Fallacious, illogical (7)
I believe the answer is:
unsound
I believe this clue is a double definition.
'fallacious' is the first definition.
(synonyms)
'illogical' is the second definition.
(I've seen this in another clue)
(Other definitions for unsound that I've seen before include "Damaged" , "Unreliable; not healthy" , "silence?" , "Ill-founded" , "Unfit or unreliable" .)