[1] In relation to the Oriel Noetics, Davison wrote in support of Edward Copleston's campaign for reform of Oxford teaching, but stood on the conservative side of the group.
[2][3][4] Davidson, with Coplestone and Whately, formed a group in the Noetics of political economists in the sense of Robert Malthus.
Finding radical and views on political questions in his parish, he opposed them in a tract, Dialogue between a Christian and a Reformer.
An Inquiry into the Origin and Intent of Primitive Sacrifice, and the Scripture Evidence respecting it; with observations on the opinions of Spencer, Bishop Warburton, Archbishop Magee, and other writers on the same subject.
His proposal was that the law should cease to be operative in ten years, and that then a voluntary contribution should be made for cases of great need.
[1] Davison used the pseudonym "Phileleutheros Orielensis" in commenting on the Elements of General Knowledge (1802) of Henry Kett.