A short list of well known paradoxes and my solutions
Zeno’s Paradox: before an object can travel a distance, it must first travel half the distance. To travel that remaining half, it must first travel half of that distance (a quarter of the total), and so on, infinitely. Because this requires an infinite number of tasks to be completed in a finite time, the paradox concludes that motion is impossible.
Solution: this assumes a starting point A and a goal point B. I posit a point C twice as far from A as B is. If the first step towards C can be completed, and that is implied in the paradox description, then travel to point B has already been achieved.
Zeno may then argue that the first step itself is impossible by the same logic. The conclusion is obviously that nothing in the universe can move, or has ever moved, or will ever move. If that logic is sound, then who is it that wrote Zeno’s Paradox?
The Barber’s Paradox: A barber in a town shaves all men, and only those men, who do not shave themselves. Does the barber shave himself?
Solution: the barber travels to another town to get shaved.
The original paradox assumes that one town is an entire universe.
Maxwell’s Demon: this one is thermodynamic, Maxwell posited a demon in a closed box with an interior barrier and a door. The demon could move hotter molecules to one side and colder to the other through the door, which apparently violates entropy.
Solution: Even demons have to eat, and produce waste heat. Entropy is retained.
The Sorites Paradox: A single grain of sand does not constitute a heap. If you have a collection of sand that is not a heap, adding just one single grain will not suddenly cross a threshold and turn it into a heap. Therefore, by strict logical induction, no matter how many single grains of sand you add, one by one, you can never create a heap. The logic states that a heap cannot exist.
Conversely, if you start with a massive heap of sand and remove a single grain, it remains a heap. If you repeat this process, removing one grain at a time until only a single grain is left, the logic dictates that the final, single grain must still be a heap.
Solution: Four grains of sand can be a heap to an ant. One grain of sand can be a mountain to a micro-organism. The observer scale is what matters.
The Ship of Theseus: The basic question comes from Plutarch. If the Ship of Theseus needs a plank replaced, it remains the same ship. If, over time, every single plank gets replaced, is it still the Ship of Theseus? If someone else collected the old planks, and built a ship from them, would that be a more authentic Ship of Theseus?
Solution: The paradox assumes identity in material or history. I posit that the Ship of Theseus is simply whichever ship Theseus happens to own. If he has repaired, replaced, or abandoned one, or simply passed away himself, then it is no longer his ship either in pieces, nor in its whole.