Paradoxes

A paradox is a self-contradictory and false proposition. For example, when someone says that "I am lying" , it is a paradox because if what he saying was true, then he would be lying, thus self-contradictory. However, if he was lying, then he would be lying about lying and would be telling the truth, thus it is a paradox. Many logic problems are based on paradox. However, there are several things that seem like paradoxes but are actually not. For example, one might think that there must be at least two barbers in a town in order for everyone's hair to be neat assuming everyone else besides the barber cannot cut their hair and the barber can only cut everyone elses' hair. However, the barber might be a female and do not need to have her hair cut. Thus, this is not a paradox.