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:
“The only way into truth is through one’s own annihilation; through dwelling a long time in a state of extreme and total humiliation.”
—Simone Weil (1909–1943)
“More than I, if truth were told,
Have stood and sweated hot and cold,
And through their veins in ice and fire
Fear contended with desire.”
—A.E. (Alfred Edward)
“As the will to truth thus gains self-consciousness—there can be no doubt of that—morality will gradually perish now: this is the great spectacle in a hundred acts reserved for the next two centuries in Europe—the most terrible, most questionable, and perhaps also the most hopeful of all spectacles.”
—Friedrich Nietzsche (1844–1900)