A paradox is a situation or puzzle that appears to contradict itself, or appears to contradict what is obviously true through valid assumptions and logic. It is also a seemingly absurd or self-contradictory statement or proposition or situation that when investigated or explained may prove to be well founded or true.
The ancient Greek Zeno is known for his invention of many paradoxes, the best known of which "proves" that a moving object can never reach its destination.
A well known family of paradoxes involve self-reference, such as the statement "this statement is untrue", or the old joke "How do you keep a fool busy? Hand him a card with this question and 'see other side' on both sides". Others involve creative signs (such as one that reads "Keep Left" with an arrow pointing right, or "Reading This Sign Is Forbidden").
Ship of Theseus
An example of applying the Ship of Theseus paradox goes as follows: suppose that the Conservapedia page "Paradox" (938 bytes) can be defined by its title and its content. If a paragraph of content is added to increase the byte count to 1,500, it would still be the same page because the title remains the same. If only the title is moved to "Paradox (concept)", the content remains the same. However, if both the title is moved and the content is altered, is it still necessarily the same page? Furthermore, suppose that after the "Paradox" page (938 bytes) is moved to "Paradox (concept)" without leaving a redirect and then has a paragraphed added to it to increase the byte count to 1,500, the original content in the once-938 byte count page is published as a page creation under "Paradox". Which would closer resemble the identity of the original "Paradox" page prior to being moved and edited: the new version under the title "Paradox (concept)" that had its title and content modified one at a time, or the new page creation under "Paradox" that exactly resembles the original page but is counted by the CP database as a different content page?