Middleman's oddly abandoned notion (4)
I believe the answer is:
idea
'notion' is the definition.
(both can mean a thought)
'middleman's oddly abandoned' is the wordplay.
'oddly abandoned' means one should take alternating letters (letters in odd-numbered positions removed).
The alternate letters of 'middleman' are 'IDEA'.
(Other definitions for idea that I've seen before include "Content of cognition" , "Light bulb above head" , "Creative spark" , "Inkling" , "Intention" .)