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:
“The worst enemy of truth and freedom in our society is the compact majority. Yes, the damned, compact, liberal majority.”
—Henrik Ibsen (1828–1906)
“To be faced with what so-and-so’s mother lets him do, or what the teacher said in class today or what all the kids are wearing is to be required to reexamine some part of our belief structure. Each time we rethink our values we reaffirm them or begin to change them. Seen in this way, parenthood affords us an exceptional opportunity for growth.”
—Ruth Davidson Bell (20th century)
“Propositions show what they say: tautologies and contradictions show that they say nothing.”
—Ludwig Wittgenstein (1889–1951)