jasperzhang121/logic

Paradox of implication: irrelevant reasoning & counter-intuitive

Logic Analysis of "Paradox of Implication: Irrelevant Reasoning & Counter-Intuitive"

This repository contains a single document authored by the writer analyzing the paradox of implication and how classical logic can allow for irrelevant reasoning that mismatches human intuition. The proposal for solving this paradox is to use relevant logic with 4-valued logic, introducing the ";" symbol and eliminating the weakening rule for adding irrelevant assumptions. The 4-valued logic uses truth values of "True," "False," "Both," and "Neither" to better capture natural language's ambiguity and to solve the counter-intuitive problem.

The article discusses the merits and demerits of this proposal and provides an example of how it works. The author also introduces a 4-valued logic table, which may have some problems and demerits. The table addresses the counter-intuitive conditional "𝑝 → 𝑞 is true unless p is true, and q is false."