The Paradoxes of Strict Implication
The Paradoxes of Strict Implication

Summary/Abstract: In order to find a solution for the paradoxes of material implication, C.I. Lewis introduces a new constant in the vocabulary of propositional logic, namely, the constant named strict implication. This constant has the role to symbolize the relation of deduction between the premises and the conclusion of an inference. Starting from the Aristotle’s analysis of inference, that the conclusion is necessarily deduced from premises, Lewis admits a modal interpretation for the strict implication. But, in this way, although the material implication paradoxes are eliminated, new paradoxes appear, namely, the paradoxes of strict implication. We can avoid this kind of paradoxes, admitting a different analysis of strict implication without a modal component. Strict implication can be reduced to material implication and the quantification of propositional variables.

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