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.
Also, there is definitely some objective fact where you cannot get the right answer:
"After thinking about it, you will decide that this statement is false, and you will not change your mind."
If you conclude that this is false, then the statement will be true. No paradox, but you are wrong.
If you conclude that this is true, then the statement will be false. No paradox, but you are wrong.
If you make no conclusion, or continuously change your mind, then the statement will be false. No paradox, but the statement is undecidable to you.