In whom we live, and move, and have our being
In St. Athanasius'
De Incarnatione, he uses the concept of nature in an unsettling way. We are used to thinking of "nature" as something permanent. Your cat has cat nature, and will remain a cat, and isn't in imminent danger of becoming a dog. But Athanasius speaks of nature differently. If God created everything out of nothing, then everything really is made out of nothing, and therefore is by nature nothing. Thus, humans naturally tend to nothing, and sin just leaves us back in our true nature.
I am sure that this is perfectly obscure. Let me explain. God is Being, the source of the existence of all things, and is in fact the only thing that has real existence in the most absolute sense. God exists, has existed, and will exist, so much so that his name is "I am." He is the only one who has a permanent nature, since everything else depends on the divine will in order to exist. We all exist at God's pleasure. "God has made man, and willed that he should abide in incorruption," says Athanasius. It is more than that--not only are we to live forever, but we are to partake in God himself: "For God has not only made us out of nothing; but He gave us freely, by the Grace of the Word, a life in correspondence with God." We are partakers in the divine nature, as 2 Peter says. By nature, we are nothing, but by gift, we are Godlike.
What happens when we sin? When we reject the gift? Athanasius repeats the answer that the Christian faith gives: death comes when we reject the gift. But this death is not something imposed by God, as an arbitrary punishment, but is instead the ordinary fate of anything created. Out of nothing, back to nothing. "For transgression of the commandment was turning them back to their natural state, so that just as they have had their being out of nothing, so also, as might be expected, they might look for corruption into nothing in the course of time." Death is only natural!
I wax Thomistic for a moment to note that this seems to conflict with the Christian understanding of human nature, which is that it is perfected in Christ. Jesus is the true human, the true representative of human nature, the cause and end of our existence. But I don't think it conflicts, as long as we are careful to distinguish different meanings of nature. Athanasius uses nature here to mean that which an entity has of itself. Later writers use nature to refer to the destiny willed by God. This second sense is the meaning behind natural law, which is the rational creatures participation in the eternal law of the world, which law includes the transcendent destiny of the human being.