Frege's system was found to be inconsistent due to Russell's paradox, due to his Basic Law V, but was Frege's logic complete in any sense?
Godel showed that no consistent formal system can be complete, but what about an inconsistent formal system?
NB: I am taking to Frege's system now to be a paraconsistent system that does not admit the princple of explosion. Any true statement must be derivable by the axioms of the system and not via explosion.