The following explanation of Natural Theology is sourced from the Gifford Lectures.
Traditionally natural theology is the term used for the attempt to prove the existence of God and divine purpose through observation of nature and the use of human reason. Seen in a more positive light natural theology is the part of theology that does not depend on revelation. To the extent “revealed theology,” which presupposes that God and divine purposes are not open to human understanding, is engaged at all by natural theology it is to address the issue of the probability that revealed theology can be reconciled with reason. During the 17th and 18th centuries attempts were made to establish a “natural religion” to which people might assent and thereby ameliorate harsh charges and actions against doubters of revealed religion. The classic work arguing for a rational derivation of divine purpose is William Paley’s Natural Theology (1802), but the rational arguments for the existence of divine reason at work in the world can be found as early as the writings of Plato (c.427-347).
Christian theology has a long history of attempting to reconcile the revelation of God in Jesus Christ with human reason. Orthodox Christian theology asserts the special quality of salvation found in the unique experience of God in Christ while at the same time holding humans responsible for responding to God’s grace. In short revelation had to be reconciled with a responsible, rational individual. Among the many attempts that have been made to reconcile natural theology with Christian faith were the efforts of Thomas Aquinas (c.1225-74) and Immanuel Kant (1724-1804). The philosopher David Hume (1711-76) argued that natural theology was mere speculation and that if Christian truth was to be believed at all, it must be believed on blind faith.
While for many people science and the scientific method seem to challenge the traditional understanding of faith, for others they complement their religious understanding. Thus the physicist and theologian John Polkinghorne explains the complementarity when he writes, “It is the desire for ontological knowledge, and not mere functional success, which motivates the labour of scientists.” (Belief in God in an Age of Science, 30) Polkinghorne along with Ian Barbour and Arthur Peacocke are scientist-theologians who have in recent years delivered the Gifford Lectures.
A more modern view of natural theology suggests that reason does not so much seek to supply a proof for the existence of God as to provide a coherent form drawn from the insights of religion to pull together the best of human knowledge from all areas of human activity. In this understanding natural theology attempts to relate science, history, morality and the arts in an integrating vision of the place of humanity in the universe. This vision, an integrating activity of reason, is religious to the extent it refers to an encompassing reality that is transcendent in power and value. Natural theology is thus not a prelude to faith but a general worldview within which faith can have an intelligible place.
Anthony Flew, A Dictionary of Philosophy, Revised Second Edition
Dagobert D. Runes, Dictionary of Philosophy
Van A. Harvey, A Handbook of Theological Terms
Keith Ward, “Natural Theology” in The Macmillan Encyclopedia of Science and Religion
John Polkinghorne, Belief in God in an Age of Science