Careless following philosopher's first assumption (7)
I believe the answer is:
premiss
'assumption' is the definition.
(synonyms)
'careless following philosopher's first' is the wordplay.
'careless' becomes 'remiss' (I've seen this before).
'following' says to put letters next to each other.
'philosopher's first' becomes 'p' (1st letter of 'philosopher').
'remiss' after 'p' is 'PREMISS'.
(Other definitions for premiss that I've seen before include "A condition stipulated beforehand" , "piece of logic" , "Assumption" , "It's assumed" , "Proposition" .)