Scope of The Concept
A statement is “vacuously true” if it resembles the statement, where is known to be false.
Statements that can be reduced (with suitable transformations) to this basic form include the following:
- , where it is the case that .
- , where the set is empty.
- , where the symbol is restricted to a type that has no representatives.
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.
Read more about this topic: Vacuous Truth
Famous quotes containing the words scope of, scope and/or concept:
“Happy is that mother whose ability to help her children continues on from babyhood and manhood into maturity. Blessed is the son who need not leave his mother at the threshold of the world’s activities, but may always and everywhere have her blessing and her help. Thrice blessed are the son and the mother between whom there exists an association not only physical and affectional, but spiritual and intellectual, and broad and wise as is the scope of each being.”
—Lydia Hoyt Farmer (1842–1903)
“Every person is responsible for all the good within the scope of his abilities, and for no more, and none can tell whose sphere is the largest.”
—Gail Hamilton (1833–1896)
“One concept corrupts and confuses the others. I am not speaking of the Evil whose limited sphere is ethics; I am speaking of the infinite.”
—Jorge Luis Borges (1899–1986)