An argument that contains contradictory premises is trivial in the sense that there is a valid argument from the premises to any well-formed formula whatsoever.
Is the statement true or false? I can't understand what it means for an argument to be 'trivial'.
True. In logic, 'trivial' is a technical term. A trivial theory is such that it has all the sentences as theorems. This is possible only if it contains an inconsistency, which enables one to derive any sentence at will.
So, why do we bother with such a term? Because we can have rational systems that have inconsistencies, but the associated theories are non-trivial. Paraconsistent logic studies such systems.
An argument that contains contradictory premises is trivial in the sense that there is a valid argument from the premises to any well-formed formula whatsoever.
An argument is valid precisely when its premises logically entail its conclusion.
In particular, an argument with contradictory premises is invariably valid (regardless of its conclusion).
It is in this sense that an argument with contradictory premises is said to be trivially valid.
Analogously, the trivial solution of a homogeneous system of linear equations is the zero vector, because this solution invariably arises as the problem’s parameters vary.
