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:
“Where there are no rights, there are no duties. To tell the truth is thus a duty; but it is a duty only in respect to one who has a right to the truth.”
—Henri Benjamin Constant De Rebecque (1767–1830)
“There is a great stir about colored men getting their rights, but not a word about colored women, and if colored men get their rights, and not colored women theirs, you see the colored men will be masters over the women, and it will be just as bad as it was before. So I’m for keeping the thing going while things are stirring; because if we wait till it is still, it will take a great while to get it going again.”
—Sojourner Truth (1797–1883)
“Partisanship should be kept out of the pulpit.... The blindest of partisans are preachers. All politicians expect and find more candor, fairness, and truth in politicians than in partisan preachers. They are not replied to—no chance to reply to them.... The balance wheel of free institutions is free discussion. The pulpit allows no free discussion.”
—Rutherford Birchard Hayes (1822–1893)