论文标题
关于戈德利安和罗瑟里亚句子的真相
On the Truth of Gödelian and Rosserian Sentences
论文作者
论文摘要
逻辑 - 哲学界存在一段长期的辩论，说明为什么哥德式的句子是一致且足够强的理论是正确的。普遍的论点似乎是这样的：因为这种理论的戈德尔句子中的每一个句子都等同于理论的一致性陈述，即使在理论中也是如此，因此这些句子的真实是遵循所讨论的理论的一致性。因此，一致理论的戈德利亚句子应该是真实的。在本文中，我们表明戈德利安的句子只有声音理论是真实的。从一致性到健全的道路上，确实有一个层次结构，这些条件是某些理论所满足并被其他理论所满足的层次结构。我们还研究了罗瑟里亚句子的真相，并为罗瑟里亚人（以及戈德利安）理论的真相提供了必要和充分的条件。
There is a longstanding debate in the logico-philosophical community as to why the Gödelian sentences of a consistent and sufficiently strong theory are true. The prevalent argument seems to be something like this: since every one of the Gödelian sentences of such a theory is equivalent to the theory's consistency statement, even provably so inside the theory, the truth of those sentences follows from the consistency of the theory in question. So, Gödelian sentences of consistent theories should be true. In this paper, we show that Gödelian sentences of only sound theories are true; and there is a long road from consistency to soundness, indeed a hierarchy of conditions which are satisfied by some theories and falsified by others. We also study the truth of Rosserian sentences and provide necessary and sufficient conditions for the truth of Rosserian (and also Gödelian) sentences of theories.
