UPDATE: This is the second post in a series of three on the same topic; the first one is here and the third one is here.
Two days ago I reported here on an ongoing debate over at the FOM list on some controversial statements made by Fields medalist Voevodsky on the status of the consistency of PA as a mathematical problem. In particular, I mentioned that Harvey Friedman had reported sending a message to Voevodsky, asking for clarifications: "how you view the usual mathematical proof that Peano Arithmetic is consistent, and to what extent and in what sense is "the consistency of Peano Arithmetic" a genuine in mathematics."
Now Friedman reports that Voevodsky has replied:
Such a comment will take some time to write ...To put it very shortly I think that in-consistency of Peano arithmetic as well as in-consistency of ZFC are open and very interesting problems in mathematics. Consistency on the other hand is not an interesting problem since it has been shown by Goedel to be impossible to proof [sic].
So, what do we make of this? I am now more and more convinced that Toby Meadows (in correspondence) has it right when he says that there are different senses of a 'mathematical open problem' floating around. Toby suggested a weak and a strong reading of 'open problem/question' in this context: