As in physics, philosophy, mathematics, economics, etc.
The ones which interest me the most have to do with the strangeness of quantum mechanics. At the core of quantum mechanics are two fundamental problems for which the physics community does not have good explanations.
One is what's called The Measurement Problem. The mathematics of quantum mechanics only predicts probabilities of things happening, yet at some point probabilities turn into realities. For example, flipping a coin goes from a superposition of probabilities of "heads" and "tails" to a definite result (either "heads" or "tails"). We know the position of an electron or the value of a flipped coin because we do something to "measure" the result. But what constitutes a "measurement"? That question leads to lots of thought experiments about what circumstances and/or objects create a "measurement."
The other is the Entanglement Problem (or sometimes "Spooky action at a distance"). Without going into too many details, there are some situations described by quantum mechanics where two objects are in some sense "entangled" such that an action with affects one of the two objects instantaneously also has an effect upon the other entangled object, no matter how far away the other object is. This observation violates relativity theory (which implies no influence can propogate faster than the speed of light). Again, lots of thought experiments have been produced trying to explain how entanglement works.
Most of the ones in philosophy – almost none of the others.
In philosophy:
Survival Lottery, Ticking Time Bomb, Zeno’s Paradox, Big Book, Utility Monster, Experience Machine, Trolley Problem, The Violinist, Condillac’s Statue, Simulated Reality, Mary’s Room, Philosophical Zombie, Ship of Theseus, China Brain, Chinese Room, Brain in a Vat, Brianstorm Machine, Swamp Man, Artificial Brain, Twin Earth, Changing Places, Time Without Change, Zeno’s Paradox, Gettier & Hay Ibn YaqZan, Prisoner’s Dilemma, Social Contract, Beetle in a Box, Inverted Spectrum, Coherence, Kavka’s Toxin.
I can’t remember which ones I’ve forgotten.
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