Paleologic thinking is where logic follows emotion. A man who feels strongly about the creation myth might become unnerved in an argument with a scientist who believes otherwise. The power by which this person feels about the creation story drives him to shun the possibility that the story might actually just be a myth. His inner logic follows, that since he feels so strongly about the myth, it must be true.
Paleogic thinking also encompasses the notion of magical thinking. If a peasant woman learns that her child is ill, she may rely on the power of magical thinking to solve the problem, that a supernatural force may heal the child. Her thinking is centered in ideas that cannot be proven, yet they’ve been handed down through generations, instilled into her own thoughts since birth. Thus her ability to change them are next to impossible.