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MrMind comments on Open thread, Oct. 12 - Oct. 18, 2015 - Less Wrong Discussion

5 Post author: MrMind 12 October 2015 06:57AM

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Comment author: MrMind 13 October 2015 08:18:48AM 2 points [-]

If there's any sort of inconsistency in ZF or PA or any other major system currently in use, it will be much harder to find than this.

Indeed, since you can prove ZFC consistent with the aid of an inaccessible cardinal. And you can prove the consistency of an inaccessible cardinal with a Mahlo cardinal, and so on.

Comment author: JoshuaZ 13 October 2015 01:00:00PM 4 points [-]

I'm not sure that's strong evidence for the thesis in question. If ZFC had a low-lying inconsistency, ZFC+an inaccessible cardinal would still prove ZFC consistent, but it would be itself an inconsistent system that was effectively lying to you. Same remarks apply to any large cardinal axiom.

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