James Barr in Biblical Faith and Natural Theology spent a lot of time talking about the image of God question only to conclude that it has little to do with natural theology.
An old argument for natural theology was that, because God made humans in the image of God, they had a capacity for natural knowledge of God. Barr went into the several ways that the image of God has been understood in theology.
There was the idea that the image of God was a spiritual or rational character endowed to man, but not to the animals.
There was the idea that there was a difference between the image of God and the likeness of God. In the Fall, we lost our likeness to God, but retained the image of God (approximately the position of Irenaeus).
There was the idea that the image of God was physical or material. Genesis 5:3 (where Adam’s son is in Adam’s likeness and image) is best interpreted this way. The God of the Hebrew Bible was anthropomorphic so man could be in his literal image. However, there are other voices in the Hebrew Bible that call this into question.
More recently scholars put forth the functional view of the image of God: that the image consists in sharing with God in dominion over creation.
Then there was Karl Barth’s off-beat interpretation. At first, Barth had said that the image of God in man was lost in the Fall. But later he developed the idea that the image as not a possession that one could lose. It was relational. It concerned the connection between the statement that God created man in his own image and the statement that God created them male and female. The image of God consisted in the relationality of God as triune and the relationality of man as male and female.
Barr attacked Barth’s view as not being what Genesis meant and also not being how Paul the Apostle understood Genesis.
This is all true. But one could argue that the “mystery” of marriage and God’s relationship to Christ in Ephesians 5 supports Barth even though that passage is not about the image of God.
In the end Barr said:
The image of God in humanity is not something that can be defined as if we could point to this or that characteristic which clearly exists and to which the phrase expressly refers. But we can say that it belongs to the confluence of a group of nodal theological issues: monotheism creation anthropomorphism condemnation of idolatry—exactly the issues out of which as we have seen the tradition of natural theology emerged.
So you cannot derive natural theology from any innate human capacity defined as the created image of God. However, Emil Brunner’s arguments against Barth look better in the light of this discussion. Brunner thought the Fall left only a tiny, but significant, point of contact between God and humanity in natural theology. Barr thought it had to be something broader than a tiny point of contact.
He thought Brunner’s further arguments for “orders of creation” opened the door for something broader. This also fit in with the Genesis idea that creation involved the “ordering” of the world and the Wisdom idea that insight into the world was insight into the created order.
One point at which I question Barr is his argument that the P creation poem or account depended on Second Isaiah. Critical scholars see Second Isaiah (the poems of Isaiah 40-55) as addressed to the Babylonian exiles. I do not see how P could depend on Second Isaiah since before the exile Jeremiah already seems to draw upon the P account (Jeremiah 4:23). In the light of the theory of Israel Knohl and Jacob Milgrom that P is pre-exilic, perhaps Second Isaiah also depended on P.