Larry_D'Anna comments on The Cartoon Guide to Löb's Theorem - Less Wrong
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The flaw is the instant you used the deduction theorem. You used it to go from
PA |- "◻C -> C" -> PA |- "C"
to
PA |- "(◻C->C) -> C"
What the induction theorem really says is
T + X |- Y implies T |- "X -> Y"
so what you really would have needed to apply the deduction theorm would have been
PA + "◻C -> C" |- C
do I win?