The mathematician is entirely free, within the limits of his imagination, to construct what worlds he pleases. What he is to imagine is a matter for his own caprice; he is not thereby discovering the fundamental principles of the universe nor becoming acquainted with the ideas of God.
Since zombies are not fully dead, they upset the essential balance of nature: no animals eat zombies, apparently, and zombies do not seem to decay, at least, not to the point of disintegration and reintegration back into the soil, so the food chain, or the circle of life, seems to end or be short-circuited by their existence. Zombies fulfill the worst potentialities of humans to create a hellish kingdom on earth of endless, sterile repetition and boredom.