Gödel argued that the incompleteness theorems entail that the mind is not a machine, or that certain arithmetical propositions are absolutely undecidable. His view was that the mind is not a machine, and that no arithmetical propositions are absolutely undecidable. I argue that his position presupposes that the idealized mathematician has an ability which I call the recursive-ordinal recognition ability. I show that we have this ability if, and only if, there are no absolutely undecidable arithmetical propositions. I argue that there are such propositions, but that no recognizable example of one can be identified, even in principle.

中文翻译：

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哥德尔的析取论证

哥德尔认为，不完备性定理意味着心灵不是一台机器，或者某些算术命题是绝对不可判定的。他的观点是心灵不是一台机器，没有任何算术命题是绝对不可判定的。我认为他的立场预设了理想化的数学家具有我称之为递归序数识别能力的能力。我证明我们有这种能力当且仅当不存在绝对不可判定的算术命题。我认为存在这样的命题，但即使在原则上，也无法识别出一个可识别的例子。