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:
“Hume, and other skeptical innovators, are vain men, and will gratify themselves at any expense. Truth will not afford sufficient food to their vanity; so they have betaken themselves to errour. Truth, Sir, is a cow that will yield such people no more milk, and so they are gone to milk the bull.”
—James Boswell (1740–1795)
“Racism keeps people who are being managed from finding out the truth through contact with each other.”
—Shirley Chisholm (b. 1924)
“Give him the darkest inch your shelf allows,
Hide him in lonely garrets, if you will,—
But his hard, human pulse is throbbing still
With the sure strength that fearless truth endows.”
—Edwin Arlington Robinson (1869–1935)