Abstract : A cladogram is usually considered as resolved when all its branching points are bifurcations. The problem we address in this contribution concerns foundations: is this “principle of dichotomy” empirically grounded in the hypothesis of dichotomous speciation? First, we survey Brundin’s (1966) and Hennig’s (1966) answers to this question: Hennig (1966), in particular, is cautious, and first claims that the principle of dichotomy is “no more than a methodological principle” (Hennig 1966: 210); but he soon concedes that it might also have empirical roots (Hennig 1966: 211). Second, we examine Platnick’s (1979) and Nelson and Platnick’s (1981) contributions, which stick to Hennig’s first intuition, and try to reduce the principle of dichotomy to a mere methodological requirement of science. Third, we suggest our own solution: the principle of dichotomy is a methodological and theoretical requirement not only of science, but also and above all of phylogenetic systematics itself. Cladograms—taxa and their relationships—are the result of a Cartesian analysis, which consists in the decomposition of taxa into homologies, i.e. hypotheses of identity. Now, identity is best represented by a ternary relationship, where two features are more identical to each other than any is to a third one. The foundation of taxa and their relationships upon homologies thus results in an intrinsically dichotomous pattern.