The greatest happiness principle, Gay supposed, represented a middle ground between the egoism of Hobbes and Hutcheson's moral sense theory.
Gay's philosophical works argued that virtue was conforming to a rule of life which promotes the happiness of others.
His short "Dissertation Concerning the Fundamental Principle of Virtue or Morality" was first published as a preface to Edmund Law's translation of William King's Latin Essay on the Origin of Evil (1731).
In the eighteenth century its influence may be found in the works of the theological utilitarians, Abraham Tucker (The Light of Nature Pursued, 7 vols., 1768–1778) and William Paley (Principles of Moral and Political Philosophy, 1785).
David Hartley said that Gay's assertion of the importance of psychological association in human nature was the origin of his Observations on Man (1749).