哥德尔的不完全性定理是否对大脑表达和交流心理概念的能力设置了绝对的限制？
Do Goedel's incompleteness theorems set absolute limits on the ability of the brain to express and communicate mental concepts verifiably?
摘要：
哥德尔形式推理的经典解释意味着任何形式数学语言的某些算术命题的真理，在任何解释下，本质上是不可验证的。然而，一种一般的、科学的话语语言不能允许它的数学命题被含糊地解释。因此，这种语言必须以可验证的方式定义数学真理。我们认为一个建设性的解释古典，塔斯基，真理，和哥德尔的推理，根据任何正式系统的皮亚诺算术是可验证的完整。我们展示了量子力学中一些自相矛盾的概念是如何在数学真理的构造性定义下自然地表达和解释的。
英文摘要：
Classical interpretations of Goedel's formal reasoning imply that the truth of some arithmetical propositions of any formal mathematical language, under any interpretation, is essentially unverifiable. However, a language of general, scientific, discourse cannot allow its mathematical propositions to be interpreted ambiguously. Such a language must, therefore, define mathematical truth verifiably. We consider a constructive interpretation of classical, Tarskian, truth, and of Goedel's reasoning, under which any formal system of Peano Arithmetic is verifiably complete. We show how some paradoxical concepts of Quantum mechanics can be expressed, and interpreted, naturally under a constructive definition of mathematical truth.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
