The Collaborative International Dictionary of English v.0.48:

Paralogism \Pa*ral"o*gism\, n. [Gr. paralogismo`s, fr.
   paralogi`zesqai to reason falsely; para` beside + logi`zesqai
   to reason, lo`gos discourse, reason: cf. F. paralogisme.]
   (Logic)
   A reasoning which is false in point of form, that is, which
   is contrary to logical rules or formul[ae]; a formal fallacy,
   or pseudo-syllogism, in which the conclusion does not follow
   from the premises.
   [1913 Webster]

WordNet (r) 3.0 (2006):

paralogism
    n 1: an unintentionally invalid argument