Philosopher’s desperately sad secret (9)
I believe the answer is:
descartes
'philosopher's' is the definition.
(Descartes is an example)
'desperately sad secret' is the wordplay.
'desperately' indicates an anagram.
'sad'+'secret'='sadsecret'
'sadsecret' anagrammed gives 'DESCARTES'.
(Other definitions for descartes that I've seen before include "Cogito ergo sum philosopher" , "One who thought" , "French mathematician and philosopher" , "Cogito, ergo sum man" , "Rene --, philosopher" .)