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:
“For though we love both the truth and our friends, piety requires us to honor the truth first.”
—Aristotle (384–322 B.C.)
““... In truth I find it ridiculous that a man of his intelligence suffer over this type of person, who is not even interesting, for she is said to be foolish”, she added with all the wisdom of people who are not in love, who find that a sensible man should only be unhappy over a person who is worthwhile; it is almost tantamount to being surprised that anyone deign having cholera for having been infected with a creature as small as the vibrio bacilla.”
—Marcel Proust (1871–1922)
“We all know that Art is not truth. Art is a lie that makes us realize truth, at least the truth that is given us to understand. The artist must know the manner whereby to convince others of the truthfulness of his lies.”
—Pablo Picasso (1881–1973)