Suppose T is unprovable iff. necessarily, everyone (unrestrictedly) fails to prove it. Suppose there is (as I'm sure there is) some true theorem T of such complexity that no possible finite being could prove it. Suppose God does not prove it either, since of course he has no need of proofs. It is then non-trivial that no one has proved the unprovable, and yet non-trivially so, since among the unprovable things are necessarily true things. It's non-trivial that some necessarily true propositions are not provable.
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Suppose T is unprovable iff. necessarily, everyone (unrestrictedly) fails to prove it. Suppose there is (as I'm sure there is) some true theorem T of such complexity that no possible finite being could prove it. Suppose God does not prove it either, since of course he has no need of proofs. It is then non-trivial that no one has proved the unprovable, and yet non-trivially so, since among the unprovable things are necessarily true things. It's non-trivial that some necessarily true propositions are not provable.
It is then non-trivial that no one has proved the unprovable, and yet non-trivially so, since among the unprovable things are necessarily true things.
Yikes, nice sentence. Let's try this,
No one has proved the unprovable, and yet non-trivially so, since among the unprovable things are necessarily true things
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