数学理性的二律背反：PM算术及其相关系统的不一致性
Antinomies of Mathematical Reason: The Inconsistency of PM Arithmetic and Related Systems
摘要：
我们给PM算术，经典集合论和相关系统的不一致性的证明，顺便暴露在哥德尔自己的哥德尔定理证明的错误。不一致性证明，即形式R和~R的公式作为PM-同构系统P中的定理出现，从命题演算的第一公理（P的公理II.1）的自反替换实例出发。哥德尔的形式主义是使用整个。
英文摘要：
We give a proof of the inconsistency of PM arithmetic, classical set theory and related systems, incidentally exposing an error in Goedel's own proof of Goedel's Theorems. The inconsistency proof, that formulae of the form R and ~R occur as theorems in the PM-isomorphic system P, proceeds from a reflexive substitution instance of the first axiom of the propositional calculus (axiom II.1 of P). Goedel's formalism is used throughout.
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