logical paradox

PARADOX (PDX) is a warez/demo group; an anonymous group of software engineers that devise ways to defeat software and video game licensing protections, a process known as cracking, which is illegal in some jurisdictions. They distribute cracks (software patches), keygens (key generators), and precracked versions of entire programs. Over the years, distribution methods have changed, starting out with physically transported floppy disks and BBS distribution. With the expansion of the internet they moved on to Usenet. Today most of their files reach the public over various peer to peer file networks.
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"ParaDOX" is Nanase Aikawa's second album. The album reached #1 on Oricon charts.
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A paradox is an apparently true statement or group of statements that leads to a contradiction or a situation which defies intuition. Typically, either the statements in question do not really imply the contradiction, the puzzling result is not really a contradiction, or the premises themselves are not all really true or cannot all be true together. The word paradox is often used interchangeably and wrongly with contradiction; but whereas a contradiction asserts its own opposite, many paradoxes do allow for resolution of some kind.
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A logical paradox consists of a statement  which if true is false and if false is true.  Thus consider "I am  lying."  If it is true and I am lying, then I am saying something  false (that is what a lie is) and if it is false and I am saying something  false, then it is true that I am lying.  Such a statement is self-contradictory  It contradicts itself.  Its truth entails its falsity and its falsity entails its truth.