An error in argument.  

Formal Fallacy.— A violation of the rules that pertain to specific kinds of arguments, e.g., the rules of a categorical syllogism.  

Material Fallacy (also called Informal Fallacy).—  A non-formal error in, or connected to, an argument pertaining to its terms, assumptions, context, or some other factor. E.g., it is a fallacy to assume what one is supposed to prove. This is the fallacy of “begging the question” or petitio principii.