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I would say that the article is based on a flawed premise that constraints of Gödel theorems do not apply to human mind. The fact that some theorems undecidabl

I would say that the article is based on a flawed premise that constraints of Gödel theorems do not apply to human mind. The fact that some theorems undecidable in a formal system can be 'seen true' or informally proven is explainable by a simple fact that formal systems are 'step behind' intuition. We have an intuitive grasp of matematical structures and inference and we created neat and comprehensible formal systems that tries to reflect that, but they are behind in some cases. We can iteratively improve them by adding more axioms and more general inference methods, but that is kind of futile as second Gödel theorem shows that it will never make them complete. But there is no reason to assume that intuition is complete in the same sense. It seems likely that if we did that step enough times, we would end in situation where we couldn't progress as intuition would fail on undecidable theorems (either by being silent, or inconsistent between people, or by being incomprehensible).

simonh 7y ago
I love this bit: >Nor could we make its inconsistency a reproach to it---are not men inconsistent too? Certainly women are, and politicians; and {53} even male non-politicians (121) contradict themselves sometimes, and a single inconsistency is enough to make a system inconsistent. Not 'love' in an agreeing sense. Boy are we in different times now. Agreed, I see no justification in assuming that human minds are consistent, in fact that seems self evidently not to be the case. Also just because a system is inconsistent, that doesn't mean it's incapable of generating or 'simulating' consistent systems. So we can conceive of a consistent system, apply it to problems and achieve all the advantages on consistency within some limited domain, while at the higher level being ourselves inconsistent. I see no reason why an automated system could not also do the same. This seems to me to break the argument completely, though I confess I'm no great philosopher and it's highly likely I'm missing something.
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simonh 7y ago

I love this bit: >Nor could we make its inconsistency a reproach to it---are not men inconsistent too? Certainly women are, and politicians; and {53} even male non-politicians (121) contradict themselves sometimes, and a single inconsistency is enough to make a system inconsistent. Not 'love' in an agreeing sense. Boy are we in different times now. Agreed, I see no justification in assuming that human minds are consistent, in fact that seems self evidently not to be the case. Also just because a system is inconsistent, that doesn't mean it's incapable of generating or 'simulating' consistent systems. So we can conceive of a consistent system, apply it to problems and achieve all the advantages on consistency within some limited domain, while at the higher level being ourselves inconsistent. I see no reason why an automated system could not also do the same. This seems to me to break the argument completely, though I confess I'm no great philosopher and it's highly likely I'm missing something.

deleted 7y ago

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