Truth
In his 1975 article "Outline of a Theory of Truth", Kripke showed that a language can consistently contain its own truth predicate, which was deemed impossible by Alfred Tarski, a pioneer in the area of formal theories of truth. The approach involves letting truth be a partially defined property over the set of grammatically well-formed sentences in the language. Kripke showed how to do this recursively by starting from the set of expressions in a language which do not contain the truth predicate, and defining a truth predicate over just that segment: this action adds new sentences to the language, and truth is in turn defined for all of them. Unlike Tarski's approach, however, Kripke's lets "truth" be the union of all of these definition-stages; after a denumerable infinity of steps the language reaches a "fixed point" such that using Kripke's method to expand the truth-predicate does not change the language any further. Such a fixed point can then be taken as the basic form of a natural language containing its own truth predicate. But this predicate is undefined for any sentences that do not, so to speak, "bottom out" in simpler sentences not containing a truth predicate. That is, " 'Snow is white' is true" is well-defined, as is " ' "Snow is white" is true' is true," and so forth, but neither "This sentence is true" nor "This sentence is not true" receive truth-conditions; they are, in Kripke's terms, "ungrounded."
Read more about this topic: Saul Kripke
Famous quotes containing the word truth:
“For though we love both the truth and our friends, piety requires us to honor the truth first.”
—Aristotle (384–322 B.C.)
“There is a city myth that country life was isolated and lonely; the truth is that farmers and their families then had a richer social life than they have now. They enjoyed a society organic, satisfying and whole, not mixed and thinned with the life of town, city and nation as it now is.”
—Rose Wilder Lane (1886–1965)
“Our culture, therefore, must not omit the arming of the man. Let him hear in season, that he is born into the state of war, and that the commonwealth and his own well-being require that he should not go dancing in the weeds of peace, but warned, self- collected, and neither defying nor dreading the thunder, let him take both reputation and life in his hand, and, with perfect urbanity, dare the gibbet and the mob by the absolute truth of his speech, and the rectitude of his behaviour.”
—Ralph Waldo Emerson (1803–1882)