I love a good paradox. Whether it relates to fantasy-like time travel (there are many) or real-life (also quite a few), I get a buzz out of twisting my melon. Please share your favorite and we'll upvote a champion. Here's mine: The simple question; are you a compulsive liar?
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The Fermi Paradox for sure. It's the contradiction between how likely alien life is in the universe and its apparent absence. Considering the billions of stars in the galaxy like the sun, the many Earth-like planets that must be orbiting some of those stars, the likelihood that some of those planets developed life, the likelihood that some of that life is as intelligent or more intelligent than humanity, the galaxy should be teeming with alien civilizations.
Needs experience to get a job; needs a job to gain experience.
You can replace any component of a ship, and it is still the same ship. So you can replace them all, one at a time, and it is still the same ship. However, you can then take all the original pieces, and assemble them into a ship. That, too, is the same ship they began with.
Banana Cream Pie Paradox.
A man finishes making the first time machine ever. Before using it, he sees his banana tree out the window and decides to make a celebratory banana cream pie.
Once it is made, he steps through the time machine to 20 years prior. He emerges onto a busy street that was there before his yard, and because he is focusing on not dropping his pie, he accidentally steps on the banana tree as a tiny sapling, killing it.
If the tree had never been there, he wouldn't have made the banana cream pie. But without the banana cream pie, the tree would be alive, allowing it to be destroyed, preventing it from being destroyed, etc.
Mind-boggling.
AA paradox
In order to stop drinking I had to admit failure in controlling my drinking. In admitting defeat I can victory and power over my disease. Admitting defeat allows me to gain control.
Don't know the name of it. But a theory that states there is alien life but they have learned not to announce where they are. The human race has placed a loudspeaker annoucing where we are for any hostile alien race.