# Proceedings of the XXII World Congress of Philosophy

## Volume 41, 2008

## Philosophy of Mathematics

**Mathematical Identity**

The Algebraic Unknown Number and Casuistry

*David Hilbert’s distinction between mathematics and metamathematics assumes mathematics is not metamathematics, cardinality of mathematics is less than cardinality of metamathematics, and metamathematics contains mathematics. Only by abandoning the last renders these characteristics consistent. Every set identifiable only in a metaset, following Kurt Gödel, the metaset is convertible into the set by translation of its constituents into constituents of the set, rendering the set indistinguishable from the metaset. Reversing Kurt Gödel, the set is convertible into the metaset by translation of its constituents into constituents of the
metaset, rendering the set indistinguishable from the metaset. Set being indistinguishable from metaset, the set of mathematics is unidentifiable as constituent of the set of metamathematics. Only inductively by exclusive resolution of all constituents of the set of all disjunctives of the sets of mathematics and metamathematics is the set of mathematics identifiable. Generated is endless arbitrary qualification of mathematical identity exhibited in continual proofs
of its axioms. Understood as clarification, when everything is unique, no concealed contradiction is contained. Constituted is the endless non-repeating digit to the left of the decimal of an algebraic unknown number. Manifest is casuistry, now neither objective nor specious identity, but instead necessary subjective identity distinguishing sets.*