Triviality

Triviality is a property of formal systems in logic. A system is trivial if its set of axioms entails every well-formed formula according to the inference rules of the system, i.e.,

Cogito ergo sum Logic and rhetoric

Key articles

Logical fallacy Syllogism Argument

General logic

Appeal to mystery Argumentum ad nauseam (français) Blaming the victim Implicit bias Moral equivalence Problem of evil

Bad logic

False analogy Flying carpet fallacy Handwave Linking to authority Release the data Self-refuting idea v - t - e

An example of triviality is a classical propositional system containing contradictory sentences for axioms; in such a system the principle of explosion can be used to infer any possible proposition or sentence.

On the other hand, a system of paraconsistent logic can be non-trivial even if it contains contradictory axioms, since its inference rules do not include the principle of explosion.

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