Truth Values and Tautologies
Considering different interpretations of the same statement leads to the notion of truth value. Simplest approach to truth values means that the statement may be "true" in one case, but "false" in another. In one sense of the term "tautology", it is any type of formula or proposition which turns out to be true under any possible interpretation of its terms (may also be called a valuation or assignment depending upon the context). This is synonymous to logical truth.
However, the term "tautology" is also commonly used to refer to what could more specifically called truth-functional tautologies. Whereas a tautology or logical truth is true solely because of the logical terms it contains in general (e.g. "every", "some", and "is"), a truth-functional tautology is true because of the logical terms it contains which are logical connectives (e.g. "or", "and", and "nor"). Not all logical truths are tautologies of such kind.
Read more about this topic: Logical Truth
Famous quotes containing the words truth, values and/or tautologies:
“It is not the number of years we have behind us, but the number we have before us, that makes us careful and responsible and determined to find out the truth about everything.”
—George Bernard Shaw (1856–1950)
“[University students] hated the hypocrisy of adult society, the rigidity of its political institutions, the impersonality of its bureaucracies. They sought to create a society that places human values before materialistic ones, that has a little less head and a little more heart, that is dominated by self-interest and loves its neighbor more. And they were persuaded that group protest of a militant nature would advance those goals.”
—Muriel Beadle (b. 1915)
“Propositions show what they say: tautologies and contradictions show that they say nothing.”
—Ludwig Wittgenstein (1889–1951)