Is it farther or further?
late 15c., "deception, false statement," from Latin fallacia "deception," noun of quality from fallax (genitive fallacis) "deceptive," from fallere "deceive" (see fail (v.)). Specific sense in logic dates from 1550s. An earlier form was fallace (c.1300), from Old French fallace.
A false or mistaken idea based on faulty knowledge or reasoning. For example, kings who have divorced their wives for failing to produce a son have held to the fallacy that a mother determines the sex of a child, when actually the father does. (See sex chromosomes.)