论文标题
稳定一致的正式系统的不完整
Incompleteness for stably consistent formal systems
论文作者
论文摘要
我们首先部分发展了稳定一致性的数学概念，该概念旨在反映人类的实际一致性。然后，我们将第一和第二的Gödel不完整定理的概括提高到稳定的$ 1,2 $一致的正式系统。我们的论点尤其是从第一原则中重新提供了原始的不完整定理，使用图灵机器语言直接构建我们的“gödel句子”，特别是我们不使用对角线引理，也不使用任何元逻辑，具有自然形式化的证据。在实践中，如此稳定的正式系统可以代表人类的数学输出，以便上述对戈德尔的著名分离的形式化，从而阻碍了智力的可计算性。
We first partly develop a mathematical notion of stable consistency intended to reflect the actual consistency property of human beings. Then we give a generalization of the first and second Gödel incompleteness theorem to stably $1,2$-consistent formal systems. Our argument in particular re-proves the original incompleteness theorems from first principles, using Turing machine language to (computably) construct our "Gödel sentence" directly, in particular we do not use the diagonal lemma, nor any meta-logic, with the proof naturally formalizable in set theory. In practice such a stably consistent formal system could be meant to represent the mathematical output of humanity evolving in time, so that the above gives a formalization of a famous disjunction of Gödel, obstructing computability of intelligence.
