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 times are so peculiar now, so mediaeval so unreasonable that for the first time in a hundred years truth is really stranger than fiction. Any truth.”
—Gertrude Stein (1874–1946)
“You cannot have both truth and what you call civilisation.”
—Iris Murdoch (b. 1919)
“I learned early to understand that there is no such condition in human affairs as absolute truth. There is only truth as people see it, and truth, even in fact, may be kaleidoscopic in its variety. The damage such perception did to me I have felt ever since ... I could never belong entirely to one side of any question.”
—Pearl S. Buck (1892–1973)