摘要
当把塔斯基对真概念提出的T-模式拓展到有向图上,塔斯基定理成立与否取决于归谬过程中使用的悖论及有向图的特征。本文证明了在使用说谎者悖论证明塔斯基定理时,在并且仅在有向图中含有奇循环时,说谎者悖论才会导致矛盾;在使用佐丹卡片悖论证明塔斯基定理时,在并且仅在有向图中含有高度不能被4整除的循环时,佐丹卡片悖论才会导致矛盾,这表明当T-模式拓展到有向图时,哥德尔关于"认识论悖论"应用于不完全性证明的思想能够被非平庸地类推于真之不可定义性的证明中。
The T-scheme,a basic principle for the notion of truth proposed by Tarski,was used in his undefinability theorem of arithmetic truth and his theory of language hierarchies. In this paper,it is generalized to the diagraph,and the generalized scheme is taken to be a new scheme for the truth predicate.A new observation is that when Tarski＇s theorem is proved on the basis of the generalized scheme instead of the T-scheme,whether Tarski＇s theorem holds depends upon which paradox is employed in reductio ad absurdum and what diagraphs the T-scheme is generalized to.Tarki＇s original theorem is equivalent to the statement that the Liar paradox will produce contradiction if the diagraph to which the T-scheme is generalized contains only a reflexive point.Generally,it is proved that if the Liar paradox is used in the proof of Tarski＇s theorem,it will produce contradiction when and only when the diagraph contains at least an odd cycle.What is more,if Jourdain＇s card paradox is used,it will produce contradiction when and only when the diagraph contains at least an cycle of height not divisible by 4.And so,both of the Liar paradox and Jourdain＇s card paradox are compact in the following sense：if they produce contradiction in a diagraph,they must do so in the finite part of this diagraph. This suggests that when the T-scheme is generalized to the diagraph,G（o｜¨）del＇s idea of using any＂epistemological antinomy＂for the proof of the incompleteness can be non-trivially extended to the proof of the undefinability of truth.
出处
《逻辑学研究》
2010年第1期73-88,共16页
Studies in Logic
基金
广东省优秀青年创新人才培育项目(育苗工程项目
编号:WYM08064)
教育部人文社会科学重点研究基地重大项目(批准号:07JJD720045)
