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540Problem about the J.R. Lucas sentence

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  • Paul Hsueh-Min Chang
    Sep 11, 2005

      On page 950, the book argues that the sentence "J. R. Lucas cannot consistently assert that this sentence is true." is necessarily true, but Lucas cannot consistently assert it. There are two arguments on that page. I found no problem with the first argument, but could not understand the second.

      Here is the second argument.

      "The sentence cannot be false, because if it were then Lucas could not consistently assert it, so it would be true."

      But, why couldn't Lucas consistently assert it if it were false? One can of course assert a false sentence and be consistent at the same time, because one is inconsistent if and only if it is impossible that all his beliefs are true. If Lucas happens to believe a false sentence, he is still consistent.

      Please help/correct me.