A new proof for the incompleteness of stoic propositional logic system
The Stoic theory of propositional logic is the second great contribution of the Ancient Greeks to logic.From the perspective of modern logic,it would be more natural to understand it as a natural deductive system rather than an axiomatic system.Zhimei Chen and Zehong Hu(2001)used arithmetic interpretation method to prove its incompleteness.However,what they proved was the system after adding two"meta-logic rules",and there are still some imperfections in the proof process.This paper adopts the Semantic Comparison Method,a widely used approach in modern logic,to intuitively and rigorously demonstrate the incompleteness of the Stoic propositional logic system.It also offers a methodology for identifying the missing rules that could render the system complete,thereby enhancing our comprehension of Stoic propositional logic.
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