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:
“Lies, fables and romances must needs be probable, but not the truth and foundation of our faith.”
—Johann G. Hamann (1730–1788)
“... the loss of belief in future states is politically, though certainly not spiritually, the most significant distinction between our present period and the centuries before. And this loss is definite. For no matter how religious our world may turn again, or how much authentic faith still exists in it, or how deeply our moral values may be rooted in our religious systems, the fear of hell is no longer among the motives which would prevent or stimulate the actions of a majority.”
—Hannah Arendt (1906–1975)
“Propositions show what they say: tautologies and contradictions show that they say nothing.”
—Ludwig Wittgenstein (1889–1951)