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:
“It is remarkable that, notwithstanding the universal favor with which the New Testament is outwardly received, and even the bigotry with which it is defended, there is no hospitality shown to, there is no appreciation of, the order of truth with which it deals. I know of no book that has so few readers. There is none so truly strange, and heretical, and unpopular. To Christians, no less than Greeks and Jews, it is foolishness and a stumbling-block.”
—Henry David Thoreau (1817–1862)
“Art is not merely an imitation of the reality of nature, but in truth a metaphysical supplement to the reality of nature, placed alongside thereof for its conquest.”
—Friedrich Nietzsche (1844–1900)
“On a huge hill,
Cragged, and steep, Truth stands, and he that will
Reach her, about must, and about must go;
And what the hill’s suddenness resists, win so;
Yet strive so, that before age, death’s twilight,
Thy Soul rest, for none can work in that night.
To will, implies delay, therefore now do:
Hard deeds, the body’s pains; hard knowledge too
The mind’s endeavours reach, and mysteries
Are like the Sun, dazzling, yet plain to all eyes.”
—John Donne (1572–1631)