Reflection on Russell's Ramified Types and Kripke's Hierarchy of Truths

摘要

Both in Kripke's Theory of Truth KTT and Russell's Ramified Type Theory RTT theauthors are confronted with some heirarchy. In RTT, the authors have a double heirarchy of orders and types. Kripke on the other hand, has a ladder of languages where the truth of a proposition in language L(sub n) can only be made in L(sub m) where m > n. The authors investigate in this paper the similarities of both hierarchies; At level n of KTT, the truth or falsehood of all order-n-propositions of RTT can be established. Moreover, there are order-n-propositions that get a truth value at an earlier stage in KTT. Furthermore, the authors show that RTT is more restrictive than KTT, as some type restrictions are not needed in KTT and more formulas can be expressed in the latter.