A Quantitative Analysis of Implicational Paradoxes in Classical Mathematical Logic

Classical mathematical logic includes a lot of “implicational paradoxes” as its logic theorems. This paper uses the property of strong relevance as the criterion to identify implicational paradoxes in logical theorems of classical mathematical logic, and enumerates logical theorem schemata of classical mathematical logic that do not satisfy the strong relevance. This quantitative analysis shows that classical mathematical logic is by far not a suitable logical basis for automated forward deduction.