Outline of a Theory of Truth in The Journal of Philosophy, Col. LXXII, No. 19, Nov. 6, 1975, pp. 690-716
New York: Journal of Philosophy, 1975. 1st Edition. FIRST EDITION IN ORIGINAL WRAPS OF KRIPKE’S “FAMOUS AND HIGHLY INFLUENTIAL PAPER GREATLY [SHAPING] MOST LATER APPROACHES TO THEORIES OF TRUTH AND THE SEMANTIC PARADOXES” (Stanford Encyclopedia of Philosophy, Consequences of the Semantic Paradoxes).
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 trick 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, defining a truth predicate over just that segment: this 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 "The sentence is true" nor "This sentence is not true" receive truth-conditions; they are, in Kripke's terms, "ungrounded" (Wikipedia). Item #736
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