This author examines and augments a particular aspect of Ian Barbour's well-known fourfold typology for relating religion and science (conflict, independence, dialogue, and integration) in order to clarify two options available for theology as it develops a robust view of creation in conversation with modern science. Within integration, Barbour identifies several subtypes, including "theology of nature." The Gifford Lectures of Arthur Peacocke and John Polkinghorne provide important examples of theology of nature, yet differences between their approaches remain unexplained within Barbour's typology. An explanation is offered here, showing that Peacocke and Polkinghorne employ two distinct strategies to construct a theology of nature: the strategy of intelligibility and the strategy of credibility. After characterizing these strategies, the author suggests that at present the relationship between them takes the form of a dilemma.