SR4 as a Gödelian Truth Predicate

The Gödelian truth predicate SR4 allows us to use Gödelian meta-logic to prove ontological truths originating outside of representational space. Since SR4 allows for the derivation of truth in this diagonalized space, we are able to use it to derive the natural numbers, ordinals, cardinals, and infinity, using the general form of the paradoxical logic from the Burali-Forti and Cantor paradoxes. We also provide a new SR4 derivation for zero based on negation space. Where the SR4 approach perhaps most differs from ZFC is that: (a) SR4 derives infinity versus ZFC which axiomatically assumes it; (b) SR4’s entire structure is based on self-reference, which ZFC avoids. These findings adds to SR4’s prior findings in avoiding Russell’s Paradox and the Liar’s Paradox and processing G ≡ ¬Prov(G) at the object level. At the highest level, it appears SR4 builds a joint computational-axiomatic logic system, which is why it seems to avoid paradoxes while deriving arithmetic foundations.