inconsistent triad (1) most generally, any three propositions such that it cannot be the case that all three of them are true; (2) more narrowly, any three categorical propositions such that it cannot be the case that all three of them are true. A categorical syllogism is valid provided the three propositions that are its two premises and the negation (contradiction) of its conclusion are an inconsistent triad; this fact underlies various tests for the validity of categorical syllogisms, which tests are often called ‘methods of’ inconsistent triads. See also ANTILOGISM , SYLLOGIS.
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