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Stuart_Armstrong comments on The Cartoon Guide to Löb's Theorem - Less Wrong
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It think the provability of consistency would be:
"There is a proof that there is no proof of the canonical false proposition F"
I'm using Peter Smith's definition (see http://www.logicmatters.net/resources/pdfs/gwt/GWT.pdf , Godel without too many tears).
In definition 59 (on page 1 of part 10), he identifies consistency with "not a proof of the canonical false statement". This is a valid statement within Peano arithmetic. And it's logical consequences are... anything.
You're confusing consistency with a proof of consistency.
Theorem 56: Consistency implies no proof of consistency.
Which is of course where you get:
Proof of consistency implies inconsistency.
Which gives you:
Proof of consistency implies anything.
I think you're right.... I was commiting the same mistake is above, using the first derivability condition and assuming that Peano arithmetic could treat it as a statement in Peano arithmetic - which it isn't.