moral obligation

moral obligation
    n 1: an obligation arising out of considerations of right and
         wrong; "he did it out of a feeling of moral obligation"
    

MORAL OBLIGATION. A duty which one owes, and which he ought to perform, but 
which he is not legally bound to fulfill. 
     2. These obligations are of two kinds 1st. Those founded on a natural 
right; as, the obligation to be charitable, which can never be enforced by 
law. 2d. Those which are supported by a good or valuable antecedent 
consideration; as, where a man owes a debt barred by the act of limitations, 
this cannot be recovered by law, though it subsists in morality and 
conscience; but if the debtor promise to pay it, the moral obligation is a 
sufficient consideration for the promise, and the creditor may maintain an 
action of assumpsit, to recover the money. 1 Bouv. Inst. n. 623.