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 truth is, I do not want that office. When the American people choose a President they require him to remain awake four years. I have come to a time in life when I need my sleep.”
—Grover Cleveland (1837–1908)
“With the breakdown of the traditional institutions which convey values, more of the burdens and responsibility for transmitting values fall upon parental shoulders, and it is getting harder all the time both to embody the virtues we hope to teach our children and to find for ourselves the ideals and values that will give our own lives purpose and direction.”
—Neil Kurshan (20th century)
“Propositions show what they say: tautologies and contradictions show that they say nothing.”
—Ludwig Wittgenstein (1889–1951)