What does it mean to "desire truth in the inward parts"? And in the "hidden part You shall make me to know wisdom"? Is it possible to know truth in our mind, but not in our heart? What is the "hidden part" he speaks of? 

Can we acknowledge  truth before men but not accept it in our hearts? Can we be living a lie, though the truth is in our mouth? 

                                              O LORD, OPEN THOU MY LIPS;

                                              THE SACRIFICES OF GOD

                                              are A broken spirit:

                                              a broken and contrite heart,

                                              O God, You will not despise 

This then, is the only response to the realization of how truly wicked and deceitful our own heart is - 

                                           Create in me a clean heart, O God;

                                          and renew a right spirit within me.

                                          Cast me not away (on the Judgment Day)

                                          from Thy presence; and take not 

                                          Thy Holy Spirit from me.

                                          Restore to me the joy of Thy Salvation 

                                          and uphold me with Thy free spirit