In this paper we wish to present some antinomies that arise in the analysis of urban-rural relations. First of all: are we to give a norm or simply to describe what happens? Second: the fight between res extensa, territory, and res cogitans, nets and knots. Third: the contrast between the theory of Central Places and the Reticular theory. And then the study of the form of boundaries between urban and rural: are they minimizing paths or tend to become fractals so long as possible?