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 Paradoxes and their Kin.
Welcome, this page is dedicated to the marvel that is the paradox. As seen above is the Ouroboros, a symbol often related to paradoxes. By the end of this sentence I hope you will have accepted him as your new pet. Thank you. It is basically a single snake biting its tail (much like a dog), hinting towards eating itself. As the snake eats itself, it grows longer, but the circumference/radius stays constant. This symbolizes self-reference, eternity and, mostly used in novels, returning to the start. This is as if you imagine walking from the head all the way round, you find yourself back at the start or if you think of it as trying to find the cause why it is eating itself, you will find it is as it needs the food for energy to re-grow the tail causing it to eat itself and so on, ad infinitum. (Well, that is another way to think about it)
Definition: The word paradox is often used interchangeably with contradiction; however where a contradiction by definition cannot be true, many paradoxes do allow resolution, though many remain unresolved or only contentiously resolved. Still more casually, the term is sometimes used for situations that are merely surprising. This is also the usage in economics, where a paradox is an unintuitive outcome of economic theory.

E.g. "I am a liar" - Paradox, as if this statement is true, it is false, hence if it is false, he isn't a liar, and the sentence is true so he is a liar, and so on.

Let x = "I am a liar"

If x=true -> x=false -> x= true  hence returning back to the "start" as in our Ouroboros.

"Good language used I do" - Contradiction, as he says s/he uses good language, but contradicted their self by the use of poor language. 

Types:

 

Related with vagueness:

Those paradoxes related to vagueness are usually to do with terminology and, yes vagueness!

"Sorites" paradox

Mr. Washington's Axe