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.