### Some articles on *vacuous*:

**Vacuous**Truth - Scope of The Concept

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**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

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**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 ...

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