paralogism
noun
pa·ral·o·gism pə-ˈra-lə-ˌji-zəm 
: a fallacious argument
Word History
Etymology
Middle French paralogisme, from Late Latin paralogismus, from Greek paralogismos, from paralogos unreasonable, from para- + logos speech, reason — more at legend
First Known Use
1565, in the meaning defined above