On S.Kripke's Proposal To The Semantic Paradoxes

Paradox is a long-standing concern for logicians. S.A.Kripke, one of the most famous logicians and analytical philosophers in America, published an important paper named "Outline of a Theory of Truth" in 1975, in which a new solution to the semantic paradoxes was proposed and the "orthodox approach" of Tarski was criticized. Centered on the notion of the "Groundedness", the proposal has greatly stimulated the research on the semantic paradoxes. Therefore, study on this solution has vital significance on logic and philosophy.In view of the fact that the domestic research on Kripke's proposal is insufficiently developed, the aim of this paper is to grasp the implication of the concepts of "Truth-value Gaps", "Groundedness", "Fixed Point" by detailed analysis and to explain the technical processing and intuitional rationality in the hope of understanding Kripke's viewpoint better.There are four chapters in this paper.Chapter I is an introduction, in which the author firstly explains the notion of Paradox and Semantic Paradox, then analyzes a series of solutions to the semantic paradoxes in history, finally summarizes the present research situation on paradox and Kripke's approach both home and abroad.Chapter II mainly introduces Tarski's view of truth and approach to the semantic paradoxes and comments on his view from Kripke and Davidson.As the most important part of this paper, Chapter III focuses on the proposal itself. Comparing various three-valued logical systems, we know why Kleene's strong three-valued logic is adopted by Kripke for the language that allows truth-value gaps and why the supervaluation technique is also appropriate. Based on the description of a certain "hierarchy oflanguages" and the construction of a fixed point, the formal expression can be given to the concept of groundedness, after the origin and the direct-viewing meaning of this concept being introduced. Then the author illustrates the characteristic of the paradoxical sentences by examples, compared with that of the ungrounded but unparadoxical sentences, and makes differences among the concepts of the minimal fixed point, the maximal fixed point and the intrinsic fixed point.Chapter IV mainly comments on Kripke's proposal. On one hand, it shows that the present proposal has relative rationality, in further comparison with the Tarski's approach. On the other hand, it indicates that Kripke's proposal has some limitations on expressing classical logical principals and handling the Strengthened Liar, which are also criticized by Gupta and Burge. Then the author emphasizes Kripke's influence on later solutions to the semantic paradoxes by the example of Herzberger. Finally, the paper puts forward some questions to be further discussed.