  In 1739, Cockburn wrote her Remarks upon some Writers in the Controversy concerning the Foundation of moral Duty and moral Obligation. It was finally published, anonymously, in 1743 in the English literary journal The History of the Works of the Learned. Remarks upon some Writers considers primarily the work of philosopher Samuel Clarke and various critics of his moral theory. In 1747, she published a critique of the moral philosophy of Dr. Thomas Rutherforth, entitled Remarks upon the Principles and Reasonings of Dr. Rutherforth’s Essay on the Nature and Obligation of Virtue, whose work was strongly critical of Samuel Clarke’s moral theory. In this work, Cockburn again defends a Clarkean view of morality.