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:
“Partisanship should be kept out of the pulpit.... The blindest of partisans are preachers. All politicians expect and find more candor, fairness, and truth in politicians than in partisan preachers. They are not replied to—no chance to reply to them.... The balance wheel of free institutions is free discussion. The pulpit allows no free discussion.”
—Rutherford Birchard Hayes (1822–1893)
“We cannot spare our children the influence of harmful values by turning off the television any more than we can keep them home forever or revamp the world before they get there. Merely keeping them in the dark is no protection and, in fact, can make them vulnerable and immature.”
—Polly Berrien Berends (20th century)
“Propositions show what they say: tautologies and contradictions show that they say nothing.”
—Ludwig Wittgenstein (1889–1951)