The term "supernatural" is kind of funny because by definition it sort of means things that do not exist. If something exists, it is part of the natural world, in that it can interact with particles via the rules of physics. If ghosts exist, for example, they cannot so much disobey the laws of physics, because scientists would simply adjust the rules of physics to match what they observed in the ghosts. The most striking example of this are cryptid animals like Nessie or Bigfoot. In a way they sort of count as supernatural, merely by the fact that they do not exist. If they were ever discovered, they would be boring old natural animals. In the sea, the division is even clearer, we can imagine a cryptid enthusiast asking a scientist "Do you believe in sea monsters?", and the scientist replying "Oh sure, there are plenty: great white shark, orca, giant squid, etc". Here the cryptid enthusiast would become frustrated and say "No, I mean like Leviathan or Kraken". The scientist might ask "is that not just a Sperm Whale and Giant Squid?". Frustration increasing, the cryptid enthusiast says "No, I mean things that do not exist." Here our poor scientist is left to contend with the true meaning of the question: "Do you believe in things that do not exist?".
There are two differences, it seems, between "sea monsters" and "sea creatures". The first is that sea monsters are named in Greek, where sea creatures are named in Latin. The second is that sea monsters do not exist.
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(The same logic can be applied to 'ghosts'.)
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The mere fact that science may not yet adequately explain an object, event, or experience does not mean the immediate explanation should automatically default to a conspiratorial, extraterrestrial, paranormal, or supernatural cause.