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Gödel did prove that it's impossible to find all truths.
While Gödel killed HIlbert's program as a matter of historical fact, it was later Tarski who proved the theorem that truth is undecidable.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
Notes for future OT posters:
1. Please add the 'open_thread' tag.
2. Check if there is an active Open Thread before posting a new one. (Immediately before; refresh the list-of-threads page before posting.)
3. Open Threads should be posted in Discussion, and not Main.
4. Open Threads should start on Monday, and end on Sunday.