On Godel Sentences and What They Say
On Godel Sentences and What They Say
复制标题
论哥德尔的句子及其言论
DOI：
10.1093/philmat/nkm015
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发表时间：
2007
影响因子：
1.1
通讯作者：
Peter W. Milne
中科院分区：
文献类型：
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作者：
Peter W. Milne
哥德尔第一不完全性定理的证明常常伴随着一些断言，比如在证明过程中构造的哥德尔语句对自身宣称它是不可证的且它是真的。这类断言的有效性与语句的构造方式密切相关。只有严格限制构造的方法，人们才能得到这样的哥德尔语句，从而无需多言就可以正确地说它们对自身宣称是不可证的且是真的；否则，一个错误的理论可能会产生错误的哥德尔语句。
Proofs of Godel's First Incompleteness Theorem are often accompanied by claims such as that the godel sentence constructed in the course of the proof says of itself that it is unprovable and that it is true. The validity of such claims depends closely on how the sentence is constructed. Only by tightly constraining the means of construction can one obtain godel sentences of which it is correct, without further ado, to say that they say of themselves that they are unprovable and that they are true; otherwise a false theory can yield false godel sentences.