I have been using a book published in 1996 by C. Allen Carter for much of what I know about Burke's ideas. I hope his assessment fairly characterizes Burke's thought. After studying Carter, I discovered that his book has not been reviewed by any text indexed in the JSTOR database, which suggests that it made very little impact on the scholarly community. Either Burke does not interest scholars, or Carter's work does not. One fact that suggests that Carter might not have a complete perspective on Burke is that Barbara Foley described Burke as having two kinds of scapegoat, which Carter does not mention. Carter himself admits that some of the categories he ascribes to Burke (the religious dimension, for example) are not ones that Burke himself explicitly named. So this book is more Carter's synthesis than pure Burke. I will below refer to this synthetic body of thought as being from "Carter and Burke."
This month: According to Carter, Burke is part of a tradition that sees the human mind as having two modes of thinking: logical and temporal. The word bicameral indicates that there are two houses of reason within the mind.
An example of the two modes can be seen in the Christian Bible. On the one hand, the Christian set of moral rules about behavior forms a logical framework within which we should be able to live our lives. On the other hand, the moral system is presented as a set of episodes in time: first, there was Adam and Eve, then there was Noah, then there was Moses, and eventually there was Christ and his disciples. The moral system builds up as a narrative of history.
Evolutionary psychology does not have a position on bicamerality per se. Neuroscience performs experiments to show how the mind works. That having been said, there is a line of argument within evolutionary literary criticism that argues that our use of narrative is an evolutionary adaptation. That is why we respond to narratives so strongly and seem to need them. That position is best argued by Jonathan Gottschall in his book The Storytelling Animal.
One can wade ankle-deep into brain science to see some results that might relate to bicamerality. From the little I have read, our brain's hippocampus has cells that form grids that allow us to remember the location of objects in space. For a review of this field, see Moser, et al. (2008). Experiments have shown that we use that grid to map out logical arguments as well. Even though this is a wetware data structure designed for spatial reasoning, we can nevertheless follow arguments by mentally traveling through our map of the landscape of abstract concepts.
People who excel at remembering lists of items often use a technique that illustrates the point. They will first memorize the layout of a large house with many rooms and articles of furniture. They then assign each item in a new list to each piece of furniture in that house. To recall the list, they imagine walking through the house, noting each piece of furniture in a temporal sequence and thereby retrieving each item in the list.
I am not saying that bicamerality itself is necessarily an accurate description of how the mind works, but there are scientific results that suggest that it is not completely wrong. It also does not seem to be an issue critical to evolutionary psychology. Nevertheless, Gottschall's theory of the importance of storytelling as an adaptation can be a reframing of the theory of bicamerality which Burke endorsed.
Carter, C. Allen. Kenneth Burke and the Scapegoat Process. U. of Oklahoma Press, 1996.
Gottschall, Jonathan. The Storytelling Animal. Boston: Houghton Mifflin Harcourt, 2012.
Moser, E. I., Kropff, E., & Moser, M. B. (2008). Place cells, grid cells, and the brain's spatial representation system. Annual Review of Neuroscience, 31, 69-89.