Internally inconsistent, illogical (10)
I believe the answer is:
incoherent
This clue is a double definition.
'internally inconsistent' is the first definition.
(I've seen this before)
'illogical' is the second definition.
(similar in meaning)
(Other definitions for incoherent that I've seen before include "drunk?" , "rambling" , "Internally inconsistent" , "difficult to understand" , "Unintelligible" .)