What are vacuous?

Some articles on vacuous:

Vacuous Truth - Scope of The Concept
... Vacuous truth is usually applied in classical logic, which in particular is two-valued, and most of the arguments in the next section will be based on this assumption ... However, vacuous truth also appears in, for example, intuitionistic logic in the same situations given above ... Indeed, the first two forms above will yield vacuous truth in any logic that uses material conditional, but there are other logics which do not ...
Vacuous Truths in Mathematics
... Vacuous truths occur commonly in mathematics ... the statement may very well reduce to a vacuous truth ... So by taking this vacuous truth to be true, our general statement stands and we are not forced to make an exception for the empty set ...

More definitions of "vacuous":

  • (adj): Devoid of significance or point.
    Example: "Vacuous comments"
    Synonyms: empty, hollow