tag:blogger.com,1999:blog-3891434218564545511.post4325705100905391768..comments2024-03-27T20:37:09.185-05:00Comments on Alexander Pruss's Blog: Deep Thoughts XXIXAlexander R Prusshttp://www.blogger.com/profile/05989277655934827117noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-3891434218564545511.post-51520020925856680952010-12-11T13:24:14.848-06:002010-12-11T13:24:14.848-06:00It is then non-trivial that no one has proved the ...<i>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.</i><br /><br />Yikes, nice sentence. Let's try this,<br /><br />No one has proved the unprovable, and yet non-trivially so, since among the unprovable things are necessarily true thingsMike Almeidahttps://www.blogger.com/profile/12001511002085064198noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-18239063659484921152010-12-11T11:12:15.103-06:002010-12-11T11:12:15.103-06:00Suppose T is unprovable iff. necessarily, everyone...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.Mike Almeidahttps://www.blogger.com/profile/12001511002085064198noreply@blogger.com