"I know one thing," Socrates famously said: "that I know nothing." This statement is a paradox in itself, demonstrating the complexities of self-referential statements, but it also suggests a crucial insight from one of the founders of Western philosophy: You should question everything you think you know. Indeed, the closer you look, the more you'll start to recognize paradoxes all around you. We've picked our favorites from Wikipedia's epic list of more than 200 types of paradoxes.To go anywhere, you must go halfway first, and then you must go half of the remaining distance, and half of the remaining distance, and so forth to infinity: Thus, motion is impossible. The dichotomy paradox has been attributed to ancient Greek philosopher Zeno, and it was supposedly created as a proof that the universe is singular and that change, including motion, is impossible (as posited by Zeno's teacher, Parmenides). People have intuitively rejected this paradox for years. From a mathematical perspective, the solution — formalized in the 19th century — is to accept that one-half plus one-quarter plus one-eighth plus one-sixteenth and so on ... adds up to one. This is similar situation to saying that 0.999... equals 1. But this theoretical solution doesn't actually answer how an object can reach its destination. The solution to that question is more complex and still murky, relying on 20th-century theories about matter, time, and space not being infinitely divisible. In any instant, a moving object is indistinguishable from a nonmoving object: Thus motion is impossible. This is called the arrow paradox, and it's another of Zeno's arguments against motion. The issue here is that in a single instant of time, zero seconds pass, and so zero motion happens. Zeno argued that if time were made up of instants, the fact that motion doesn't happen in any particular instant would mean motion doesn't happen. As with the dichotomy paradox, the arrow paradox actually hints at modern understandings of quantum mechanics. In his book "Reflections on Relativity," Kevin Brown notes that in the context of special relativity, an object in motion is different from an object at rest. Relativity requires that objects moving at different speeds will appear different to outside observers and will themselves have different perceptions of the world around them. If you restored a ship by replacing each of its wooden parts, would it remain the same ship? Another classic from ancient Greece, the Ship of Theseus paradox gets at the contradictions of identity. It was famously described by Plutarch: The ship wherein Theseus and the youth of Athens returned from Crete had thirty oars, and was preserved by the Athenians down even to the time of Demetrius Phalereus, for they took away the old planks as they decayed, putting in new and stronger timber in their places, in so much that this ship became a standing example among the philosophers, for the logical question of things that grow; one side holding that the ship remained the same, and the other contending that it was not the same. See the rest of the story at Business Insider
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