The phrase "I always lie" is a logical paradox. If it is true, then it is not true. Everyday paradoxes include "you have to be cruel to be kind," "less is more," and "if you didn't get this message, call me."
A logical paradox is a statement that contradicts itself absolutely. An everyday paradox may seem contradictory, but, in fact, be a memorable way of expressing an idea. Some paradoxes may be humorous, for example, "I can resist everything except temptation."
In literature, George Orwell's "Animal Farm" contains the famous paradox, "All animals are equal, but some are more equal than others." Paradoxes in literature and poetry can communicate irony as well as bring pleasure to the reader.