Analysing Wen's Proposal in Algebraic Semantics

Abstract

Wen Lan recently published his monograph to solve the semantic paradoxes, which insightfully captures the corresponding relation between arguments of paradoxes and proofs of the unsolvability of certain equation systems in Boolean Algebra. After introducing the main idea of his proposal, we present the Tarski Undefinability of Truth (TUT) theorem in algebraic semantics, then under a certain translation, the conclusion of which can be understood as a prerequisite of Wen's proposal, and his proposal can also be expressed by paracomplete theories of truth. Finally, we indicate that Wen's proposal is by no means retaining the full classical logic to resolve semantic paradoxes, then we argue that, although Wen provides an insightful analysis of the algebraic structure of paradoxes, it is still insufficient from both the view of solving semantic paradoxes and the theory of truth.