new kind is the most general way of introducing reference to abstract entities, and this abstract entities can be construed as classes. The definition of Peano&s;s primitives and the proof of Peano&s;s axioms can be carried out in one way or another not only in Frege&s;s own formal system but also in Russell&s;s theory of types and in the other systems of set theory constructed in order to remedy the situation produced by the paradoxes, which of course showed Frege&s;s system inconsistent.