Triviality

Cogito ergo sum Logic and rhetoric

Key articles

Logical fallacy Syllogism Argument

General logic

Moving the goalposts Ultracrepidarianism Argument from ignorance Nazi analogies سفسطه‌ی حد وسط Bad faith

Bad logic

Poisoning the well Post hoc, ergo propter hoc Regression fallacy Appeal to flattery Association fallacy Evidência suprimida 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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