Conceited logic I state to be wrong (11)
I believe the answer is:
egotistical
'conceited' is the definition.
('egotistical' can be a synonym of 'conceited')
'logic i state to be wrong' is the wordplay.
'to be wrong' is an anagram indicator (I've seen 'is wrong' mean this).
'logic'+'i'+'state'='logicistate'
'logicistate' anagrammed gives 'EGOTISTICAL'.
(Other definitions for egotistical that I've seen before include "Self-important" , "Conceited and boastful" , "Highly self-absorbed" , "Selfish" , "Excessively conceited" .)