Triviality

Cogito ergo sum Logic and rhetoric

Key articles

Logical fallacy Syllogism Argument

General logic

Refuting Texas sharpshooter fallacy Argument from silence Post hoc, ergo propter hoc (español) Genuine but insignificant cause Apelación a la piedad

Bad logic

Post hoc, ergo propter hoc Straw man Argumentum ad nauseam Ipse dixit Fallacy Files Reductio ad absurdum v - t - e

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

$\forall \phi .\left[X\vdash \phi \right]$

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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