在哥德尔对他的形式推理及其后果的解释中，是否有一个“漏洞”？
Is there a "loophole" in Goedel's interpretation of his formal reasoning and its consequences?
摘要：
我们正式定义了“数学对象”和“集合”。然后，我们认为，表达式，如“（Ax）F（x）"，和“（Ex）F（x）"，在一个正式的理论P的解释M，可以采取的意思是“F（x）是真的所有x在M”，和“F（x）是真的一些x在M”，分别当且仅当，谓词字母“F”是一个数学对象在P。和“（Ex）F（x）"，只能分别表示“F（x）对于M中的任何给定x为真”和“F（x）对于M中的任何给定x为假不是真”，这表明谓词“F（x）”对于任何给定的x值都是明确定义的，并且可以单独有效地判定，但是对于这种判定性可能没有统一的有效方法（算法）。我们展示了如何量子力学的一些矛盾的概念，然后可以表示在建设性的解释标准皮亚诺算术。
英文摘要：
We formally define a "mathematical object" and "set". We then argue that expressions such as "(Ax)F(x)", and "(Ex)F(x)", in an interpretation M of a formal theory P, may be taken to mean "F(x) is true for all x in M", and "F(x) is true for some x in M", respectively, if, and only if, the predicate letter "F" is a mathematical object in P. In the absence of a proof, the expressions "(Ax)F(x)", and "(Ex)F(x)", can only be taken to mean that "F(x) is true for any given x in M", and "It is not true that F(x) is false for any given x in M", respectively, indicating that the predicate "F(x)" is well-defined, and effectively decidable individually, for any given value of x, but that there may be no uniform effective method (algorithm) for such decidability. We show how some paradoxical concepts of Quantum Mechanics can then be expressed in a constructive interpretation of standard Peano's Arithmetic.
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。
