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:
“I could better eat with one who did not respect the truth or the laws, than with a sloven and unpresentable person. Moral qualities rule the world, but at shorter distances, the senses are despotic.”
—Ralph Waldo Emerson (1803–1882)
“What use soever be made of truth, yet truth is truth, and now the question is not, what is fit to be preached, but what is true.”
—Thomas Hobbes (1579–1688)
“Brutus. Now, as you are a Roman, tell me true.
Messala. Then like a Roman bear the truth I tell,
For certain she is dead, and by strange manner.
Brutus. Why, farewell, Portia. We must die, Messala.”
—William Shakespeare (1564–1616)