You want a proof. I guess that means that you want to be more convinced that the Propositional Calculus is consistent than you are convinced of your own sanity. Any proof I could think of would involve mental operations of a greater complexity than anything in the Propositional Calculus itself. So what would it prove? Your desire for a proof of consistency of the Propositional Calculus makes me think of someone who is learning English and insists on being given a dictionary which defines all the simple words in terms of complicated ones…
—
The character of Imprudence in the dialogue between Prudence and Imprudence in Chapter Seven of Douglas Hofstadter’s Gödel, Escher, Bach.
This criticism is very spot-on.
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