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 secret of genius is to suffer no fiction to exist for us; to realize all that we know; in the high refinement of modern life, in arts, in sciences, in books, in men, to exact good faith, reality, and a purpose; and first, last, midst, and without end, to honor every truth by use.”
—Ralph Waldo Emerson (1803–1882)
“There is a sort of homely truth and naturalness in some books which is very rare to find, and yet looks cheap enough. There may be nothing lofty in the sentiment, or fine in the expression, but it is careless country talk. Homeliness is almost as great a merit in a book as in a house, if the reader would abide there. It is next to beauty, and a very high art. Some have this merit only.”
—Henry David Thoreau (1817–1862)
“There are in me, in literary terms, two distinct characters: one who is taken with roaring, with lyricism, with soaring aloft, with all the sonorities of phrase and summits of thought; and the other who digs and scratches for truth all he can, who is as interested in the little facts as the big ones, who would like to make you feel materially the things he reproduces.”
—Gustave Flaubert (1821–1880)